Particle Physics of the early Universe
Alexey BoyarskySpring semester 2014
Early Universe
EARLY UNIVERSE
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Thermal history of the Universe
Today you all got used to pictures like this
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History
HOW DID WE LEARN ALL THAT?
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Cosmological model of Einstein
Einstein applys GR to the whole Universe assuming spatial 1917 – early1920shomogeneity and isotropy (for isotropy there were observational evidence, for
homogeneity — it was a bold extrapolation, due to Hubble’s observations of fainter and fainter
“nebulae”)
The metric is given by
ds2 = −dt2 +R2(dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2)︸ ︷︷ ︸3-sphere
– static cylinder
Closed Universe – finite total volume V = 2π2R3
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Cosmological model of Einstein
Plug this metric into theEinstein’s equation:
Rµν −1
2gµνR−Λgµν = 8πGTµν
Tµν = diag(ρ,−p,−p,−p)
The solution exists ifcosmological constant andmatter are related as
Λ =1
R2, ρ =
2
8πGR2
Total mass of the Universe M = ρ · 3π2R3 = πR2G
Everything is a function of density that can be measuredexperimentally⇒full solution of the Universe constructed?
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Cosmological model continued
de Sitter (1917) finds a different solution
ds2 = −R2 cos2 χdt2 +R2(dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2)︸ ︷︷ ︸3-sphere
To satisfy GR equations this requires
Λ =3
R2, ρ = 0
– curved Universe without matter??
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Cosmological model continued1922
Friedmann write the general ansatz for homogeneous andisotropic metric
ds2 = −dt2+a2(t)
(dχ2
1− κχ2+ χ2dθ2 + χ2 sin2 θdφ2
), κ = −1, 0, 1
Three homogeneous and isotropic spaces (κ – sign of curvature)
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Cosmological model continued
Plug this metric into the Einstein’s equation, using the general formof the stress-energy tensor being
Tµν = diag(ρ,−p,−p,−p)
The Eistein’s equations relate “matter” (some functions ρ(t) andp(t)) with the dynamics of the scale factor – Friedmann equation:
a2(t)
a2(t)≡ H2(t) =
8πG
3ρ− κ
a2
1922-1924
Second Friedmann equation:
a
a= −4πG
3(ρ+ 3p)
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Cosmological model continued
Energy conservation:
∂ρ
∂t= −3H(ρ+ p) = −3
a
a(ρ+ p)
Lemaıtre rediscovers these equations
Main predictions: the Universe is expanding. Static Universe wouldrequire very specific equations of state (ρ = −κ 3
8πGR2static and ρ =
−3p). Such a solution will be nevertheless unstable
Problems 1a-1c
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Cosmology in a couple of words
Matter-dominated Universe: p = 0 and ∂ρ∂t = −3Hρ or ρa3 = const
and a ∝ t2/3
Radiation-dominated Universe: p = 13ρ and ∂ρ
∂t = −4Hρ or ρa4 =
const and a ∝ t1/2
Temperature T ∝ a−1. In radiation-dominated epoch ρ = π2
30gEFFT4
Einstein’s Λ-term: ρ(t) = −p(t) = const, a = e√
Λ3 t
Hubble equation — interplay between kinetic energy Ek = a2
2 andpotential energy Ep = −GMa(t) :
a2
2− G
4π3 ρ(t)a3(t)
a(t)= −κ
2
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Hubble expansion
Slipher discovers redshifts of the spectral lines in the nearbygalaxies . De Sitter speculates for the first time that this can be 1912-1913
due to cosmological expansion in his model
Hubble discovers that “spiral nebulae” are far from us (M31, M33) 1925
Hubble estimates the distance to the nearby galaxies andestablishes redshift-distance relation 1926
cz = H0r
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Hubble constant history
https://www.cfa.harvard.edu/˜dfabricant/huchra/hubble
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Expansion of the Universe – the first pillar ofcosmology
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Reminder: redshift
Universe stretches:
1 + z ≡ λobserved
λemitted=a(tobs)
a(temit)
Doppler effect:a galaxy is receding
1 + z ≡ λobserved
λemitted=
√1 + v/c
1− v/c
where Hubble velocityv = H0 × distance
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The initial state of the Universe
The initial state of the Universe remained a problem
If Universe is filled with cosmological constant – its energydensity does not change
If Universe is filled with anything with non-negative pressure: thedensity decreases as the Universe expands
In the past the Universe was becoming denser and denser, ρ ∝ 1t2
,=⇒ ultradense cold state of the initial Universe?
High density baryonic matter — a Universe-size neutron star?Neutrons cannot decay anymore (n → p + e + νe) as thereare no available Fermi levels for fermions. The state is stableand remains such until cosmological singularity (ρ ∝ 1/tn)
Problems 1c,2a,5a
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The Universe in the past
The origin of elements (Hydrogen, Helium, metals) remained achallenging problem 1920s-1930s
See e.g.review byZel’dovich,Section 13
Ultradense (ρn ∼ 1g/cm3) neutron star would mean that no hydrogenis left (as soon as density has dropped to allow neutron decay n→ p+e+ νe,each proton is bombarded by many neutrons so that p+ n→ d+ γ, d+ n→t+ γ) Zel’dovich in
Wikipediaorhere
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Binding energy
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Nucleosynthesis
If (as people thought) the density of plasma, needed for nuclearreactions to take place was ρ ∼ 107 g/cm3⇒very rapid expansionof the Universe (age ∼ 10−2 sec). Not enough to establish thermalequilibrium? Paper by
Gamow (1946)
Paper byGamow (1948)
Gamow suggested: consider the plasma temperature Td ∼ 109 K(∼ 100 keV)
He computed the total energy density of radiation as
ρrad = σSBT4 = 8.4 g/cm3
(T
109 K
)4
Gamow then assumed that the energy density of the Universe isdominated by radiation and estimated its age as
ρrad =3
32πGN
1
t2or t [sec] ∼ 1
(T [MeV])2
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Nucleosynthesis
Gamow estimates the density of matter by comparing reaction rateand expansion rate of the Universe:
(v nσp+n→d+γ)−1
︸ ︷︷ ︸time between p-ncollisions
∼ td
Using σ ∼ 10−29 cm2, thermal velocity v ∼√
Tm, one gets n(i)
b ∼1018 cm−3 and therefore ρ
(i)b ∼ 10−6 g/cm3 ⇒the Universe was
radiation dominated!
Cross-section is the effective area that each incoming particle ”sees” – theprobability of some scattering event.
The number of photons at temperature Td is given by
nγ =2ζ(3)
π2T 3d ≈ 1028 cm−3
(T
109 K
)3
(1)
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Nucleosynthesis
Prediction of the Gamow’s theory: baryon-to-photon ratio ηB ≡nbnγ∼ 10−10
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Relic radiation
If so, what is the temperature of radiation bath today? For Gamow(also Alpher, Herman – a series of papers, see detailed account inPeebles) the density at z = 0 was n(0)
b ∼ 10−5 cm−3
Hubble constant estimates were higher than today and all matter today wasconsidered to be baryonic. So H2
0 = 8πG3 ρb
na3 ≈ const and Ta ≈ const (indeed, for radiation ρ ∝ T 4 and ρ ∝ a−4)
Therefore T (0) ∼ 109 K
(n
(0)b
n(i)b
)1/3
∼ 20 K
In reality the number density of baryons today is n(0)b ∼ 10−7 cm−3 which would
give Tcmb ∼ 5 K based on the above estimates
⇒the Univese today should be filled with radiation whosespectrum peaks at λ = 2.9 mm·K
T
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Formation of structures
The Universe was hot (radiation-dominated at epoch ofnucleosynthesis. But the density of radiation dropped faster thanthe density of matter:
ρradρb∼ 1
a
⇒matter-radiation equality (at T ∼ 103 K!)
The growth of Jeans instabilities did not start until that matter-dominated epoch (see below)
Gamow estimates the size of the instability as Paper byGamow (1948)
kBTeq ∼GNρmatterR
3
R
Putting in the Teq ∼ 103 K one gets R ∼ 1 kpc similar to a typicalgalaxy size(!)
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Hot Big Bang theory was born
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Challenges to Hot Big Bang
In 1950s this was not so obvious!
There was no relict radiation from recombination
You should get about 30% of Helium (which was considered to be wrong,as its abundance was measured ∼ 10%)
In low density hot matter you cannot produce heavy nuclei (A = 5and A = 8) in this way. With Hubble constant at that time H0 ∼500km/sec/Mpc the age of the Universe ≈ the age of the Earth⇒heavy elements could not be produced in stars, should be in theUniverse “from the very beginning”.
Problems 5c for H0 = 500 km/sec/Mpc
It was concluded by many that “Hot Big Bang” is ruled out see e.g.Zel’dovichUFN 1963
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Cosmic Microwave background
Accidentally discovered by Arno Penzias and Robert Wilson: 1965
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COBE
Data from COBE (1989 – 1996) showed a perfect fit between the blackbody curve and that observed in the microwave background.
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CMB spectrum
Cosmic microwave background radiation is almost perfect blackbody
CMB temperature T = 2.725 K
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Properties of CMB
Temperature of CMB T = 2.725 K
CMB contribution to the total energy density of the Universe:Ωγ ' 4.5× 10−5
Spectrum peaks in the microwave range at a frequency of160.2 GHz, corresponding to a wavelength of 1.9 mm.
410 photons per cubic centimeter
Almost perfect blackbody spectrum (δT/T < 10−4)
COBE has detected anisotropies at the level δT/T ∼ 10−5
Go to CMB anisotropies section
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Predictions of Hot Big Bang model
CMB
Baryon-to-photon ratio from BBN and CMB (independently)
Primordial abundance of light elements. Most notably, 4He
These predictions are consistent and allow fornon-trivial experimental cross-checks
Let us look at the BBN in more details
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Nuclear network
To produce chemical elements one needs to pass through“deuterium bottleneck” p+ n↔ D + γ
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Deuterium bottleneck
We saw that for each baryon there were ∼ 1010 photons.
Binding energy of deuterium isED = 2.2 MeV (or TD = 2.5×1010 K).
At T = ED 85% of all photons haveE > TD⇒any deuterim nucleuswill be quickly photo-disassociated via D + γ → p+ n
Production of deuterium becomes efficient when temperature dropsso that the number of photons with E > ED will be ∼ 10−10
nγ(E > ED)
nγtot∼ ηB =⇒ ηB
(2.5TBBNmp
)32
eED
TBBN ∼ 1 (2)
TBBN ≈ 70 keV and tBBN =M∗Pl
2T 2BBN
≈ 120s
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Neutron/proton ratio
How many neutrons and protons are there (so far we did not distinguishbetween them)
At high temperatures chemical equilibrium between protons andneutrons is maintained by weak interactions n + ν p + e−,n+ e+ p+ ν, n p+ e− + νe
Description of these processes is given by Fermi 4-fermion theory:
LFermi = −GF√2
[p(x)γµ(1− γ5)n(x)][e(x)γµ(1− γ5)ν(x)] (3)
Fermi coupling constant GF ≈ 10−5 GeV−2
Problem: demonstrate the dimensionality of the Fermi coupling constant
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The content of MeV plasma
If temperatures was at least few MeV, we expect plasma to containelectron-positron pairs in equilibrium amounts (γ+ γ e+ + e− forT & me)
We also know that the plasma contained some number of protonsand neutrons (their origin will be discussed later)
Weak reactions were in equilibrium until T ∼ 1 MeV
Many weak reactions that produce neutrinos (νe) are responsible forkeeping p and n in thermal equilibrium
p+ e− n+ νe n+ e+ p+ νen p+ e− + νe
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Cross-section, reaction rates
Cross-section (in units length2) in 2→ 2 reactions is defined as
σ ∼∫
d3k
(2Ep)(2π)3
d3k′
(2Ek′)(2π)3|M|2δ4(
∑
in
p−∑
out
k)
where |M|2 is a matrix element – probability of scattering – for a particularchoice of incoming and outgoing momenta pin and kout
cross-section can depend only on Lorentz invariant quantities– masses of particles– coupling constants– 3 Lorentz-invariant combinations of incoming and outgoing
momenta, Mandelstam variables:
s = (p+ p′)2 = (k + k′)2 = 4E2cm
t = (k − p)2 = (k′ − p′)2
u = (k − p′)2 = (k′ − p)2
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Cross-section, reaction rates
If all incoming particles are relativistic, E m, we expect that totalcross-section is a function of center-of-mass energy only
Example: QED
σ ∼ α2
E2cm
the real answer e.g. for e+ + e− → γ + γ is given by σ = πα2
2E2cm
up to somelog(E/me) corrections
Example: Fermi theory. Coupling constant GF has dimension[GF ] = GeV−2, cross-section [σ] = GeV−2.
σ ∼ G2FE
2cm
To check whether these reactions are in equilibrium, comparedscattering rate due to Fermi interaction with the Hubble expansionrate:
Γ ∼ G2FT
3
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Cross-section, reaction rates
For reactions with neutrons and protons one should also take intoaccount that they are not relativistic and their number density isgiven by Boltzmann distribution.
These reactions go out of equilibrium at Tν ≈ 1 MeV
The difference of concentrations of n and p at that time is
nnnp
= exp
(−mn −mp
Tν
)≈ 1
6
mn −mp = 1.2 MeV
Almost all neutrons will end up in 4He. The mass abundance ofHelium is
Yp ≡4nHenn + np
=4(nn/2)
nn + np=
2(nn/np)
1 + nn/np
If ηB ∼ 1, Helium abundance would be 1/31+1/6 ≈ 0.28
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Cross-section, reaction rates
However, as we saw due to ηB 1 formation of deuterium(preceeding formation of Helium) does not happen until T ∼ 70 keV
Therefore there is a time-delay between freeze-out of weak reactionand time of Helium formation. The unstable neutrons (lifetimeτn ∼ 900 sec decay and therefore by the time of Helium formationnn/np ≈ 1/7, which gives Yp ≈ 25%
⇒4He is the second most abundant element in the Universe (afterhydrogen)
The Helium abundance is known with a precision of a few% (e.g.Yp = 0.2565±0.0010(stat.)±0.0050(syst,)) and is indeed very close Izotov &
Thuan (2010)to 25%
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CMB
As temperature of the Universe drops, all protons will recombinewith electrons to form neutral hydrogen: e + p → H + γ. Bindingenergy EH = 13.6 eV
If ηB 1 at T ∼ 13.6 eV for each hydrogen atom there are manyionizing photons.
As in the case of BBN and deuterium production, the temperatureshould drop significantly so that the number of energetic photons issmall
To find the number of “fast” photon, we describe high-energy tailof Bose-Einstein distribution as f(k) ≈ 1/(2π)3 exp[−k/T ] and findthe temperature when
nγ(E > EH)
nγ,tot≈ ηB (4)
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CMB
This gives the solution Tdec ∼ EH/23 ≈ 0.6 eV
Again, knowing Tdec and Tcmb today (Tcmb = 2.725 K), one canindependently determine the baryon-to-photon ratio and confirmthe BBN prediction
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BBN predictions confirmed
Curves – theoreticalpredictions of Big Bangnucleosynthesis
Horizontal stripes –values that follow fromobservations.
Golden stripe – measuredvalue of η from CMBobservations!
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BBN and particle physics
Nowadays BBN has become a tool to determine properties(bounds) on light particles/decaying particles/evolution of fundamentalconstants
The Helium abundance is known with a precision of a few% (e.g.Yp = 0.2565± 0.0010(stat.)± 0.0050(syst,)) Izotov &
Thuan (2010)
Neutron lifetime provides a “cosmic chronometer”, measuring thetime between Tν (temperature of freeze-out of weak reactions) and Td(temperature of deuteron production):
nnnp
∣∣∣∣Td
=nnnp
∣∣∣∣Tν
e−t/τn
This time depends on the temperature Td and number of relativisticspecies at that time
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Effective number of relativistic d.o.f.
Total energy density at radiation dominated epoch (i.e. the Hubbleexpansion rate/lifetime of the Universe) depends on the effectivenumber of relativistic degrees of freedom:
3
8πGNH2 = ρrad =
π2
30g∗T
4 or
where the number of relativistic degrees of freedom is given by
g∗ =∑
boson species
gi +7
8
∑
fermion species
gi
where relativistic species (having 〈p〉 & m) count
Problems 6b, 6d
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BBN and particle physics
The primordial Helium abundance may change if
There are more than 3 neutrino species (Roughly: one extra neutrino ora particle with similar energy density is allowed at about 2σ level)
There was any other particle with the mass MeV and lifetime ofthe order of seconds or more that was contributing to g∗ at BBNepoch (1 second – lifetime of the Universe at T ∼ 1 MeV)
There were heavy particles with lifetime in the range 0.01 – fewseconds (that were decaying around BBN epoch)
Newton’s constant (entering Friedmann equation) changed betweenBBN epoch and later times (e.g. CMB or today)
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NEUTRINO IN THE EARLY
UNIVERSE
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Neutrino properties
there are 3 neutrinos (for each generation): νe, νµ, ντ
neutrinos are stable
neutrinos are electrically neutral
neutrinos have tiny masses (much smaller than mass of theelectron)
neutrinos participate in weak interactions
How neutrinos are produced in the early Universe?
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Neutrinos in primordial plasma
Neutrino reaction rates?
Recall: weak interaction strength is Fermi coupling constantGF ≈ 10−5 GeV−2
In the processes like e+ + e− → να + να the interaction rate
Γee→νν = ne(T )× σWeak
whereσWeak ∝ G2
F × E2e
What is the typical energy of electrons in this reaction?
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If in the expanding Universe particles that are in thermal equilibriumhave either Fermi-Dirac or Bose-Einstein distributions
At temperatures T m electron distribution function is
fe(p) = 4
∫d3p
(2π)3
1
ep/T + 1
Number density of the electrons
ne(T ) = 4
∫d3p
(2π)3
1
ep/T + 1∝ T 3
Average energy of the electron Ee = c× 〈p〉 i.e
Ee =4
ne(T )
∫d3p
(2π)3
p
ep/T + 1∼ T
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As a result Ee ∼ T
Reaction rate Γee→νν ∼ G2FT
5
Compare the characteristic interaction time Γ−1ee→νν with the age of
the Universe tUniv = 1/H(T ). To establish equilibrium we needΓ−1ee→νν tUniv or Γee→νν H(T )
At what temperatures neutrinos are in equilibrium?
One can see that temperature when
Γ ∼ G2FT
5 = T 2
√8πGN
3g∗(T )
is roughly Tdec ∼ 1 MeV
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g∗ in Standard Model
The Friedmanns equation for RD epoch can be written as:
H2(T ) =8πGN
3g∗(T )
π2
30T 4
︸ ︷︷ ︸ρrad
where g∗ – effective number of relativistic degrees of freedom.
As a result, 2 . g∗ . 110 for Standard Model:
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Neutrino in the early Universe: summary
We saw that
Neutrinos are produced in the early Universe and are in thermalequilibrium in plasma at T & Tdec ∼ 1 MeV
As all equilibrium ultra-relativistic particles their average energy is〈Eν〉 ∼ T , their number density is ∼ T 3
Their interaction rate with other particles Γν ∼ G2FT
5
What happens below Tdec?
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Freeze-out
If Γ . H particle go out of thermal equilibrium – freeze-out.
After the freeze-out, the comoving number density is conserved(particles are no longer produced or destroyed):
nco(T > Tdec) = nco(Tdec) ∝ T 3dec
The average momentum of decoupled particles changes with time(redshifts). Average momentum at the time of decoupling was ∼1 MeV. Average momentum today is ∼ 10−3 eV
As a result today in the Universe there are lots (about 100 cm−3)neutrinos (exercise: reproduce this number)
Their energy density today:
ρν =∑
mν × n or numerically Ωνh2 ≈
∑mν
94 eV
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THE NATURE OF DARK MATTER
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Dark Matter in the Universe
Stellar Disk
Dark Halo
Observed
Gas
M33 rotation curve
Expected: v(R) ∝ 1√R
Observed: v(R) ≈ const
Expected:masscluster =
∑massgalaxies
Observed: 102 times more massconfining ionized gas
Lensing signal (direct massmeasurement) confirmsother observations
Jeans instabilityturned tiny densityfluctuations into allvisible structures
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Do we believe that DM exists?
Stellar Disk
Dark Halo
Observed
Gas
M33 rotation curve
Back to DM Newton dynamics: V(R) ∼ 1√R
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Intracluster gas
Cluster Abell 2029. Credit: X-ray: NASA/CXC/UCI/A.Lewis et al. Optical: Pal.Obs. DSS
Dark Matter ∼ 85%Intracluster gas ∼ 15%Galaxies ∼ 1%
DM in clusterBaryons in cluster
≈ ΩDM
Ωbaryons
Temperature of ICM: 1− 10 keV ∼ 107 − 108 K
Back to DM page
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Gravitational lensing
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Dark Matter in the Universe
These phenomena are independent tracers of gravitationalpotentials in astrophysical systems. They all show that dynamicsis dominated by a matter that is not observed in any part ofelectromagnetic spectrum.
Stellar Disk
Dark Halo
Observed
Gas
M33 rotation curve
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"Bullet" cluster
Cluster 1E 0657-56Red shift z = 0.296
Distance DL = 1.5 Gpc
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Merging system in the plane of the sky? Subclusterpassedthrough thecenter ofthe maincluster.
? DM andgalaxies arecollisionless.
? Gashas beenstrippedaway (shockwave, MachnumberM = 3.2
andTshock ∼30 keV)
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Mass determined via gravitational lensing
? Comparingthe weakgravitationallensing datawith velocitydistribution forgalaxies
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Cosmological evidence for dark matter
We see the structures today and 13.7billions years ago, when the Universe was380 000 years old (encoded in anisotropiesof the temperature of cosmic microwavebackground)
All the structure is produced from tinydensity fluctuations due to gravitationalJeans instability
In the hot early Universe beforerecombination photons smeared outall the fluctuations
The structure has formed already, δρ/ρ ∼ 1 has to be long ago.i At CMB δρ/ρ ∼ 10−5, then grow δρ/ρ ∼ a (matter domination)
atodayadec
= 1 + zdec ∼ 103 Not enough!Go to CMB + Structure formation part
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A few basic questions
Is evidence for DM convincing?Yes
There are still other options nevertheless
Is DM made up of particles?Plausible assumption .
But no hard evidence. More exotic possibilities such as primordial black holes orMACHOs are not completely ruled out
We will study the scenario of dark matter particle and itsconsequences for particle physics.
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Properties of a DM candidate
DM is not baryonic
DM is not a SM particle (neutrinos could be but . . . )
Any DM candidate must be
– Produced in the early Universe and have correct relic abundance
– Very weakly interacting with electromagnetic radiation (“dark”)
– Be stable or cosmologically long-lived
There are plenty of non-SM candidates
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Neutrino Dark Matter?
In 1979 when S. Tremaine and J. Gunn published in Phys. Rev. Lett.a paper “Dynamical Role of Light Neutral Leptons in Cosmology”
– The smaller is the mass of Dark matter particle, the larger is thenumber of particles in an object with the mass Mgal
– Average phase-space density of any fermionic DM should besmaller than density of degenerate Fermi gas
⇒ If dark matter is made of fermions – its mass is bounded frombelow:
Mgal4π
3R3
gal
14π
3v3∞
≤ 2mDM4
(2π~)3
[0808.3902]
Objects with highest phase-space density – dwarf spheroidalgalaxies – lead to the lower bound on the fermionic DM mass
MDM & 300− 400 eV
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Neutrino Dark Matter?
However, if you compute contribution to DM density from massiveactive neutrinos (mν . MeV), you get
Ων DMh2 =
∑mν
∫d3k
(2π)3
1
ekT + 1
=
∑mν[eV]
94 eV
Using minimal mass of 300 eV you get ΩDMh2 ∼ 3 (wrong by about
a factor of 30!)
Sum of masses to have the correct abundance∑mν ≈ 11 eV
Massive Standard Model neutrinos cannot be simultaneously“astrophysical” and “cosmological” dark matter: to account for themissing mass in galaxies and to contribute to the cosmological
expansion
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Neutrino dark matter
If at some moment neutrino decoupled there exists a cosmologicalneutrino background whose comoving number density is
nCNB ∝ T 3dec ν
Neutrinos are massive and become non-relativistic in the matter-dominated epoch
As neutrinos are massive they contribute to the total matter densityΩM today
DM particles erase primordial spectrum ofdensity perturbations on scales up to the DMparticle horizon – free-streaming length
λcoFS =
∫ t
0
v(t′)dt′
a(t′)
Comoving free-streaming is approximately equal to the horizon atthe time of non-relativistic transition tnr (when〈p〉 ∼ m)
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Neutrino dark matter
Neutrino DM would homogenize the Universe at scales belowλcoFS > 1 Gpc. This contradicts to the observed large scale structure
and data on CMB anisotropies
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Neutrino dark matter
DM particles erase primordial spectrum ofdensity perturbations on scales up to the DMparticle horizon – free-streaming length
λcoFS =
∫ t
0
v(t′)dt′
a(t′)
Comoving free-streaming is approximately equal to the horizon atthe time of non-relativistic transition tnr (when〈p〉 ∼ m)
Upper bound on neutrinomasses
∑mν < 0.58 eV
(WMAP+LSS, 95% CL).
Neutrinos are relativistic after recombination (znr < 850)
Neutrino DM would homogenize the Universe at scales belowλcoFS > 1 Gpc. This contradicts to the observed large scale structure
and data on CMB anisotropies
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Properties of a DM candidate
DM is not baryonic
DM is not a SM particle (neutrinos could be but . . . )
Any DM candidate must be
– Produced in the early Universe and have correct relic abundance
– Very weakly interacting with electromagnetic radiation (“dark”)
– Be stable or cosmologically long-lived
There are plenty of non-SM candidates
Alexey Boyarsky PPEU 69
Interactions of a DM candidate
DM interacts with the rest of the matter gravitationally
Other possible interactions?
It is possible that DM particles interact only in the early (very) hotUniverse with some unknown particles
To be produced from the SM matter the DM particles should interact
It may be absolutely stable and interact with SM particles viaannihilation only: DM+DM→SM. . .
It may decay with very small rate, ensuring cosmologically long life-time: DM→SM. . .
Go back
Alexey Boyarsky PPEU 70
Example : WIMPs
Example: Non-relativistic weaklyinteracting particles
Alexey Boyarsky PPEU 71
Weakly interacting massive particles
Consider weakly interacting neutral particles (as neutrinos) but withthe mass mχ MeV. These particles would be non-relativisticwhen they decouple
In this case, their number density at temperatures Tdec T mχ
is given by the Boltzmann distribution:
neqX (T ) =
(mχT
2π
)3/2
e−mχ/T , T ≥ Tdec
At later times (T < Tdec) the comoving number density of particlesis conserved:
nχ(T ) = nχ(Tdec)
(T
Tdec
)3
neqχ (T )
– freeze-out (At T < Tdec the number density of these particles is muchlarger than equilibrium (for a temperature T ))
Alexey Boyarsky PPEU 72
WIMP freeze-out
We need to find the temperature of decoupling (of freeze-out) Tdec,such that
H(Tdec) = Γ(Tdec) ≡ 〈σv〉n(Tdec)
(for neutrino we took v = c = 1). Assuming mχ Tdec we can estimate〈σv〉 ∼ σ0 ×
√T/mχ where σ0 ∼ G2
Fm2χ (Ecm ∼ mχ).
Therefore we arrive
T 2
M∗= σ0
√T
mχ
(mχT
2π
)3/2
e−mχ/T
mχ
Tdec' log
(M∗mχσ0
(2π)3/2
)∼ log
(M∗m
3χG
2F
(2π)3/2
)
We see that e.g. for GeV scale particles and weak cross-sectionsmχ Tdec. Therefore, these particles indeed decouple non-relativistically, as we assumed.
Alexey Boyarsky PPEU 73
WIMP freeze-out
The number density of X-particles at the moment of their decouplinggets diluted due to the expansion of the Universe which gives theirpresent-day number desnity
nχ,0 =
(afa0
)3
nχ(Tdec).
Using the conservation of comoving entropy we rewrite it as
nX,0 =
(s0
sf
)nχ(Tdec),
where s0 = 2× 4π2
90
(T 3γ + 3× 7
8 × T 3ν
)≈ 2.8× 103 cm−3 is the present-
day entropy of the Universe, sf = g∗(Tdec) × 4π2
90 T3dec is the entropy at
the time of decoupling.
Alexey Boyarsky PPEU 74
WIMP freeze-out
Finally, the present-day abundance of X-particles is
ρχ = mχnχ,0 ∼ mχT 2dec
M∗σ0
s0
T 3dec
∝ log(σ0mχ)
σ0
and abundance
Ωχ =ρχρcrit
= 3× 10−10
(1 GeV2
σ0
)1√
g∗(Tdec)log
(MPl∗mχσ0
(2π)3/2
).
Note that this expression depends on mχ only logarithmically. Notealso the strong dependence on σ0: the weaker is the interaction, themore particles is created.
Alexey Boyarsky PPEU 75
WIMP "miracle"
Taking electroweak cross-section
σ0 'α2W
M2W
' 10−7 GeV−2
mass Mχ = 100 GeV, g∗(Tdec) = 100, the log value is ' 30, so that forelectroweak-scale interaction one would obtain Ωχ ' 10−2. Thus wepredict DM abundance within an order of magnitude.
Thus, weakly-interacting massive particles (WIMPs) are consideredas probable dark matter candidates.
WIMPs can be searched in direct detection experiments (interactionof galactic WIMPs with laboratory nucleons). back
Alexey Boyarsky PPEU 76
Another example.
Sterile neutrinos: a minimal unified modelof all observed BSM phenomena.
Alexey Boyarsky PPEU 77
νMSM: all masses below electroweak scale
Just add 3 right-handed (sterile) neutrinos NIR to MSM: Asaka,
Shaposhnikov,PLB 620, 17(2005)LνMSM = LSM + iN
IR ∂/NI
R −(LαM
DαIN
IR +
MI
2(N
IR)cNIR + h.c.
)
10−6
10−2
102
106
1010
10−6
10−2
102
106
1010tcu
bs
d
τ
µ
ννν
N
NN
N
N
e 1
1
3
3
1
2
3
Majorana masses
massesDirac
ν
quarks leptons
2NeV
The spectrum of the MSM
ν
ν
ν
2
Alexey Boyarsky PPEU 78
νMSM: all masses below electroweak scale
A very modest and simple modification of the SM which can explainwithin one consistent framework
X . . . neutrino oscillations
X . . . baryon asymmetry of the Universe
X . . . provide a viable (warm or cold) Dark Matter candidate
This model may be verified by existing experimentaltechnologies. It is importnat to confirm it or rule it out.
Alexey Boyarsky PPEU 79
Searching for decayingdark matter
Alexey Boyarsky PPEU 80
Decaying DM
DM with radiative signatures: DM → γ + ν, γ + γ, e+ + e− . . .
νNs
e± ν
W∓
γW∓
•
(a)
ℓ ℓ
ν
p− k
G
p
γ
k
ℓ
6R
•
(b)
ℓ ℓ
ν
p− k
G
p
γ
k
ℓ 6R
Alexey Boyarsky PPEU 81
Decaying DM
Appears in many models:
Right-handed neutrinoDodelson & Widrow’93;Asaka, Shaposhnikov et al.’05
Gravitino with broken R-parityTakayama & Yamaguchi’00Buchmuller’07
Volume ModulusQuevedo’07
Alexey Boyarsky PPEU 82
Monochromatic line in X-ray observations
DM decay should produce a linein X-ray spectra of various objects.
It should be visible against e.g powerlaw spectrum of diffuse extragalacticbackground.
Alexey Boyarsky PPEU 83
Properties of decaying DM
The properties of decaying DM are much less studied.
Crucial property: the flux from DM decay
FDM =Eγ
mDM
ΓMfovDM
4πD2L
≈ ΓΩfov
8π
∫
line of sight
ρDM(r)dr (z 1, Ωfov 1)
The flux FDM ∼∫ρDM(r)dr and NOT to
∫ρ2
DM(r)dr, as in the case
of annihilating DM.
The difference is HUGE.
Alexey Boyarsky PPEU 84
Decay signal from MW-sized galaxyMoore et al.2005
Alexey Boyarsky PPEU 85
Annihilation signal from MW-sized galaxyMoore et al.2005
Alexey Boyarsky PPEU 86
Decay vs. annihilation
In the case of decaying Dark Matterthe signal, if detected, is easyto distinguish from astrophysicalbackgrounds
We have a lot of freedom in choosingobservation targets and, therefore, canunambiguously check DM origin of asuspicious signal.
Alexey Boyarsky PPEU 87
For decaying DM "indirect"search becomes very
promising!
Alexey Boyarsky PPEU 88
VELOCITIES OF DARK MATTERPARTICLES
Alexey Boyarsky PPEU 89
Primordial properties of super-WIMPs
Feeble interaction strength of super-WIMP DM particles means thatin general they have not an equilibrium primordial velocity spectrum
For super-WIMPs primordial velocity spectrum carries theinformation about their production
In case of such DM particles free-streaming does not describe thesuppression of power spectrum back
1x10-3
2x10-3
3x10-3
4x10-3
0 1 2 3 4 5 6
q2 f(q
)
q/T
L= 2L= 4L= 6L= 8L= 10L= 12L= 14L= 16L= 25
0.1
1
1 30 1 10
Tra
nsfe
r fu
nction T
(k)
k [h/Mpc]
L= 0L= 2L= 4L= 6L= 8L= 10L= 12L= 14L= 16L= 25
Alexey Boyarsky PPEU 90
Subhalo mass function
We see much less satellites than naively expected
Where are these “missing satellites”? Moore et al.’99
Maccio &Fontanot’09
Is suppression of number of substructures due to the free-streaming?
Alexey Boyarsky PPEU 91
How to probe primordial velocities?
Effects of primordial velocities – not just a cut-off in matter powerspectrum at free-streaming scale
Primordial velocities affect:– Power-spectrum of density fluctuations (suppress normalization
at large scale)
– Halo mass function (number of halos of small mass decreases)
– Dark matter density profiles in individual objects
Scales probed by CMB experiments (linear regime of perturbationgrowth)
k ' `× H0
2=
`
6000
h
Mpc
Is sensitive up to scales k . 0.1 h/Mpc
Smaller scales?
Alexey Boyarsky PPEU 92
Lyman-α forest and cosmic web
Image: Michael Murphy, Swinburne University of Technology, Melbourne, Australia
Neutral hydrogen in intergalactic medium is a tracer of overall matterdensity. Scales 0.3h/Mpc . k . 3h/Mpc
Alexey Boyarsky PPEU 93
The Lyman-α method includes
Astronomical data analysis of quasar spectra
Astrophysical modeling of hydrogen clouds
N-body simulations of DM clustering at non-linear stage
Solving numerically Boltzmann equations for SM in the earlyUniverse
Finding global fit to the whole set of cosmological data (CMB, LSS,Ly-α), using Monte-Carlo Markov chains
Main challenge: reliable estimate of systematic uncertainties
Alexey Boyarsky PPEU 94
Lyman-α forest and warm DM
Previous works (Viel et al.’05-’06; Seljak et al.’06) put bounds on free-streaming λFS . 100 kpc (“WDM mass” > 10 keV)
Pure warm DM with such free-streaming would not modify visiblesubstructures
In Boyarsky, Lesgourgues, Ruchayskiy, Viel’08 we revised these boundsand demonstrated that
Boyarsky+JCAP’09;PRL’09– The primordial spectra are not
described by free-streaming
– There exist viable models withthe mass as low as 2 keV,consistent with the Lyman-α
1 keV/m s
F WD
M
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
Alexey Boyarsky PPEU 95
Halo (sub)structure in CDM+WDM universework inprogress
Alexey Boyarsky PPEU 96
Halo (sub)structure in CDM universe
Alexey Boyarsky PPEU 97
Halo (sub)structure in CDM+WDM universe
PRELIMINARY: Aq-A-2 halo in CDM and CDM+WDM simulations (Gao, Theuns, Frenk, O.R., . . . )
Simulated CWDM model (right) is fully compatible with the Lyman-αforest data but provides a structure of Milky way-size halo differentfrom CDM (left)
Alexey Boyarsky PPEU 98
Window of parameters of sterile neutrino DM
Sin
2 (2θ)
MDM [keV]
10-16
10-14
10-12
10-10
10-8
10-6
0.3 1 10 100
Ω > ΩDM
Ω < ΩDM
Alexey Boyarsky PPEU 99
Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy etal. 2005-2008
Sin
2 (2θ)
MDM [keV]
10-16
10-14
10-12
10-10
10-8
10-6
0.3 1 10 100
Excluded from X-rays
Alexey Boyarsky PPEU 100
Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy etal. 2005-2008
Sin
2 (2θ)
MDM [keV]
10-16
10-14
10-12
10-10
10-8
10-6
0.3 1 10 100
Excluded from X-rays
Exc
lud
ed f
rom
PS
D e
volu
tio
n a
rgu
men
ts
Alexey Boyarsky PPEU 101
Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy,Lesgourgues,Viel[0812.3256]
Boyarsky,Ruchayskiy,Shaposhnikov[0901.0011]
sin
2(2
θ 1)
M1 [keV]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
5 50 1 10
ΩN1 < ΩDM
Ph
as
e-s
pa
ce
de
ns
ity
co
ns
tra
ints
X-ray constraints
ΩN1 > ΩDM
L6=25L6=70
NRP
L6max
=700BBN limit: L
6BBN
= 2500
Alexey Boyarsky PPEU 102
Window of parameters of sterile neutrino DMBoyarsky,Ruchayskiy,Lesgourgues,Viel[0812.3256]
Boyarsky,Ruchayskiy,Shaposhnikov[0901.0011]
sin
2(2
θ 1)
M1 [keV]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
5 50 1 10
ΩN1 < ΩDM
Ph
ase-s
pace d
en
sit
yco
nstr
ain
ts
X-ray constraints
ΩN1 > ΩDM
L6=25L6=70
NRP
L6max
=700BBN limit: L
6BBN
= 2500
Sterile neutrino is still viable and very attractive DM candidate. TheνMSM should be verified.
To explore the allowed window, more theoretical efforts, both onparticle physics and astrophysics sides, and new methods ofanalysis of the full set of the cosmological and astrophysical data isneeded.
Alexey Boyarsky PPEU 103
Baryon asymmetry of the Universe
In general, all elementary particles can be divided into three groups:
Truly neutral, like photon, intermediate Z-boson, Majorana neutrino,π0, etc. They do not carry any charges.
Particles, like proton, neutron, and electron
Antiparticles, like antiproton, antineutron, and positron
CPT theorem: particles and antiparticles have the same mass, thesame lifetime, but opposite charges (electric, baryonic, leptonic, etc).
Naturally, a matter is a substance which consists of particles, andantimatter is a substance consisting of antiparticles.
Alexey Boyarsky PPEU 104
Baryon asymmetry in the present universe
Main questions: Why do the Earth, the Solar system and ourgalaxy consists of of matter and not of antimatter?
Why we do not see any traces of antimatter in the universe exceptof those where antiparticles are created in collisions of ordinaryparticles?
This looks really strange, as the properties of matter and antimatterare very similar.
Alexey Boyarsky PPEU 105
Antiprotons in the universe
Alexey Boyarsky PPEU 106
Positrons in the universe
Alexey Boyarsky PPEU 107
Baryon asymmetry of the Universe
There are two possibilities:
Observed universe is asymmetric and does not contain anyantimatter
The universe consists of domains of matter and antimatterseparated by voids to prevent annihilation. The size of thesezones should be greater than 1000 Mps, in order not to contradictobservations of the diffuse γ spectrum.
The second option, however, contradicts to the large scale isotropy ofthe cosmic microwave background.
Thus, we are facing the question: Why the universe is globallyasymmetric?
Alexey Boyarsky PPEU 108
Matter-antimatter asymmetry in particle physics
Parity is broken in weak interactions
CP is conserved (ν(~v) −→ ν(−~v)
CP-violation in kaon decays (1964 Cronin, Fitch,. . . ) In a small fractionof cases (∼ 10−3), long-lived KL (a mixture of K0 and K0 decays into pair oftwo pions, what is forbidden by CP-conservation.
If CP were exact symmetry, an equal number of K0 and K0 wouldproduce an equal number of electrons and positrons in the reaction
K0 → π−e+νe, K0 → π+e−νe,
However, the number of positrons is somewhat larger (∼ 10−3) thanthe number of electrons.
Alexey Boyarsky PPEU 109
Matter-antimatter puzzle
There is indeed a tiny difference between particles and antiparticles,on the level of 10−3, observed in particle physics experiments
How can this very small distinction betransformed in the 100% asymmetryof the universe we observe today?
Alexey Boyarsky PPEU 110
Thermal history of baryon asymmetry
At t ∼ 10−6s after the big Bang for 1010 quarks we have (1010 − 1)antiquarks. Somewhat later the symmetric background annihilatesinto photons and neutrinos while the asymmetric part survives andgives rise to galaxies, stars, planets.
1
t10−6
s
n − n
n + n
B
B B
B
annihilation ofsymmetric background
ηB
Alexey Boyarsky PPEU 111
Sakharov conditions
Sakharov: To generate baryon asymmetry of the Universe 3conditions should be satisfied
I. Baryon number should not be conserved
II. C-symmetry and CP-symmetry must be broken
III. Deviation from thermal equilibrium in the Universe expansion
Alexey Boyarsky PPEU 112
Baryon number non-conservation
Baryon charge is conserved in particle physics processes. As aconsequence proton is stable (proton lifetime > 6.6× 1033 years fordecays such as p→ π0 + e+ or p→ π0 +µ+. This bound is 5× 1023
times longer than the age of the Universe
The conservation of baryon number would mean that the totalbaryon charge of the Universe remains constant in the process ofevolution.
If initial conditions were matter-antimater symmetric1 – no baryonasymmetry could have been generated without baryon numberviolation
1See the discussion of initial conditions below
Alexey Boyarsky PPEU 113
C- and CP-non-conservation
C- and CP-symmetries change baryon number of particles:C |p〉 = |p〉, C |e−〉 = |e+〉, etc.
If these symmetries were conserved in the early Universe thiswould mean that for any process, changing baryon number, thereis another process, restoring baryon number. Namely, if
X1 +X2 + · · · → Y1 + Y2 + . . .
change baryon number by +1, then there is a process:
X1 + X2 + · · · → Y1 + Y2 + . . .
in which baryon number changes by−1 and their probabilities arethe same.
Alexey Boyarsky PPEU 114
Deviation from thermal equilibrium
In thermal equilibrium for any process there is a reverse one
Asymmetries do not grow, moreover, they tend to decay
In the SM all the conditions seems to be satisfied:
– CP is violated
– Baryon number may not be non-conserved: it can be createdfrom lepton number by non-perturbative processes active at hightemperature
– There may be phase transitions ( E-W, QCD).
However, experimental bounds on the SM parameters show thatthis does not happen!
Back to beyond SM problems
Alexey Boyarsky PPEU 115
Phase transitions in the early Universe
PHASE TRANSITIONS IN THE
EARLY UNIVERSE
Alexey Boyarsky PPEU 116
Phase transitions
In the presence of the temperature, the potential for the field φ canchange:
V (φ) = λ
[φ4
4+φ2
2
(T 2
4− v2
)]
Tc = 2v
From http://www.phys.uu.nl/˜prokopec
Alexey Boyarsky PPEU 117
Phase transitions
Two main types of phase transitions:
I order – Discontinuity of 〈φ〉T (left).
II order – No discontinuity of 〈φ〉T (right).
Alexey Boyarsky PPEU 118
1st order phase transition
Alexey Boyarsky PPEU 119
2nd order phase transition
Back to Sakharov
Alexey Boyarsky PPEU 120
Search for decaying DM: main challenges
Control of astrophysical andinstrumental background
Reliable determination of darkmatter content of an object
Alexey Boyarsky PPEU 121
DM in Andromeda galaxy (2007)0709.2301
0.1
1
10
10 30 60 90 1 10
DM
co
lum
n d
ensi
ty (
g/c
m2 )
Off-center angle, arcmin
K2GFBGKING
MOOREN04
NFWBURK
KERM31AM31BM31C
Alexey Boyarsky PPEU 122
Mass-to-light ratio in Andromeda galaxy?
Corbelli et al. A&A 2009
Chemin et al. ApJ 2009
Mass-to-light ratio of bulge and disk components vary by afactor ∼ 4
Alexey Boyarsky PPEU 123
DM in Andromeda galaxy (2010)
Red -W & D, M31bGreen -W & D, M31cBlue -W & D, M31d
Dashed -Chemin09, ISODotted -Corbelli09, R_B = 28 kpc
5 10 15 20r,kpc
100
1000
500
200
300
150
700
S_DM, M_Sunpc^2Dark matter column density
Alexey Boyarsky PPEU 124
DM distribution in individual objects
Knowledge of dark matter distribution in individual objects is crucialfor astrophysical searches of decay/annihilation signals
Dark matter column density is uncertain within a factor of few (muchmore for
∫ρ2dl)
Uncertainty in modeling of the baryonic contribution
Dwarf spheroidal galaxies PRL’06
Alexey Boyarsky PPEU 125
Universal properties of DM distribution
Fortunately, it is possible to minimize the dependenceof the results on astrophysical uncertainties related toindividual objects.
One can exploit a universal property of DMdistributions.
Alexey Boyarsky PPEU 126
Constant surface density?Kormendy,Freeman’94;Donato et al.2009;PRL’06
Dark matter surface density remains for different types of galaxies?
Alexey Boyarsky PPEU 127
An evidence in favor of MOND?Gentile et al.Nature’09
Baryonic surface density for different types of galaxies.
Alexey Boyarsky PPEU 128
Observations vs. simulations0911.1774S changesslowly.There is auniversalscaling.
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
n d
ensi
ty,
lg (
S/M
sun p
c-2)
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos, ΛCDM N-body sim.Subhalos from Aquarius simulation
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
n d
ensi
ty,
lg (
S/M
sun p
c-2)
DM halo mass [Msun]
M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-rays
S ∼(Mhalo
)≈0.2
Alexey Boyarsky PPEU 129
Observations vs. simulations0911.1774S changesslowly.There is auniversalscaling.
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
n d
ensi
ty,
lg (
S/M
sun p
c-2)
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos, ΛCDM N-body sim.Subhalos from Aquarius simulation
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
n d
ensi
ty,
lg (
S/M
sun p
c-2)
DM halo mass [Msun]
M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-raysAverage data from WL
S ∼(Mhalo
)≈0.2
Go back to the intro
Alexey Boyarsky PPEU 130
Universal properties of DM distributions?
Going through the literature we collected a “catalog” of ∼1000 DMBoyarsky et al.0911.1774
density profiles for ∼300 individual objects, ranging from dwarfspheroidal satellites of the Milky Way to galaxy clusters
Different methods (rotation curves, X-rays, weak lensing, . . . ). Differentobservational groups fit the mass distribution with different velocityprofiles (isothermal sphere, Navarro-Frenk-White, Burkert, . . . )
Important questions:
– What properties to compare?– Often fits to different DM density profiles exist for the same object.
How to relate their parameters?– Any universality is observed?
Alexey Boyarsky PPEU 131
Comparing DM density profiles
Fitting the same (simulated) data with two different profiles onefinds a relation between parameters of two DM density distribution,fitting the same data 0911.1774
5 10 15 20
r
rc
0
4
6
8
10
12vc
2
HaL
– NFW vs. ISO :rs ' 6.1 rc; ρs ' 0.11 ρc
– NFW vs. BURK :rs ' 1.6rB ; ρs ' 0.37ρB
– For most observed objectsρ?r? = const
Observable not sensitive to the choice of dark matter density profile– Dark matter column density
§ =
∫
l.o.s.
ρDM(r)dl ∝ ρ?r?
Alexey Boyarsky PPEU 132
Observations vs. simulations0911.1774S changesslowly.There is auniversalscaling.
0
1
2
3
4
5
6
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
colu
m d
ensi
ty, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos from N-body simulationsSubhalos from Aquarius simulation
S ∼(Mhalo
)≈0.2
Alexey Boyarsky PPEU 133
Universal scaling of DM column density
0.5
1
1.5
2
2.5
3
3.5
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
den
sity
, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
The relation between § and Mhalo is observed for isolated halos of 0911.1774
all scales (for all observed halo masses from 108M to 1015M).
Slope of subhalos (Aquarius simulation) is reproduced
The median value and scatter coincide remarkably well with puredark matter numerical simulations
Alexey Boyarsky PPEU 134
Universal scaling of DM column density
0.5
1
1.5
2
2.5
3
3.5
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
co
lum
den
sity
, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
No visible features – universal (scale-free) dark matter down to thelowest observed scales and masses
No deviations from CDM down to Mhalo = 1010M
new proof that dark matter exists!
Alexey Boyarsky PPEU 135
Independent determination of mass
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
colu
mn d
ensi
ty, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos, ΛCDM N-body sim.Subhalos from Aquarius simulation
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
colu
mn d
ensi
ty, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-rays
Alexey Boyarsky PPEU 136
Independent determination of mass
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
colu
mn d
ensi
ty, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsIsolated halos, ΛCDM N-body sim.Subhalos from Aquarius simulation
0
1
2
3
4
5
6
7
107
108
109
1010
1011
1012
1013
1014
1015
1016
DM
colu
mn d
ensi
ty, lg
(S
/Msu
n p
c-2)
DM halo mass [Msun]
M and S - caustics, clustersM and S - caustics, groupsM - caustics, S - X-raysM - WL, S - WLM - WL, S - X-raysAverage data from WL
Alexey Boyarsky PPEU 137
Qualitative understanding?
This behaviour can be understood qualitatively in the framework ofCDM
The sphere of influence of the DM halo (sphere of zero velocity,turn-around radius)
Rta ∝(GM
H2
)1/3
Self-similar density profiles: characteristic scale r? ∝ Rhalo whereRhalo ≈ Rta
ThereforeS ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3
ta
Observationally, the “concentration parameter” c = r?/Rta is a weakfunction of mass
Alexey Boyarsky PPEU 138
DM column density in infall model
0
1
2
3
4
5
6
107 108 109 1010 1011 1012 1013 1014 1015 1016
DM column density, log10[S/Msun pc-2]
DM halo mass M200 [Msun]
Subhalos from Aquarius simulationIsolated halos from ΛCDM N-body simulationsPredictions from the Secondary infall modelClusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphs
S ∼(Mhalo
)1/3−0.1
arxiv:0911.3396
Alexey Boyarsky PPEU 139
Qualitative understanding?
This behaviour can be understood qualitatively in the framework ofCDM
The sphere of influence of the DM halo (sphere of zero velocity,turn-around radius)
Rta ∝(GM
H2
)1/3
Self-similar density profiles: characteristic scale r? ∝ Rhalo whereRhalo ≈ Rta
ThereforeS ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3
ta
Observationally, the “concentration parameter” c = r?/Rta is a weakfunction of mass
Alexey Boyarsky PPEU 140
Restrictions on modifications of gravityA.Boyarsky,O.Ruchayskiy1001.0565
0
1
2
3
4
5
6
7
8
107 108 109 1010 1011 1012 1013 1014 1015 1016
DM column density, log10[S/Msun pc-2]
DM halo mass [Msun]
Clusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphsNorm. branch, α = 0 ; rc = 150 MpcSelf-acc. branch, α = 0 ; rc = 150 MpcNorm. branch, α = 1/4 ; rc = 300 MpcSelf-acc. branch, α = 1/4 ; rc = 300 MpcBest-fit model S ∝ M0.23
Alexey Boyarsky PPEU 141
Direct astrophysical detection.
As column density does not vary too much, decaying DM producesan all-sky signal with some hot spots.
Objects of different scales and nature can be used to put robustbounds.
Ones a candidate line is found, spacial distribution can becompared with DM column density map.
DM origin can thus be unambiguously checked.
For decaying DM"indirect" search becomes
"direct" !
Alexey Boyarsky PPEU 142
Restrictions on sterile neutrino DMBoyarsky et al.MNRAS-2008
10-30
10-25
10-20
10-15
10-10
10-5
100 101 102 103 104
sin2 (
2θ)
Ms [keV]
XMMChandra
HEAO-1
SPI (INTEGRAL)
MWM31
MW
Galactic center
Alexey Boyarsky PPEU 143
Restrictions on life-time of decaying DM
Boyarsky+ :XRB HEAO-12005;
Bullet clusterChandra 2006;
LMC XMMMW XMM2006-2007
MW ChandraRiemer-Sørensen+.;Abazajian+ 2007
M31Watson+ 2006;Boyarsky+ 2007
dSps(UMi,Draco,W1, Sc,Forn), Suzaku,Chandra, XMMBoyarsky+2006,2010;Loewenstein,Kusenko2008-2009
Life
-tim
e τ
[sec
]
MDM [keV]
1025
1026
1027
1028
1029
10-1 100 101 102 103 104
XMM, HEAO-1 SPI
τ = Universe life-time x 108
Chandra
PSD
exc
eeds
deg
ener
ate
Fer
mi g
as
Alexey Boyarsky PPEU 144
New mission: EDGE/XENIA
Spectrometers with big FoV andspectral resolution better than10−3 are needed
Future missions (XEUS orConstellation X ) will have betterspectral resolution but verysmall FoV
XENIA (former EDGE),proposed for NASA’s CosmicOrigins by the team fromNASA/MSFC, INAF, SRON +ISDC, EPFL,. . . ).
ART−XSpectrometer @ 1 keVEDGE Low−Energy
@ 6 keVEDGE wide FoV
A.Boyarsky, etal. (2007)
Alexey Boyarsky PPEU 145
THANK YOU FOR YOURATTENTION
Alexey Boyarsky PPEU 146
Qualitative understanding?
Gravitational collapse: gravitational potential energy U ∝ GMR
balances kinetic energy of cosmological expansion K ∝ H2R2
The sphere of influence of the DM halo (sphere of zero velocity,turn-around radius)
Rta ∝(GM
H2(t)
)1/3
Self-similar solutions would give
S ∝ ρ?r? ∝ ρtaRta ∝ c(M) ·M1/3ta
Observationally, the “concentration parameter” c = r?/Rta is a weakfunction of mass
Alexey Boyarsky PPEU 147
DM column density in infall model
0
1
2
3
4
5
6
107 108 109 1010 1011 1012 1013 1014 1015 1016
DM column density, log10[S/Msun pc-2]
DM halo mass M200 [Msun]
Subhalos from Aquarius simulationIsolated halos from ΛCDM N-body simulationsPredictions from the Secondary infall modelClusters of galaxiesGroups of galaxiesSpiral galaxiesElliptical galaxiesdSphs
S ∼(Mhalo
)1/3−0.1
arxiv:0911.3396
Alexey Boyarsky PPEU 148
Example: Lyman-α forest
Absorption lines of neutral hydrogen trace DM distribution atdifferent red-shifts
Neutral hydrogen absorption line at λ = 1215.67A
From the Earth observer point of view we see the forest:λ = (1 + z)1215.67A
Alexey Boyarsky PPEU 149
Observational data
Alexey Boyarsky PPEU 150
Parameters of Aquarius simulation
Name mp ε Nhr Nlr N50
[M] [pc]
Aq-A-1 1.712× 103 20.5 4,252,607,000 144,979,154 1,473,568,512Aq-A-2 1.370× 104 65.8 531,570,000 75,296,170 184,243,536
Basic parameters of the Aquarius simulations. mp is the particlemass, ε is the gravitational softening length, Nhr is the number of highresolution particles, and Nlr the number of low resolution particlesfilling the rest of the volume. M200 = 1.839 × 1012M is the virialmass of the halo, defined as the mass enclosed in a sphere withmean density 200 times the critical value. r200 = 245 kpc gives thecorresponding virial radius. M50 = 2.524× 1012M. Finally, N50 givesthe number of simulation particles within r50 = 433 kpc. Springel et
al.’08
Back to CDM+WDM halo simulation
Alexey Boyarsky PPEU 151
Literature
A very interesting and instructive article about how the pro http://people.bu.edu/gorelik/cGh_Bronstein_UFN-200510_Engl.htm
Very nice lectures on cosmology and early universe
http://arxiv.org/abs/hep-ph/0004188
Alexey Boyarsky PPEU 152
Plan
1. May be some question about h and c, Bronstein. Question: whythe mass of electron is 511 keV, however the energy e2mc/~ = mc2.Renormalisability, QED, gravity. 2. Dirac equation, positron,
Quantum field theory: collection of free particles, interactions,perturbation theory.
3. Neutrino: the first particle found as missing energy.
4. The theory of beta decay (1934)(Cheng-Lie) . alpha decay ( stronginteractions).
First p, n, nu etc. Parity violation ( 1956-57) Then many other similarprocesses, more general Lagrangian ( V-A theory).
Weak and strong interactions? fast and slow. (definitions ?)
Alexey Boyarsky PPEU 153
CMB anisotropies
PHYSICS OF COSMIC MICROWAVEBACKGROUND
Alexey Boyarsky PPEU 154
CMB anisotropy map
CMB temperature is anisotropic over the sky with δT/TCMB ∼ 10−5
WMAP-5 results with subtracted galactic contribution (courtesy of WMAP Science team)
Alexey Boyarsky PPEU 155
CMB anisotropies (cont.)
The temperature anisotropy δT (n) is expanded in sphericalharmonics Ylm(n):
δT (~n) =∑
l,m
almYlm(n)
alm’s are Gaussian random variables (before sky cut)
CMB anisotropy (TT) power-spectrum: 2-point correlation function
〈δT (n) δT (n′)〉 =∞∑l=0
2l + 1
4πClPl(n · n′)
Pl(n · n′) – Legendre polynomials
Multipoles Cl’s
Cl =1
2l + 1
l∑m=−l
|alm|2
probe correlations of angular scale θ ∼ π/l
Alexey Boyarsky PPEU 156
WMAP + small scale experiments
The WMAP 5-year TT power spectrum along with recent results from the ACBAR(Reichardt et al. 2008, purple), Boomerang (Jones et al. 2006, green), and CBI(Readhead et al. 2004, red) experiments. The red curve is the best-fit ΛCDMmodel to the WMAP data.
Alexey Boyarsky PPEU 157
What (how) can we learn from CMB?
back to DM
Alexey Boyarsky PPEU 158
Intermission:structure formation basics
Alexey Boyarsky PPEU 159
Evolution of structures?
How did the structures evolve fromthis ⇑ to this ⇓?
Alexey Boyarsky PPEU 160
Structure formation
Total energy of the Universe
Etot =R2(t)
2−G(
4π3 ρR
3(t))
R(t)= 0
m
H2(t) =R2(t)
R2(t)=
8πG
3ρ
Friedmann equation
R(t)
ρ > ρ
Uniform density ρ
ρ < ρ
Will ollapse
into a galaxy
Will grow
into a void
Jeans instability in expanding Universe: interplay of twoconcurrent processes:
– Gravitational attraction within an overdense region(U ∼ GM
R
)
– Overall expansion of the Universe(K ∼ H2R2
2
)
Alexey Boyarsky PPEU 161
Analytical model: spherical collapse
Constant density overdensity ρ inside expanding FRW Universewith the average matter density ρ(t) (assume for simplicity ΩDM =ΩM = Ωcrit)
Overdensity expands with the Universe until the pull of gravityovercomes the kinetic energy of cosmological expansion
ρ(tmax) =9π2
16ρ(tmax)
Overdensity recollapses and “virializes”, so that rvir = rmax/2 overa period of time tvir ≈ 2tmax
Finally, one obtains
ρ(tvir) =9π2
16× 8× 4ρ(tvir) ≈ 178ρ(tvir)
Alexey Boyarsky PPEU 162
Analytical model: secondary infall
Evolution of the radius r(t) of a spherical shell is governed by theNewtonian dynamics
d2r
dt2=Gm(t)
r2,
– m(t) is the mass inside the radius r(t).
– Initial velocities follow Hubble flow r(ti) = H(ti)ri
For initial perturbations with power-law profiles δMiMi
=(M0Mi
)ε, the
halo density profie evolves in a “self-similar” manner
ρ(r, t) =M(t)
R3(t)× F
(r
R(t)
).
F (x) does not depend on mass/size
Alexey Boyarsky PPEU 163
Secondary infall model: phase-spaceSikivie,Tkachev,Wang’96
Alexey Boyarsky PPEU 164
Turn-around radius
Gravitational potential energy U ∝ GMR balances kinetic energy of
cosmological expansion K ∝ H2R2
The sphere of influence of the DM halo (sphere of zero velocity,turn-around radius)
Rta ∝(GM
H2(t)
)1/3
Grows with time while Hubble expansion decelerates
The density inside the turn-around radius is the same for objectsof all masses and is determined by cosmology
ρta(t) ∝ ρM(t)
Alexey Boyarsky PPEU 165
Cosmic web
Gravitationally collapsing structures form a“cosmic web”
Relativistic particles free stream out ofoverdense regions and smooth primordialinhomogeneities
Overdensity
Alexey Boyarsky PPEU 166
Jeans instability I
Consider Newtonian perfect fluid filling all the space
∂ρ
∂t+ ~∇ · (ρ~v) = 0
∂v
∂t+ (~v · ~∇)~v +
1
ρ~∇p+ ~∇φ = 0
~∇2φ = 4πGNρ
p – pressure, ρ – density, φ –gravitational potential
Homogeneous solution: ρ = ρ, ~v = 0, p = p0
Following Jeans we assume that uniform fluid, filling all space has φ = 0
Is it stable? Let ρ = ρ+ δρ, p = p0 + δp, etc. Find perturbed solution
Alexey Boyarsky PPEU 167
Jeans instability II
Perturbations:
∂2δ
∂t2− v2
s∇2δ = (4πGN ρ)δ, δ ≡ δρ
ρ= e−iωt+i
~k·~x
ω2 = v2sk
2 − 4πGN ρ. , where vs – speed of sound.
Modes are unstable for k < kJ :
kJ =
(4πGN ρ
v2s
)1/2
Arbitrarily small perturbations of size bigger than λJ = 2πk−1J will
collapse under the pull of self-gravity
Alexey Boyarsky PPEU 168
Jeans instability in expanding Universe
In non-expanding Universe Jeans unstable modes grow exponentiallyfast
Expansion slows down the growth of instabilities (i.e. pulls apartcollapsing structures)
How do structures collapse in expanding Universe?
Alexey Boyarsky PPEU 169
Jeans instability in expanding Universe
Expanding Universe Non-expanding Universe
δ(τ) =δρ(τ)
ρ(τ)δ(t) =
δρ(t)
ρρ = const
ρ ∼ a−4 RDa−3 MD
ρ = const
δ+a
aδ+v2
s(k2−k2
J)δ = 0 derivatives
with respect to conformal time τδ + v2
s(k2 − k2
J)δ = 0
k2J =
4πGN ρ(τ)a2(τ)
v2s(τ)
k2J =
4πGN ρ
v2s
v2s(τ) = p(τ)
ρ(τ) =
≈ 1
3 RD≈ 0 MD
v2s = const
Perturbations grow at most power-like
Perturbations grow exponentially
δ(τ) ∼ a(τ) ∼ τ2δ(t) ∼ e
√4πGN ρt
Alexey Boyarsky PPEU 170
Real CMB physics
Neutrinos
BaryonsDark
Matter
Metric
ComptonScattering
Coulom
b
Scattering
Photons Electrons
From S. Dodelson’s“Modern Cosmology”
Alexey Boyarsky PPEU 171
Growth of perturbations
System of coupled Boltzmann equations
Radiation perturbations (δγ and tightly coupled to it δb at RD epoch)remain frozen in time (for scales larger than Jeans length)
Radiation perturbations oscillate (acoustic oscillations) for smallerthan Jeans length scales
In RD epoch DM perturbations grow only logarithmically in τ forsmall scales (kτ >
√3)
DM starts to grow after τeq – time when density of matter and
radiation equates: zeq =Ωγ+ΩνΩDM+Ωb
In MD epoch DM perturbations grow quadratically in τ
Alexey Boyarsky PPEU 172
Cosmological parameters and CMB
0
1000
2000
3000
4000
5000
6000
7000
8000
500 10 100 1000
l(l+
1) C
l / 2
π [µ
K2 ]
l
ΩΛ = 0.7
Ωb = 0.05; Ωdm = 0.25
Ωb = 0.25; Ωdm = 0.0
Alexey Boyarsky PPEU 173
Large scale structure
Alexey Boyarsky PPEU 174
Large scale structure
Alexey Boyarsky PPEU 175
Large scale structure
Alexey Boyarsky PPEU 176
Free-streaming
Relativistic particles cannot be gravitationally bound
They free stream out of overdense regions and smooth primordialinhomogeneities on the scales below free-streaming horizon
λcoFS =
∫ t
0
v(t′)dt′
a(t′)=
∫ tnr
0
dt′
a(t′)+
∫ teq
tnr
dt′
a2(t′)+ . . .
Suppression mass scale: MFS =4π
3ρ
(λFS
2
)3
Go back to the neutrino DM page
Alexey Boyarsky PPEU 177
Free-streaming (numbers)
Free-streaming length for fermions “almost” in equilibrium: Bond,Efstathiou,Silk
λFS = 1.2 Mpc( 〈p〉〈pν〉
)(1 keVmDM
)
The free-streaming mass:
MFS = 1.77M3Pl
m2DM' 2.9× 1012M
(1 keVmDM
)2
Go back to the neutrino DM page
Alexey Boyarsky PPEU 178
Thermal relics
Thermal relics (sometimes called also generic warm dark matter )decouple relativistic and have Fermi-Dirac-like primordial velocitydistribution function
f(v) =1
1 + exp(mvTR)
Dark matter abundance ΩDMh2 =
mTR
94 eV
(TRTν
)3
The WDM transfer function is suppressed as
T (k) =(
1 +
(k
kFS
)2ν)−5/ν
, ν ≈ 1.2
The free-streaming scale kFS = 20.4h
Mpc
(mTR
keV
)1.11(
0.25× 0.72
ΩDMh2
)0.11
Go back to the primordial velocities page
Alexey Boyarsky PPEU 179
TOCEarly Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Thermal history of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Cosmological model of Einstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Cosmological model continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Cosmological model continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Cosmology in a couple of words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Hubble expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Hubble constant history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Reminder: redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14The initial state of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15The Universe in the past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Binding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Relic radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Formation of structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22Challenges to Hot Big Bang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Cosmic Microwave background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25COBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Alexey Boyarsky PPEU 180
TOC
CMB spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Properties of CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Predictions of Hot Big Bang model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Nuclear network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Deuterium bottleneck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31Neutron/proton ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32The content of MeV plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Cross-section, reaction rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38BBN predictions confirmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40BBN and particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Effective number of relativistic d.o.f. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42BBN and particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Neutrino properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45Neutrinos in primordial plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47g∗ in Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Neutrino in the early Universe: summary . . . . . . . . . . . . . . . . . . . . . . . . . 50
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TOC
Freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Dark Matter in the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Do we believe that DM exists? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54Intracluster gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55Gravitational lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56Dark Matter in the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Cosmological evidence for dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A few basic questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Properties of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63Neutrino Dark Matter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Neutrino dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Properties of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69Interactions of a DM candidate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Example : WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Weakly interacting massive particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72WIMP freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
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WIMP freeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74WIMP ”miracle” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76νMSM: all masses below electroweak scale . . . . . . . . . . . . . . . . . . . . . . 78νMSM: all masses below electroweak scale . . . . . . . . . . . . . . . . . . . . . . 79. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Properties of decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Decay signal from MW-sized galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Annihilation signal from MW-sized galaxy . . . . . . . . . . . . . . . . . . . . . . . . . 86Decay vs. annihilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Primordial properties of super-WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Subhalo mass function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91How to probe primordial velocities? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92Lyman-α forest and cosmic web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93The Lyman-α method includes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Lyman-α forest and warm DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Halo (sub)structure in CDM+WDM universe . . . . . . . . . . . . . . . . . . . . . . 96
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Halo (sub)structure in CDM universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Halo (sub)structure in CDM+WDM universe . . . . . . . . . . . . . . . . . . . . . . 98Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . . 99Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 100Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 101Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 102Window of parameters of sterile neutrino DM . . . . . . . . . . . . . . . . . . . . 103Baryon asymmetry of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Baryon asymmetry in the present universe . . . . . . . . . . . . . . . . . . . . . . 105Antiprotons in the universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Positrons in the universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Baryon asymmetry of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Matter-antimatter asymmetry in particle physics . . . . . . . . . . . . . . . . . . . . . . . . . 109Matter-antimatter puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Thermal history of baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Sakharov conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Baryon number non-conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113C- and CP-non-conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
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Deviation from thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Phase transitions in the early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 116Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181st order phase transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1192nd order phase transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Search for decaying DM: main challenges . . . . . . . . . . . . . . . . . . . . . . . 121DM in Andromeda galaxy (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Mass-to-light ratio in Andromeda galaxy? . . . . . . . . . . . . . . . . . . . . . . . 123DM in Andromeda galaxy (2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124DM distribution in individual objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Universal properties of DM distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 126Constant surface density? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127An evidence in favor of MOND? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Universal properties of DM distributions? . . . . . . . . . . . . . . . . . . . . . . . .131Comparing DM density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132
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Observations vs. simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Universal scaling of DM column density . . . . . . . . . . . . . . . . . . . . . . . . . 134Universal scaling of DM column density . . . . . . . . . . . . . . . . . . . . . . . . . 135Independent determination of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Independent determination of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138DM column density in infall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140Restrictions on modifications of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 141Direct astrophysical detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Restrictions on sterile neutrino DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Restrictions on life-time of decaying DM . . . . . . . . . . . . . . . . . . . . . . . . . 144New mission: EDGE/XENIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Qualitative understanding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147DM column density in infall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Example: Lyman-α forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Observational data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150
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Parameters of Aquarius simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153CMB anisotropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154CMB anisotropy map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155CMB anisotropies (cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156WMAP + small scale experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157What (how) can we learn from CMB? . . . . . . . . . . . . . . . . . . . . . . . . . . . .158. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Evolution of structures? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Structure formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Analytical model: spherical collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Analytical model: secondary infall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Secondary infall model: phase-space . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Turn-around radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165Cosmic web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Jeans instability I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Jeans instability II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
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Jeans instability in expanding Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 169Jeans instability in expanding Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 170Real CMB physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Growth of perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Cosmological parameters and CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175Large scale structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176Free-streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Free-streaming (numbers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178Thermal relics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
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