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Dark Matter and Dark EnergyDark Matter and Dark Energy
Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidatesRocky III: Dark energy ideas
SLAC Summer Institute, August 2003Rocky Kolb, Fermilab & The University of Chicago
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Epicycle II – Dark matterEpicycle II Epicycle II –– Dark matterDark matterWhat is dark matter?
“In questions like this, truth is only to be had by laying together many variations of error.”
-- Virginia WolfA Room of Ones Own
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Particle Dark Matter CandidatesParticle Dark Matter CandidatesParticle Dark Matter Candidates• neutrinos (hot dark matter)
• sterile neutrinos, gravitinos (warm dark matter)
• LSP (neutralino, sneutrino, …) (cold dark matter)
• LKP (lightest Kaluza-Klein particle)
• axions, axion clusters
• solitons (B-balls; Q-balls; Odd-balls,….)
•••
• supermassive relics
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Supermassive relics(Nonthermal dark matter)
SupermassiveSupermassive relicsrelics((NonthermalNonthermal dark matter)dark matter)
Production Mechanisms:
• Bubble collisions Chung, Kolb, Riotto
• Preheating Chung
• Reheating Chung, Kolb, Riotto
• Gravitational Chung, Kolb, Riotto; Kuzmin & Tkachev
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new application: dark matter(Chung, Kolb, & Riotto; Kuzmin & Tkachev)
• require (super)massive particle “X”• stable (or at least long lived)• initial inflationary era followed by radiation/matter
Arnowit, Birrell, Bunch, Davies, Deser, Ford, Fulling, Grib, Hu, Kofman, Lukash, Mostepanenko, Page, Parker, Starobinski, Unruh, Vilenkin, Wald, Zel’dovich,…
first application:
(Guth & Pi; Starobinski; Bardeen, Steinhardt, & Turner; Hawking; Rubakov; Fabbi & Pollack; Allen)
Expanding universe particle creationExpanding universe particle creationExpanding universe particle creation
density perturbations from inflationgravitational waves from inflation
It’s not a bug, it’s a feature!
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Fourier modes [a(τ) = expansion scale factor]
Mode equation (τ = conforml time)
Particle creation in nonadiabatic region
2measure of nonadiabaticity or k
k
HH
ωω
′∝
3† *
3/ 2( , ) ( ) ( )(2 ) ( )
ik x ik xk k k k
d xX x a h e a h ea
τ τ τπ τ
⋅ − ⋅ = + ∫
( ) ( ) ( )( ) ( ) ( )
2 2 2
2
6 1 0
0k X k
k k k
h k M a a a h
h h
τ ξ τ
τ ω τ τ
′′ ′′ + + + − = ′′ + =
0
Scalar field X of mass MXScalar field X of mass MScalar field X of mass MXX
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Background fields in chaotic inflationBackground fields in chaotic inflationBackground fields in chaotic inflation
nonadiabatic region: particle creation
preheating, reheating, …?HHMφ
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Chung, Kolb& Riotto; Kuzmin & Tkachev
GeV10 to101for1 1510INFLATON ≈⇒≈≈Ω XXX MMM
INFLATONMMX
chaoticinflation
Particle productionParticle productionParticle production
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• Inflaton mass (in principle measurable from gravitational wave background, guess ) may signal a new mass scale in nature.
• Other particles may exist with mass comparable to the inflaton mass.
• Conserved quantum numbers may render the particle stable.
GeV1012
Superheavy particlesSuperheavySuperheavy particlesparticles
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Model explorationModel explorationModel explorationGravitational Production:• Fermions Kuzmin & Tkachev• Non-conformal couplings Kuzmin & Tkachev• Small-field models Crotty, Chung, Kolb, Riotto• Hybrid models Crotty, Chung, Kolb, Riotto
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Model explorationModel explorationModel exploration
natural hybrid
( )IXXIX
RHXXIX
HMhHM
TMhHM
−∝Ω→≥
≈Ω→≤
exp GeV10GeV10
2
9
2
112
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• supermassive: 109 - 1015 GeV (~ 1012 GeV ?)
• abundance may depend only on mass
• abundance may be independent of interactions
sterile?
electrically charged?
strong interactions?
weak interactions?
• unstable (lifetime > age of the universe)?
Wimpzilla characteristics:WimpzillaWimpzilla characteristics:characteristics:
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Gravitino productionGravitinoGravitino productionproductionGiudice, Riotto, TkachevLinde, Kallosh, Kofman, Van ProeyenNilles, Peloso, SorboNilles, Olive, Peloso……
(perhaps it is a bug after all…)
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WIMPZILLA footprints:WIMPZILLA footprints:WIMPZILLA footprints:
Isocurvature modes: CMB, Large-scale structureDecay: Ultra High Energy Cosmic RaysAnnihilate: Galactic Center, SunDirect Detection: Bulk, Underground Searches
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WIMPZILLA decayWIMPZILLA decayWIMPZILLA decayX UHE cosmic rays
1013 GeV = 1022 eVKuzmin & Rubakov; Birkel & Sarkar; Ellis, Gelmini, Lopez, Nanopoulos & Sarkar; Berezinsky, Kachelriess, & Vilenkin;Benakli, Ellis, & Nanopoulos; Berezinsky, Blasi, & Vilenkin; Blasi; Berezinsky & Mikhaliov;Dubovsky & Tinyakov; Medina-Tanco & Watson;Blasi & Seth; Ziaeepour; Crooks, Dunn, & Frampton
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Blasi ‘99Blasi ‘99
QCDQCDSUSY QCDSUSY QCD
1013 GeV
1014 GeV
UHE cosmic rays mostly photons; characteristic spectrum; UHE neutrinos; lower-energy crud;
clumping anisotropies
τ ~ 1020 years
WIMPZILLA decayWIMPZILLA decayWIMPZILLA decay
GZK cutoff
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Clustering of UHE eventsClustering of UHE eventsClustering of UHE events
probability fromisotropic distribution:<1%
model follows Navarro,Frenk, White dark matterdistribution
Blasi & Sheth astro-ph/0006316
UHE cosmic rays
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Epicycle III – Dark EnergyEpicycle III Epicycle III –– Dark EnergyDark Energy
“In questions like this, truth is only to be had by laying together many variations of error.”
-- Virginia WolfA Room of Ones Own
What is the nature of dark energy
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Mass density of space:
Cosmo-illogical constant?CosmoCosmo--illogical constant?illogical constant?
( ) ( )4 430 -3 4 310 g cm 10 eV 10 cmρ−− − −
Λ =
Cosmological constantCosmological constantCosmological constant
The unbearable lightness of nothing!( ) ( )2 229 338 10 cm 10 eVGπ ρ
− −ΛΛ = = =
Numerology:( )4 8 4
SUSY
3 45
exp 2
10 eV 10 cmV W V PlM M M
m Rν
ρ α ρ− −
= − =
= =
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Cosmic coincidenceCosmic coincidenceCosmic coincidence
BBNEWKGUT
ΛΩ
M RΩ + Ω
RECDM B B VISIBLE B DARK υρ ρ ρ ρ ρ ρΛ − −∼ ∼ ∼ ∼ ∼
Cosmic Coincidence?
Every party represented!
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Anything interesting at z~1?Anything interesting at z~1?Anything interesting at z~1?W
ebb et al.
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1. No unbroken symmetry demands Λ=02. Nothing sets the scale3. Scale seems unrelated to any other energy scale
. . . seems to require
. . . fifth-force experiments?
4. Deal with it!
Non l’avrei giammai creduto;Ma faro quel che potro.
Mozart/Da Ponte, Don Giovanni, Act II
` `
Λ: the uninvited guestΛΛ: the uninvited guest: the uninvited guest
33~ 10 eVm −
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Fourier modes of all fields are harmonic oscillators with a zero-point energy
Quantum uncertaintyQuantum uncertaintyQuantum uncertainty
classical
0E =quantum
12E ω=
3 2 2
all particlesd k k mρ = ± +∑ ∫
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3 2 2 3 4C
all particles all particles
d k k m d k kρΛ
= ± + ±∑ ∑∫ ∫
Quantum uncertaintyQuantum uncertaintyQuantum uncertainty
( )( )
4
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44 12
3
: bad prediction
: 10 eV
: 10 eV
10 eV: Observed
C
C Pl Pl
C SUSY SUSY
C
M M
M M
ρ
ρ
ρ
ρ
Λ
Λ
Λ
−Λ
Λ = ∞ = ∞ =
Λ = = =
Λ = = =
Λ = =
Photons couple to virtual particlesLamb shift
Gravitons couple to virtual particlesCosmological constant
e+
e-
γ
e+
e-
g
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Spontaneous symmetry breakingSpontaneous symmetry breakingSpontaneous symmetry breaking
φ15 4 3 4
2 4 -1 4
-12 4
GUT: (10 GeV) SUSY: (10 GeV)EWK: (10 GeV) CHIRAL: (10 GeV)
OBSERVED: (10 GeV)
high-temperature
low-temperature
V(φ)
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Balancing other contributionsBalancing other contributionsBalancing other contributions• Many possible contributions. • Why then is total so small?• Perhaps unknown dynamics sets globalvacuum energy equal to zero……but we’re not there yet!
V(φ)
φ0
Λ
V(φ)
φ0
Λ
Frieman, Freese, Hill, Olinto, …..
Universe hung up Universe rolling along
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Balancing other contributionsBalancing other contributionsBalancing other contributions• But why now?• Tracker potentials, relate dark
energy to other contributions.*
• Why now?….. “close to matter domination”• Why now?….. “it’s just that time”
Wetterich; Ratra & Peebles; …
, ,ne φ φ− − …
Field equation for tracker:
( )2
3 08
3 M
H dV dGH φ
φ φ φπ ρ ρ
+ + =
= + +…
Can have ρφ track (stalk) ρM - effective mass of the fielddecreases as H: close but no cigar
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Punctuated vacuum dominationPunctuated vacuum dominationPunctuated vacuum domination
Dodelson, Kaplinghat, Stewart
dark energydestiny≠
ΛΩ
φ
( )( ) 1 sinV e φφ α φ−= +
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For now…parameterizeFor now…parameterizeFor now…parameterize
1 for constant 1 1 3 for dynamicaldark energy
V Vw pw
w
ρ== − Λ
− < ≤ −
SNIa combinedclusters
Perlmutter, Turner, White
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For now…parameterizeFor now…parameterizeFor now…parameterizeH
igh-z supernova team
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w < −1 ?ww < < −−1 1 ??• null dominant energy condition: energy doesn’t propagate
outside the light cone
• model with w < −1: negative kinetic energy scalar field
• instability cured with higher derivative terms?
p pρ ρ ρ≤ ⇒ − ≤ ≤
( )2 2expL φ φ= − − −
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Aether of the 21st century?AetherAether of the 21of the 21stst century?century?
• It’s an infrared issue!
• Scalars (quintessence, trackers, ….)?
• Tensors (gravity at large distances)?
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Braneless cosmologyBranelessBraneless cosmologycosmology• Old Friedmann law
200 00
2 23Pl
Pl
G M T
H M ρ
−
−
=
=
Friedmann (1921)
SNIa evidence for dark energy:
( )dzH z∫
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Brane cosmologyBrane cosmologyBrane cosmology• Israel junction condition (Israel 1966)
An
: unit vector normal to the brane: the induced metric
: the extrinsic curvature
A
AB AB A BC
AB A C B
nh g n n
h nκ
= −
= ∇
iii
3*
BRANEM Tµν µνκ − = −
[ ].... discontinuity across the brane=
[ ] ( )discontinuity in second derivative of scale factor
a a a yδ′′ ′′ ′= +
the
brane
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Brane cosmologyBrane cosmologyBrane cosmology• New Friedmann law Binetruy, Deffayet, Langlois (2000)
62 2*
46 36 ( , 0)M cH
a t yρ
−Λ= + +
=
• Possible solution Randall & Sundrum (2000)
Introduce a tension σ on the brane ρ ρ σ→ +6 6 6
2 2 2* * *46 36 18 36 ( , 0)
M M M cHa t y
σ σρ ρ− − − Λ
= + + + + =
unconventialcorrections
cosmological constant
(cancels?)Friedmannequation
6* 8
18 3M Gπσ
−
=
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Brane cosmologyBrane cosmologyBrane cosmology• Friedmann equation modified today
• Gravitational force law modified at large distance
• Tired gravitons
• Gravity repulsive at cosmological distance
• n=1 KK graviton mode very light
• 3+1 Lorentz invariance broken
Freese & Lewis( ) 12cutoff1 nH Aρ ρ ρ − = +
Five-dimensional at cosmic distances Deffayet, Dvali & Gabadadze
Gravitons metastable - leak into bulk Gregory, Rubakov & SibiryakovDvali, Gabadadze & Porrati
Kogan, Mouslopoulos, Papazoglou, Ross & Santiago( ) 1Gpcm −∼
Chung, Kolb & Riotto
Csaki, Erlich, Hollowood & Terning
In the IR!
GpcR ∼
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16 MS d x g R d x g LG R
µπ
= − − + −
∫ ∫
Carroll, Duvvuri, Turner, Trodden – dark energy
Modify gravityModify gravityModify gravity
( )4 2 4116 MS d x g R R d x g L
Gα
π= − + + + −∫ ∫…
Starobinski - inflation
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How do we sort it out?How do we sort it out?How do we sort it out?
• Something is established-ΛCDM too good to ignoreSNIaSubtractionAgeLarge-scale structure…..
• Is it “just” a cosmological constant? Is ?• If what is the dynamics? 1w ≠ −
1w = −
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How do we sort it out?How do we sort it out?How do we sort it out?
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Cosmology in the “precision” eraCosmology in the “precision” eraCosmology in the “precision” era• ΛCDM is a most predictive cosmological model
• Fundamental parts are a mystery
• nature of dark matter• nature of dark energy• dynamics of inflation
• The best is yet to come!
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ν
ν
ν
Heavy Elements: Ω=0.0003
Cold Dark Matter: Ω=0.25
Dark Energy (Λ): Ω=0.70
Stars:Ω=0.005
Free H & He:Ω=0.04
CRITICAL
TOTAL 1i iρ ρΩ ≡
Ω =
Cosmic PieCosmic PieCosmic Pie
ΛCDMΛΛCDMCDM
Neutrinos (ν): Ω=0.0047