Using Microhalos to Probe the Universe’s First Second · Giudice, Kolb, Riotto 2001; Gelmini, Gondolo 2006; Gelmini, Gondolo, Soldatenko, Yaguna 2006, ALE 2015 Kayla Redmond & ALE

Adrienne ErickcekUNC Chapel Hill

CIPANPPalm Springs, CAMay 30, 2018

Using Microhalos to Probe the Universe’s First Second

CIPANP: May 30, 2018Adrienne Erickcek

What happened before BBN?

2

The (mostly) successful prediction of the primordial abundances of light elements is one of cosmology’s crowning achievements.

•The elements produced during Big Bang Nucleosynthesis are our first direct window on the Universe.

•They tell us that the Universe was radiation dominated during BBN.

But we have good reasons to think that the Universe was not radiation dominated before BBN.•Primordial density fluctuations point to inflation.

•During inflation, the Universe was scalar dominated.

•Other scalar fields may dominate the Universe after the inflaton decays.

•The string moduli problem: scalars with gravitational couplings come to dominate the Universe before BBN.

Acharya, Kumar, Bobkov, Kane, Shao, Watson 2008Acharya, Kumar, Kane,Watson 2009

Giblin, Kane, Nesbit, Watson, Zhao 2017 Summary: Kane, Sinha, Watson 1502.07746

Carlos, Casas, Quevedo, Roulet 1993Banks, Kaplan, Nelson 1994


What do we know about inflation?

3

Observational probes of inflation are mostly limited to large scales.



3




3

But surprises could be lurking on smaller scales.•inflaton interactions: particle production or coupling to gauge fields

•multi-stage and multi-field inflation with bends in inflaton trajectory

•any theory with a potential that gets flatter: running mass inflation

•hybrid models that use a “waterfall” field to end inflation

Silk & Turner 1987; Adams+1997; Achucarro+ 2012

Stewart 1997; Covi+1999; Covi & Lyth 1999

Chung+ 2000; Barnaby+ 2009,2010; Barnaby+ 2011

Lyth 2011; Gong & Sasaki 2011; Bugaev & Klimai 2011; Guth & Sfakianakis 2012




3












3












3











Cosmic Timeline

4

NowT = 2.3 104 eV

t = 13.8 Gyr

Matter- EqualityT = 3.2 104 eV

t = 9.5 Gyr

MatterDomination

mat a3

CMBT = 0.25 eV

t = 380, 000 yr

Matter-Radiation Equality

t = 57, 000 yrT = 0.74 eV

rad a4

RadiationDomination

0.07 MeV < T < 3 MeV0.08 sec < t < 4 min

Inflation

Big Bang Nucleosynthesis

= consta eHta t1/2 a t2/3


Cosmic Timeline

4

NowT = 2.3 104 eV

t = 13.8 Gyr


t = 9.5 Gyr

MatterDomination

mat a3

CMBT = 0.25 eV

t = 380, 000 yr


t = 57, 000 yrT = 0.74 eV

rad a4

RadiationDomination

0.07 MeV < T < 3 MeV0.08 sec < t < 4 min

Inflation



Talk TimelineIdea I: Probing inflation with ultra-compact microhalos (UCMHs)Idea II: Probing the pre-BBN thermal history with microhalos


UCMH Formation

5

If a region has an initial density , then all the dark matter in that region collapses at early times ( ) and forms an Ultra-Compact Minihalo. Ricotti & Gould 2009

> 1.001

1.002

1.0001 0.9999

0.999

z > 1000


UCMH Formation

5

If a region has an initial density , then all the dark matter in that region collapses at early times ( ) and forms an Ultra-Compact Minihalo. Ricotti & Gould 2009

> 1.001

1.0001 0.9999

0.999

UCMHs

z > 1000


UCMHs Probe Power Spectrum

6

An upper bound on the UCMH number density leads to an upper bound on the primordial power spectrum.

Josan & Green 2010; Bringmann, Scott, Akrami 2012


UCMHs Probe Power Spectrum

6

An upper bound on the UCMH number density leads to an upper bound on the primordial power spectrum.

Josan & Green 2010; Bringmann, Scott, Akrami 2012

/ r9/4

These bounds assume that UCMHs have a radial-infall density profile.


Simulations of UCMHs

7

1. Modify GadgetV2 to include smooth radiation component.

100 101

k (kpc1)

150

200

250

300

350

P(k,z

=99

6)

P(k,z

=8

106)

GADGET-2 with radiation

linear theory prediction

Sten Delos, ALE, Bailey, Alvarez PRD 2018,1712.05421

See also Gosenca+ 2017



7


100 101

k (kpc1)

150

200

250

300

350

P(k,z

=99

6)

P(k,z

=8

106)



2. Generate initial conditions from a power spectrum with a spike.





7


100 101

k (kpc1)

150

200

250

300

350

P(k,z

=99

6)

P(k,z

=8

106)



2. Generate initial conditions from a power spectrum with a spike.

z = 8 106 z = 715 z = 100 z = 100

z=1255 z=1183 z=1116

z=1054 z=996 z=9410.00.30.60.91.21.51.82.12.42.73.0

log

10(/

)

3. Make an UCMH!




UCMH Density Profiles: Spike

8

106 105 104 103 102

r (kpc)

104

105

106

r3/2

(M

kpc

3/2)

| z=1000

| z=400

| z=200

| z=100

| z=50

r3/2 1.3 106 M kpc3/2

1/ksp

ike

z=1000

r vir| z

=50

r vir| z

=100

r vir| z

=200

r vir| z

=400 z=400

z=200z=100z=50

106 105 104 103 102

106107108109101010111012101310141015

(M

kp

c3)

|z=1000

|z=400

|z=200

|z=100

|z=50

/r

9/4

•Nine simulated UCMHs

•All have similar density profiles:

•Stable with redshift, unless there’s a merger....

=s

(r/rs)1.5(1 + r/rs)1.5


UCMH Density Profiles: Plateau

9

We also formed UCMHs using a plateau feature

z = 8 106 z = 100 z = 100z = 494


UCMH Density Profiles: Plateau

9

We also formed UCMHs using a plateau feature

z = 8 106 z = 100 z = 100z = 494

and these UCMHs have NFW proflies!

104 103

r (kpc)

106

r3/2

(M

kpc

1)

NFW fitM99 fit


UCMHs: Summary and Outlook

10

•UCMHs that form from spikes in the primordial power spectrum have Moore profiles ( ), while plateaus in the primordial power spectrum generate UCMHs with NFW profiles ( ).

/ r1.5

/ r1

•The dark matter annihilation rate within the UCMHs is reduced by a factor of 200, which reduces upper bound on UCMH abundance by 3000.

•But we have so many more halos to consider...

STAY TUNED

z = 100Sten Delos, ALE, Bailey, Alvarez coming soon


Cosmic Timeline

11

NowT = 2.3 104 eV

t = 13.8 Gyr


t = 9.5 Gyr

MatterDomination

mat a3

CMBT = 0.25 eV

t = 380, 000 yr


t = 57, 000 yrT = 0.74 eV

rad a4

RadiationDomination

0.07 MeV < T < 3 MeV0.08 sec < t < 4 min

Inflation



Talk TimelineIdea I: Probing inflation with ultra-compact microhalos (UCMHs)Idea II: Probing the pre-BBN thermal history with microhalos


Evolution of the pre-BBN Universe

12

V ()

The Universe was once dominated by a scalar field

•the inflaton

•string moduli

Eventually, the scalar/particle decays into radiation, reheating the Universe.

For , oscillating scalar field matter. V 2 •over many oscillations, average pressure is zero.

•scalar field energy density evolves as

•or we could form oscillons, which are effectively massive particles a3

TRH > 3 MeV Ichikawa, Kawasaki, Takahashi 2005; 2007de Bernardis, Pagano, Melchiorri 2008

Fast-rolling scalar: = P =) / a6

Other massive particles could come to dominate the Universe:•axinos or gravitinos

•hidden sector particles e.g. Dror, Kuflik, Melcher, Watson 2018 Berlin, Hooper, Krnjaic 2016


Cosmic Timeline

13

NowT = 2.3 104 eV

t = 13.8 Gyr


t = 9.5 Gyr

MatterDomination

mat a3

CMBT = 0.25 eV

t = 380, 000 yr


t = 57, 000 yrT = 0.74 eV

rad a4

RadiationDomination

0.07 MeV < T < 3 MeV0.08 sec < t < 4 min

Inflation

BBN

Reheating

T =?


EMDEor

Kination


Probing Dark Matter Production

14

Kination: Universe dominated by a fast rolling scalar field •faster expansion rate at a given temperature implies earlier freeze-out

•larger annihilation cross section needed to match observed DM abundance

•already on the verge of being ruled out by HESS and Fermi observations

Thermal DM production during an early matter-dominated era (EMDE) requires much smaller annihilation cross sections!

What hope do we have of probing these scenarios?Giudice, Kolb, Riotto 2001; Gelmini, Gondolo 2006; Gelmini, Gondolo, Soldatenko, Yaguna 2006, ALE 2015

Kayla Redmond & ALE 201710-3

10-2

10-1

100

101

102

103

101 102 103 104

T RH

(GeV

)

mχ (GeV)

HESS ConstraintsFermi Constraints

Unitary ConstraintBBN Constraint

bb

10-3

10-2

10-1

100

101

102

103

101 102 103 104T R

H (G

eV)

mχ (GeV)

ττ


Structure Growth during an EMDE

15

dm

/0

1

10

100

1000

10000

100 101 102 103 104 105 106 107

scale factor (a)

Evolution of the Matter Density Perturbation

horizon entry

linear growth logarithmicgrowth

EMDE

radiation domination

ALE & Sigurdson 2011; Fan, Ozsoy, Watson 2014; ALE 2015


RMS Density Fluctuation

16

•Enhanced perturbation growth affects subhorizon scales:

•Define to be mass within this comoving radius.

R < k1RH

MRH

MRH ' 105 ML1GeV

TRH

3

101

102

103

104

105

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

σ(M

)

M/M⊕

TRH = 0.1 GeVTRH = 1.0 GeVTRH = 10 GeV

TRH > 100 GeV

Microhalos!


Free-streaming

17

Free-streaming will exponentially suppress power on

scales smaller than the free-streaming horizon: fsh(t) = t

tRH

va

dt

Structures grown during reheating only survive if

(M

)

M/ML

101

102

103

104

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4

No Cut-offkfsh = 40 kRHkfsh = 20 kRHkfsh = 10 kRH

kfsh = 5 kRHTRH>100 GeV

TRH = 1GeV

kfsh/kRH > 10


The Microhalo Abundance

18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

10 100

Boun

d Fr

actio

n w

ith M

<MRH

Redshift (z)

kcut = 40 kRH

kcut = 20 kRH

kcut = 10 kRHTRH = 10 GeV1 GeV

0.1 GeV

kfsh =

40kRH

109

z 400 100 50

0.6 0.9 0.9

0.05 0.3

Std. 0 0.04

kfsh =

10kRH

104

To estimate the abundance of halos, we used the Press-Schechter mass function to calculate the fraction of dark matter contained in halos of mass M.

ALE 2015


Estimating the Boost Factor

19

Dark matter annihilation rate: =hvi2m2

Z2(r)d3r hvi

2m2

J

Boost Factor:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

10 100

Boun

d Fr

actio

n w

ith M

<MRH

Redshift (z)

kcut = 40 kRH

kcut = 20 kRH


0.1 GeV

zf = 400

zf = 50101

102

103

104

105

106

107

106 107 108 109 1010 1011 1012 1013 1014

1+B

Mhalo (M⊙)

kcut/kRH = 10

kcut/kRH = 20

kcut/kRH = 40

1 +B(M) JR2(r) 4r

2dr/ (zf )

0c3hftot(M < MRH, zf )

Boost from MicrohalosALE 2015



19


Z2(r)d3r hvi

2m2

J

Boost Factor:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

10 100

Boun

d Fr

actio

n w

ith M

<MRH

Redshift (z)

kcut = 40 kRH

kcut = 20 kRH


0.1 GeV

zf = 400

zf = 50101

102

103

104

105

106

107

106 107 108 109 1010 1011 1012 1013 1014

1+B

Mhalo (M⊙)

kcut/kRH = 10

kcut/kRH = 20

kcut/kRH = 40

1 +B(M) JR2(r) 4r

2dr/ (zf )



An EMDE could make an “isolated” bino a viable DM candidate with a detectable annihilation signature in

dwarf galaxies.ALE, Sinha, Watson 2016



19


Z2(r)d3r hvi

2m2

J

Boost Factor:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

10 100

Boun

d Fr

actio

n w

ith M

<MRH

Redshift (z)

kcut = 40 kRH

kcut = 20 kRH


0.1 GeV

zf = 400

zf = 50101

102

103

104

105

106

107

106 107 108 109 1010 1011 1012 1013 1014

1+B

Mhalo (M⊙)

kcut/kRH = 10

kcut/kRH = 20

kcut/kRH = 40

1 +B(M) JR2(r) 4r

2dr/ (zf )



An EMDE could make an “isolated” bino a viable DM candidate with a detectable annihilation signature in

dwarf galaxies.ALE, Sinha, Watson 2016

Two source of uncertainty:1. free-streaming cut-off2. do the first-generation

microhalos survive?


The DM temperature

20

momentum transfer rate

expansion rate

/ T 6

•fully coupled:

•fully decoupled:

H ) T / a2

H ) T ' T

adT

da+ 2T = 2

H(T T )

Isaac Waldstein, ALE, Cosmin Ilie

2017

To determine the free-streaming cut-off, we need the DM temperature.

T 2

3

*|~p |2

2m

+


The DM temperature

20


expansion rate

/ T 6

•fully coupled:

•fully decoupled:

H ) T / a2

H ) T ' T

adT

da+ 2T = 2

H(T T )

HT / T 6

T 4T / T 3 / a9/8

T / a9/8

•But during an EMDE

•quasi-decoupled:

10-8

10-6

10-4

10-2

100

102

104

100 102 104 106 108 1010

Tem

pera

ture

(GeV

)

scale factor (a)

TTχ

decoupling

reheating

= H

EMDE

RD


2017


T 2

3

*|~p |2

2m

+


The DM temperature

20


expansion rate

/ T 6

•fully coupled:

•fully decoupled:

H ) T / a2

H ) T ' T

adT

da+ 2T = 2

H(T T )

HT / T 6

T 4T / T 3 / a9/8

T / a9/8

•But during an EMDE

•quasi-decoupled:

10-8

10-6

10-4

10-2

100

102

104

100 102 104 106 108 1010

Tem

pera

ture

(GeV

)

scale factor (a)

TTχ

decoupling

reheating

= H

EMDE

RD


2017


T 2

3

*|~p |2

2m

+

But what are the implications for free-streaming? It depends....


10−10 10−9 10−8 10−7 10−6 10−5

M (M⊙)

1013

1014

1015

1016

1017

1018

dn/d

lnM

(Mpc

−3 ) EMDE

Standard

Mcut MRH

P-S Sharp a = 2.7

P-S Top-hat

(15 pc/h)3

(30 pc/h)3

(60 pc/h)3

(120 pc/h)3

EMDE Microhalo Simulations

21

10−1 100

r/R200

10−1

100

101

102

103

ρ[M

⊙pc

−3 h

2]

EMDE

CDM

Halo Mass (M⊙/h)

3.2× 10−7

1.0× 10−7

3.2× 10−8

1.0× 10−8

3.2× 10−9

10−1 100

r/R200

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

dlogρ/dlogr

Halo Mass (M⊙/h)

3.2× 10−7

1.0× 10−7

3.2× 10−8

1.0× 10−8

3.2× 10−9Std.

Sheridan Green, ALE+ coming soon

EMDE parameters:TRH = 30 MeV

kcut = 20kRH


EMDE Microhalo Simulations

22Sheridan Green, ALE+ coming soon

EMDETRH = 30 MeV

kcut = 20kRH

EMDE

no EMDE

EMDE

no EMDE


Boost Factor from Simulations

23

10−9 10−8 10−7 10−6

M (M⊙)

1014

1015

1016

1017

1018

dn/d

lnM

(Mpc

−3 )

500.00

185.62

113.67

81.76

63.74

52.17

44.10

38.16

33.61

30.00

27.11

24.49

22.13

20.00

106 107 108 109 1010 1011 1012 1013

Mhost (M⊙)

104

105

1+B

Predicted ze = 400, ftot = 0.05

ze = 20, btot = 68.0

ze = 30, btot = 33.9

ze = 38.2, btot = 21.6

ze = 113.7, btot = 1.8

1 +B(M) JR2(r) 4r

2dr/ (zf )


assumes all halos have same profile at zf

include substructure:

ftot

! btot

Sheridan Green, ALE+ coming soon


Perturbations during Kination

24

10-1

100

101

102

103

100 101 102 103 104 105 106

scale factor (a/aI)

k = 2400 kRH δχ/ΦinitialΦ/Φinitial

0

0.5

/ a

100

101

102

103

10-5 10-4 10-3 10-2 10-1 100 101 102 103

δ χ(1

10 a

RH)/Φ

initi

al

(k/kRH)

Transfer FunctionDodelson ModelKination Model

/pk

/ aRH

ahor/

rk

kRH

Kayla Redmond, Anthony Trezza, ALE coming soon


Summary: Mind the Gap after Inflation

•There is a gap in the cosmological record between inflation and the onset of Big Bang nucleosynthesis:

•Dark matter microhalos offer hope of probing the gap.

•Both kination and an early matter-dominated era (EMDE) enhance the growth of sub-horizon density perturbations.

•The microhalos that form after an EMDE significantly boost the dark matter annihilation rate.

•We can use gamma-ray observations to probe the evolution of the early Universe, but first we have to determine the size of the smallest microhalos and if they survive to the present day.

Radiationdomination

Matterdomination

Infla

tion

Dar

k En

ergy

Big Bang Nucleosynthesis (BBN) Today

25

1015 GeV & T & 103 GeV


Bonus Slides

26


Don’t Mess with BBN

27

Reheat Temperature = Temperature at Radiation Domination

C. Light element abundances

We now investigate how the big bang nucleosynthesis isaffected by the nonthermal neutrino distributions and/orthe neutrino oscillations. We calculate the light element (D,4He, and 7Li) abundances as functions of TR, again withand without the neutrino oscillations. The cosmologicaleffects of incomplete neutrino thermalization are moststrikingly seen in 4He abundance since electron-type neu-trinos play a special role in determining the rate of neutron-proton conversion during BBN. This has been alreadyknown from the previous papers, Refs. [21,22], in whichthe oscillations are neglected, but we find that the neutrinooscillations prominently matter in regard to the TR depen-dence of 4He abundance.

We show how Yp varies with respect to TR in Fig. 4. Thisis calculated by plugging the solutions of the evolutionequations derived in Sec. II into the Kawano BBN code[45] (with updated reaction rates compiled by Angulo et al.[46]). Required modifications are the temperature depen-dence of the neutron-proton conversion rates, !n!p and!p!n, and the evolution equation for the photon tempera-ture. The calculation of !n$p (see e.g. Ref. [47]) involvesthe integration of the electron neutrino distribution func-tion f!e

which does not necessarily take the Fermi distri-bution form in our case. For the photon temperatureevolution, the contributions from " and neutrinos aresupplemented in the same way as Eq. (23).

There are two effects caused by incomplete thermaliza-tion of neutrinos competing to make up the dependence ofYp on TR as shown in Fig. 4: slowing down of the expan-sion rate and decreasing in !n$p. The former is just a resultof the decrease in the neutrino energy density (of all

species). The latter is due to the deficit in f!e. They com-

pete in a sense that they work in opposite ways to deter-mine the epoch of neutron-to-proton ratio freeze-out: theformer makes it later and the latter makes it earlier. Then,the competition fixes the n-p ratio at the beginning ofnucleosynthesis and eventually determines Yp. Roughlyspeaking, for larger TR, the former dominates to decreaseYp but, for smaller TR, the latter dominates and increasesYp. This is clearly seen in the case without the oscillationsbut not for the case including the oscillations because theincompleteness in the !e thermalization is made severer bythe mixing [see panels (c) and (d) in Fig. 1] and this effectdominates already at high TR.

Before going forward, it may be worthwhile to lookslightly more into the explanation of the TR dependenceof Yp. First, let us forget about modifying !n$p or tem-perature evolution and just calculate 4He abundance usingthermally distributed neutrinos with N!’s indicated inFig. 3 for each value of TR. This corresponds to includingthe effect of slowing down the expansion rate due to theincomplete thermalization but neglecting the electron neu-trino deficiency. Accordingly, lowering TR only acts todelay the n-p ratio freeze-out and decrease Yp (shown bythe thinner curves in Fig. 4). In an actual low reheatingtemperature scenario, a lack of !e reduces !n$p. Thiscounterbalances the effect of slowing down expansionand boosts Yp in total at lower TR. To see this is reallythe case, we plot !n!p for some values of TR in Fig. 5. We

0.23

0.24

0.25

0.26

1 10

10 100

Γ (s )−1

TR (MeV)

Y p

No oscillation

Including oscillation

FIG. 4 (color online). The 4He abundance (mass fraction) Ypas a function of the reheating temperature TR (shown on thebottom abscissa) or the decay width ! (shown on the topabscissa). The cases with and without the oscillations are drawn,respectively, by the solid and dashed curves. Thinner curves arecalculated with Fermi distributed neutrinos with N! of Fig. 3(namely, only the change in the expansion rate due to theincomplete thermalization is taken into account). The horizontalline represents ‘‘standard’’ Yp calculated by BBN with neutrinosobeying the Fermi distribution and N! ! 3:04. The baryon-to-photon ratio is fixed at # ! 5" 10#10.

0

1

2

3

1 10

10 100

3.04

TR (MeV)

Nν

Γ (s )−1

No oscillation


FIG. 3 (color online). The effective neutrino number N! as afunction of the reheating temperature TR (shown on the bottomabscissa) or the decay width ! (shown on the top abscissa). Thecases with and without the oscillations are drawn, respectively,by the solid and dashed lines. The horizontal line denotes N! !3:04 with which N! for high TR should coincide (see the text).

OSCILLATION EFFECTS ON THERMALIZATION OF . . . PHYSICAL REVIEW D 72, 043522 (2005)

043522-7

Ichikawa, Kawasaki, Takahashi PRD72, 043522 (2005)

C. Light element abundances

We now investigate how the big bang nucleosynthesis isaffected by the nonthermal neutrino distributions and/orthe neutrino oscillations. We calculate the light element (D,4He, and 7Li) abundances as functions of TR, again withand without the neutrino oscillations. The cosmologicaleffects of incomplete neutrino thermalization are moststrikingly seen in 4He abundance since electron-type neu-trinos play a special role in determining the rate of neutron-proton conversion during BBN. This has been alreadyknown from the previous papers, Refs. [21,22], in whichthe oscillations are neglected, but we find that the neutrinooscillations prominently matter in regard to the TR depen-dence of 4He abundance.

We show how Yp varies with respect to TR in Fig. 4. Thisis calculated by plugging the solutions of the evolutionequations derived in Sec. II into the Kawano BBN code[45] (with updated reaction rates compiled by Angulo et al.[46]). Required modifications are the temperature depen-dence of the neutron-proton conversion rates, !n!p and!p!n, and the evolution equation for the photon tempera-ture. The calculation of !n$p (see e.g. Ref. [47]) involvesthe integration of the electron neutrino distribution func-tion f!e

which does not necessarily take the Fermi distri-bution form in our case. For the photon temperatureevolution, the contributions from " and neutrinos aresupplemented in the same way as Eq. (23).

There are two effects caused by incomplete thermaliza-tion of neutrinos competing to make up the dependence ofYp on TR as shown in Fig. 4: slowing down of the expan-sion rate and decreasing in !n$p. The former is just a resultof the decrease in the neutrino energy density (of all

species). The latter is due to the deficit in f!e. They com-

pete in a sense that they work in opposite ways to deter-mine the epoch of neutron-to-proton ratio freeze-out: theformer makes it later and the latter makes it earlier. Then,the competition fixes the n-p ratio at the beginning ofnucleosynthesis and eventually determines Yp. Roughlyspeaking, for larger TR, the former dominates to decreaseYp but, for smaller TR, the latter dominates and increasesYp. This is clearly seen in the case without the oscillationsbut not for the case including the oscillations because theincompleteness in the !e thermalization is made severer bythe mixing [see panels (c) and (d) in Fig. 1] and this effectdominates already at high TR.

Before going forward, it may be worthwhile to lookslightly more into the explanation of the TR dependenceof Yp. First, let us forget about modifying !n$p or tem-perature evolution and just calculate 4He abundance usingthermally distributed neutrinos with N!’s indicated inFig. 3 for each value of TR. This corresponds to includingthe effect of slowing down the expansion rate due to theincomplete thermalization but neglecting the electron neu-trino deficiency. Accordingly, lowering TR only acts todelay the n-p ratio freeze-out and decrease Yp (shown bythe thinner curves in Fig. 4). In an actual low reheatingtemperature scenario, a lack of !e reduces !n$p. Thiscounterbalances the effect of slowing down expansionand boosts Yp in total at lower TR. To see this is reallythe case, we plot !n!p for some values of TR in Fig. 5. We

0.23

0.24

0.25

0.26

1 10

10 100

Γ (s )−1

TR (MeV)Y p

No oscillation


FIG. 4 (color online). The 4He abundance (mass fraction) Ypas a function of the reheating temperature TR (shown on thebottom abscissa) or the decay width ! (shown on the topabscissa). The cases with and without the oscillations are drawn,respectively, by the solid and dashed curves. Thinner curves arecalculated with Fermi distributed neutrinos with N! of Fig. 3(namely, only the change in the expansion rate due to theincomplete thermalization is taken into account). The horizontalline represents ‘‘standard’’ Yp calculated by BBN with neutrinosobeying the Fermi distribution and N! ! 3:04. The baryon-to-photon ratio is fixed at # ! 5" 10#10.

0

1

2

3

1 10

10 100

3.04

TR (MeV)

Nν

Γ (s )−1

No oscillation


FIG. 3 (color online). The effective neutrino number N! as afunction of the reheating temperature TR (shown on the bottomabscissa) or the decay width ! (shown on the top abscissa). Thecases with and without the oscillations are drawn, respectively,by the solid and dashed lines. The horizontal line denotes N! !3:04 with which N! for high TR should coincide (see the text).

OSCILLATION EFFECTS ON THERMALIZATION OF . . . PHYSICAL REVIEW D 72, 043522 (2005)

043522-7

Ichikawa, Kawasaki, Takahashi PRD72, 043522 (2005)

Lowering the reheat temperature results in fewer neutrinos.•slower expansion rate during BBN

•neutrino shortage gives earlier neutron freeze-out; more helium

•earlier matter-radiation equality affects CMB

TRH > 3 MeVIchikawa, Kawasaki, Takahashi 2005; 2007

de Bernardis, Pagano, Melchiorri 2008


DM Production during an EMDE

28

10-4510-4010-3510-3010-2510-2010-1510-1010-5100

100 102 104 106 108 1010

ρ/ρ i

nitia

l

scale factor (a)

ScalarRadiation

MatterMatter Eq.

a3/2

a3

= 0.25

= 0.0002

TRH = 50GeVm = 5TeV

10-5

10-4

10-3

10-2

10-1

100

101

10-37 10-36 10-35 10-34 10-33 10-32 10-31 10-30 10-29 10-28Ωχh

2

Annihilation Cross Section ⟨σv⟩ (cm3/s)

mχ = 200TRH mχ = 300TRH mχ = 400TRH mχ = 500TRH

freeze-in

freeze-out

Giudice, Kolb, Riotto 2001; Gelmini, Gondolo 2006; Gelmini, Gondolo, Soldatenko, Yaguna 2006, ALE 2015

DMSM

Thermal DM production during an early matter-dominated era (EMDE) requires much smaller annihilation cross sections!

What hope do we have of probing these scenarios?

TRH = 300GeV


The Radiation Perturbation

29

During radiation domination, the radiation density

perturbation oscillates.

r r

r k2rhorizon entry

Radiation Domination

-5

0

5

10

15

20

100 101 102 103 104 105

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

-5

0

5

10

15

20

100 101 102 103 104 105

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

horizon entry

scalar domination

+S()+S()

Adding a period of scalar dominationdramatically alters the evolution!

max = 60k/kRH = 11

max = 0.0850 fork

kRH= 11

Grows during scalar

domination



30

-5

0

5

10

15

20

100 101 102 103 104 105

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

horizon entry

scalar dominationk/kRH = 11 -5

0

5

10

15

20

25

100 101 102 103 104 105 106 107

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

scalar domination k/kRH = 114

horizon entry



30

-5

0

5

10

15

20

100 101 102 103 104 105

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

horizon entry

scalar dominationk/kRH = 11 -5

0

5

10

15

20

25

100 101 102 103 104 105 106 107

scale factor (a)

δr / Φ0θr / (H1 Φ0)

Φ / Φ0

scalar domination k/kRH = 114

horizon entry

0 Tr(k)0Impact of Scalar Domination:

Tr 1.5 2 < k/kRH < 4Tr = 10/9 k/kRH < 0.1

What impact does this have on the

dark matter perturbations?

kRH = 35 (TRH/3 MeV) kpc1

k/kRH > 20Tr < 103


The Thermal Matter Perturbation

31

1

10

100

1000

10000

100000

1e+06

100 101 102 103 104 105 106 107 108

δ χ / Φ

0

scale factor (a)

1

10

100

1000

10000

100000

1e+06

100 101 102 103 104 105 106 107 108

δ χ / Φ

0

scale factor (a)

freeze-out

horizonentry

scalar domination


scalar domination


freeze-out

horizonentry

= eq =1

4

3

2+

m

T

Before freeze-out:

TRH = 60GeVm = 18TeV

k/kRH = 74 k/kRH = 370

After freeze-out: linear growth

After reheating: logarithmic growth, same as nonthermal case

|eq||eq|


The Dark Matter Perturbation

32

1

10

100

1000

10000

10-4 10-3 10-2 10-1 100 101 102

dm

(103

a RH)/

0

k/kRH

super-horizon

entered horizon during radiation

domination

entered horizon

during scalar domination

The Matter Density Perturbation during Radiation Domination

standard evolution

Hu & Sugiyama1996

dm aRH

ahor k2

k2RH

= dm =230

k2

k2RH

1 + ln

a

aRH


The Evolution of the Bound Fraction

33

0.0

0.1

0.2

0.3df

/dln

Mz = 400 z = 200

0.0

0.1

0.2

0.3

df/d

lnM

z = 100 z = 50

0.0

0.1

0.2

0.3

10-5 10-4 10-3 10-2 10-1 100 101 102

df/d

lnM

M/MRH

z = 25

10-5 10-4 10-3 10-2 10-1 100 101 102

M/MRH

z = 10

No Cut-o↵

kcut/kRH = 10kcut/kRH = 20kcut/kRH = 40


Independent of Reheat Temperature

34

0

0.1

0.2

0.3

10-5 10-4 10-3 10-2 10-1 100

df/d

lnM

M/MRH

TRH = 10 GeVTRH = 1 GeV

TRH = 0.1 GeVNo Cut-o↵

kcut/kRH = 10kcut/kRH = 20kcut/kRH = 40


The Annihilation Rate

35

ann

Volume

/ hvin2 / hvi

m2

2

•The annihilation rate is highest for small dm masses and low reheat temperatures.

•The boost factor from enhanced substructure is critical for detection.

hvim2

TRH!1

=2.6 1015

GeV4

1TeV

m

2

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

10-12

100 101 102 103 104

⟨σv⟩

/mχ2 [

GeV

-4]

TRH [GeV]

mχ/TRH = 100

150

200

300400

mχ = 1 TeV

mχ = 100 GeV



36


Z2(r)d3r hvi

2m2

J

Halo filled with microhalos:

J = NJmicro

+ 4

Z R

0

(1 f0

)22halo

(r) dr

Number of microhalos:

N =

Z(survival prob.)

Mhalo

M

df

d lnMd lnM

Assume microhalo NFW profile with c = 2 at formation redshift.Anderhalden & Diemand 2013

Ishiyama 2014•early forming microhalos:

•dense cores:

•assume that microhalo centers survive outside of inner kpc: reduces number of microhalos by 1%.

•assume that microhalos are stripped to : reduces by <20%r = rs Jmicro

zf & 50micro

(rs) > 2halo

(r) for r > 1 kpc

Using Microhalos to Probe the Universe’s First Second · Giudice, Kolb, Riotto 2001; Gelmini, Gondolo 2006; Gelmini, Gondolo, Soldatenko, Yaguna 2006, ALE 2015 Kayla Redmond & ALE

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