The Early Universe’s Imprint on Dark Matterkicp-workshops.uchicago.edu/2018-dm/depot/invited-talk-erickcek... · Gelmini, Gondolo 2006 Gelmini, Gondolo, Soldatenko, Yaguna 2006

Adrienne ErickcekUNC Chapel Hill

Towards Dark Matter DiscoveryKICP, University of Chicago

April 13, 2018

The Early Universe’s Imprint on Dark Matter

KICP DM Workshop: April 13, 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

Recent Summary: Kane, Sinha, Watson 1502.07746

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


Cosmic Timeline

3

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

temperature

time

energy

10-3 GeVSet the stage for

Big Bang nucleosynthesis

inflation galaxies, us

cosmic m

icrowave background

generated

1015 GeV(?)Inflation

?

Mustafa Amin’s modified version of PDG10-13 GeV

today

A Different View of the Gap


Evolution of the pre-BBN Universe

5

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.

•density in scalar field evolves as

•scalar field density perturbations grow as Jedamzik, Lemoine, Martin 2010;

Easther, Flauger, Gilmore 2010 a 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/mediators


Cosmic Timeline

6

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

BBN

ReheatingT =?

= consta eHta t1/2 a t2/3

Implications:1. Dark matter production2. Early structure growth

EMDEor

Kination


DM Origin 1: Nonthermal

7

10-35

10-30

10-25

10-20

10-15

10-10

10-5

100

100 101 102 103 104 105 106 107 108

ρ/ρcri

t,0

scale factor (a)

ScalarRadiation

Mattera3

a3

a3/2

a4

Matter

Radiation (1 f) rad

f mat

Branching ratio determinespresent-day dark matter density:

f 0.43(Teq/TRH)

Teq = 0.75 eVWe need a very small branching ratio:

f < 107

“reheating”


DM Origin 2: Thermal

8

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

MatterRadiation

a3

= 0.25

= 0.0002

TRH = 50GeVm = 5TeV

Giudice, Kolb, Riotto 2001

Freeze-out: / 1

hvihvi0.25 = 2 1029cm3/s

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: / hvi

freeze-in

freeze-out


DM Origin 3: Nonthermal with Annihilations

9

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.

Matter

Radiation

Gelmini, Gondolo 2006Gelmini, Gondolo, Soldatenko, Yaguna 2006

a3/2

Branching ratio can be order unity: annihilations then destroy excess DM at reheating.

f = 0.5

This scenario requires a larger annihilation cross section:

Freeze-out: / 1

hvi

hvi0.25 ' m/20

TRH (3 1026cm3/s)


From Miracle to Mess!

10

1e-5

1e-3

0.1

10

1e3

Ωh2

1e-5

1e-3

0.1

10

1e3

Ωh2

1e-5

1e-3

0.1

10

1e3

Ωh2

1e-5

1e-3

0.1

10

1e3

Ωh2

102 103 104

Neutralino Mass (GeV)

1e-5

1e-3

0.1

10

1e3

Ωh2

102 103 104

Neutralino Mass (GeV)102 103 104

Neutralino Mass (GeV)102 103 104

Neutralino Mass (GeV)

TRH=10 GeV TRH=1 GeV TRH=100 MeV TRH=10 MeVη = 0

η = 1e-9η = 1e-6

η = 1e-3η = 1/2

Gelmini, Gondolo, Soldatenko, Yaguna PRD74, 083514 (2006)

m

h2

Lower TRH

f = 0

Increasingf/m

m

10 MeV100 MeV


Probing Dark Matter Production

11

10-3

10-2

10-1

100

101

102

103

101 102 103 104

T RH

(GeV

)

Mχ (GeV)

Mass vs. Reheat Temp. for bb Annihilation Channel

HESS ConstraintsFermi Constraints

TF = TRHBBN Constraint

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

10-3

10-2

10-1

100

101

102

103

101 102 103 104T R

H (G

eV)

Mχ (GeV)

Mass vs. Reheat Temp. for ττ Annihilation Channel

HESS ConstraintsFermi Constraints

TF = TRHBBN Constraint

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

TF < TRH

TF > TRH

Kination: Universe dominated by a fast rolling scalar field / a6

•faster expansion rate implies earlier freeze-out

•larger annihilation cross section needed to match observed abundance

But an early matter-dominated era (EMDE) requires smaller annihilation cross sections!

What hope do we have of probing these scenarios?

Kayla Redmond & ALE 2017

Microhalos from an EMDE

Nonthermal Dark Matter: ALE & Sigurdson, Phys. Rev D 84, 083503 (2011)

Nonthermal Dark Matter with Annihilations:Fan, Ozsoy, Watson, Phys. Rev. D 90, 043536 (2014)

Thermal Dark Matter: ALE Phys. Rev. D 92, 103505 (2015)


The Dark Matter Perturbation

13

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

•nonthermal dark matter immediately begins linear growth after horizon entry

•thermal DM is coupled to radiation prior to freeze-out, then grows linearly

•the amplitude of the perturbations during RD is the same for both thermal and nonthermal dark matter


The Dark Matter Perturbation

14

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


RMS Density Fluctuation

15

•Enhanced perturbation growth affects scales with

•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

16

Free-streaming will exponentially suppress power on scales smaller than the free-streaming horizon: fsh(t) =

t

tRH

va

dt

Modify transfer function: T (k) = exp k2

2k2fsh

T0(k)

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


From Perturbations to Microhalos

17

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.

df

d lnM=

2

d ln

d lnM

c

(M, z)exp

1

22c

2(M, z)

Key ratio: c

(M, z)

differential bound fraction

•Halos with are rare.

•Define by

(M, z) < c

(M, z) = c

M(z)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10 100

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

TRH > 100 GeV

M/

ML

TRH = 1GeV

z


The Evolution of the Bound Fraction

18

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

19

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 Total Bound Fraction

20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 100

Bou

nd F

ract

ion

with

M<M

RH

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


The Annihilation Rate

21

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


Towards the Boost Factor

22

0.000.050.100.150.200.250.300.35

10-4 10-3 10-2 10-1 100 101 102 103 104

z=100z=50z=25

z=10z= 7z= 5z= 3

df

d lnM

M/MLTRH = 8.5 MeV

The Press-Schechter formalism indicates that formation of the microhalos is strongly hierarchical: its microhalos all the way down.

Simulated Earth-mass microhalos

Standard

0.02 pc 0.02 pc

TRH = 30 MeVMRH = 3 106 M

z = 30z = 30


Estimating the Boost Factor

23

Dark matter annihilation rate: =hvi2m2

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


Estimating the Boost Factor II

24

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

Bou

nd F

ract

ion

with

M<M

RH

Redshift (z)

kcut = 40 kRH

kcut = 20 kRH

kcut = 10 kRHTRH = 10 GeV1 GeV

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


Moving Toward Constraints

25

ann

Volume

/ hvin2 / hvi

m2

2

dSphs: B = 20, 000

IGRB: B = 75, 000

101 102 103 104

DM Mass (GeV/c2)

1027

1026

1025

1024

1023

1022

1021

hvi

(cm

3s

1)

bb

4-year Pass 7 Limit

6-year Pass 8 Limit

Median Expected

68% Containment

95% Containment

Thermal Relic Cross Section(Steigman et al. 2012)

Fermi-LAT Collaboration 2015

Stacked dSphs

•Rough comparisonhvim2

obs

vs. (1 +B)hvim2

M=0.25

•dSphs: total boost for halo.

•IGRB: EMDE boost relative to standard boost.

IGRB

dSphs

10-17

10-16

10-15

10-14

10-13

10-12

10-11

100 101 102

(1+B

)⟨σ

v⟩/m

χ2 [G

eV-4

]

TRH [GeV]

mχ = 100 TRHmχ = 150 TRH

dSphsIGRB

IGRB (S)

106M

kcut = 20kRH

kcut = 40kRH

zf = 400


Moving Toward Constraints

25

ann

Volume

/ hvin2 / hvi

m2

2

dSphs: B = 20, 000

IGRB: B = 75, 000

101 102 103 104

DM Mass (GeV/c2)

1027

1026

1025

1024

1023

1022

1021

hvi

(cm

3s

1)

bb

4-year Pass 7 Limit

6-year Pass 8 Limit

Median Expected

68% Containment

95% Containment

Thermal Relic Cross Section(Steigman et al. 2012)

Fermi-LAT Collaboration 2015

Stacked dSphs

•Rough comparisonhvim2

obs

vs. (1 +B)hvim2

M=0.25

•dSphs: total boost for halo.

•IGRB: EMDE boost relative to standard boost.

IGRB

dSphs

10-17

10-16

10-15

10-14

10-13

10-12

10-11

100 101 102

(1+B

)⟨σ

v⟩/m

χ2 [G

eV-4

]

TRH [GeV]

mχ = 100 TRHmχ = 150 TRH

dSphsIGRB

IGRB (S)

106M

kcut = 20kRH

kcut = 40kRH

zf = 400

This mechanism can make “isolated” bino DM detectable.

ALE, Sinha, Watson 2016

Two source of uncertainty:1. small-scale cut-off

2. do the first-generationmicrohalos survive?


Kinetic Decoupling during an EMDE

26

First potential source of a small-scale cut-off: interactions between dark matter and relativistic particles

10-1

100

101

102

103

104

105

106

100 102 104 106 108 1010 1012

|δ| /

Φ0

scale factor (a)

Horizon Entry

γ = H

Reheating

|δφ| ∝ a

mχ = 4000 GeV

TRH = 5 GeV

k = 158.1 kRH = 9.96 kdec

|δχ||δr||δφ|

|δχγ = 0|

100

102

104

106

108

1010

100 102 104 106 108 1010 1012|δ

| / Φ

0scale factor (a)

Horizon Entryγ = H Reheating

|δφ| ∝ a

mχ = 4000 GeVTRH = 5 GeVk = 15811 kRH = 996 kdec

|δχ||δr||δφ|

|δχγ = 0|

Interactions do not significantly suppress the perturbations,even if the dark matter remains coupled to the relativistic particles well into the EMDE...

Isaac Waldstein, ALE, Cosmin Ilie, coming soon


Kinetic Decoupling during an EMDE

26

First potential source of a small-scale cut-off: interactions between dark matter and relativistic particles

10-1

100

101

102

103

104

105

106

100 102 104 106 108 1010 1012

|δ| /

Φ0

scale factor (a)

Horizon Entry

γ = H

Reheating

|δφ| ∝ a

mχ = 4000 GeV

TRH = 5 GeV

k = 158.1 kRH = 9.96 kdec

|δχ||δr||δφ|

|δχγ = 0|

100

102

104

106

108

1010

100 102 104 106 108 1010 1012|δ

| / Φ

0scale factor (a)

Horizon Entryγ = H Reheating

|δφ| ∝ a


|δχ||δr||δφ|

|δχγ = 0|

Interactions do not significantly suppress the perturbations,even if the dark matter remains coupled to the relativistic particles well into the EMDE...

Isaac Waldstein, ALE, Cosmin Ilie, coming soon

100

102

104

106

108

1010

100 102 104 106 108 1010 1012

|δ| /

Φ0

scale factor (a)

Horizon Entry

γ = H

Reheating|δφ| ∝ a


|δχ||δr||δφ|

|δχγ = 0|

see also Choi, Gong, Shin 2015 and even through reheating!


The DM temperature

27

momentum transfer rate

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

Isaac Waldstein, ALE, Cosmin Ilie

2017

What about free-streaming? We need the DM temperature.

T 2

3

*|~p |2

2m

+


The DM temperature

27

momentum transfer rate

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

Isaac Waldstein, ALE, Cosmin Ilie

2017

What about free-streaming? We need the DM temperature.

T 2

3

*|~p |2

2m

+

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


Microhalo Simulations

28

Sheridan Green, ALE+ coming soon

No EMDE EMDETRH = 30 MeVkcut = 20kRH

z = 500 ! 30

EMDE

RD

EMDE

RD


Simulation Results

29

Lots of microhalos with steep profiles and copious substructure.

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 )

Press-Schechter

Sheth-Tormen

(15 pc/h)3

(30 pc/h)3

(60 pc/h)3

(120 pc/h)3

EMDE

RD

10−3 10−2 10−1

M/Mh

101

102

103

104

dn/dm

[Npc

−3 h

4M

−1

⊙]

Substructure Mass Function for 10−6 M⊙/h Hosts

Redshiftdndm ∝ m−1

z = 30

z = 20

fsub > 0.5

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× 10−9RD


Boost Factor from Simulations

30

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 )

0c3hftot(M < MRH, zf )

assumes all halos have same profile at zf

include substructure:

ftot

! btot

Sheridan Green, ALE+ coming soon


Perturbations during Kination

31

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

)/Φin

itial

(k/kRH)

Transfer FunctionDodelson ModelKination Model

/pk

/ aRH

ahor/

rk

kRH

Kayla Redmond, 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 formation time 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

32

1015 GeV & T & 103 GeV

Documents

The Early Universe’s Imprint on Dark Matterkicp-workshops.uchicago.edu/2018-dm/depot/invited-talk-erickcek... · Gelmini, Gondolo 2006 Gelmini, Gondolo, Soldatenko, Yaguna 2006