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
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
3
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
3
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
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
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
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
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
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
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
What do we know about inflation?
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
Observational probes of inflation are mostly limited to large scales.
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
Talk TimelineIdea I: Probing inflation with ultra-compact microhalos (UCMHs)Idea II: Probing the pre-BBN thermal history with microhalos
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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.
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
2. Generate initial conditions from a power spectrum with a spike.
Sten Delos, ALE, Bailey, Alvarez PRD 2018,1712.05421
See also Gosenca+ 2017
CIPANP: May 30, 2018Adrienne Erickcek
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
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!
Sten Delos, ALE, Bailey, Alvarez PRD 2018,1712.05421
See also Gosenca+ 2017
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
UCMH Density Profiles: Plateau
9
We also formed UCMHs using a plateau feature
z = 8 106 z = 100 z = 100z = 494
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
Cosmic Timeline
11
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
Talk TimelineIdea I: Probing inflation with ultra-compact microhalos (UCMHs)Idea II: Probing the pre-BBN thermal history with microhalos
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
Cosmic Timeline
13
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
Reheating
T =?
= consta eHta t1/2 a t2/3
EMDEor
Kination
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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!
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
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
CIPANP: May 30, 2018Adrienne Erickcek
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
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
An EMDE could make an “isolated” bino a viable DM candidate with a detectable annihilation signature in
dwarf galaxies.ALE, Sinha, Watson 2016
CIPANP: May 30, 2018Adrienne Erickcek
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
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
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?
CIPANP: May 30, 2018Adrienne Erickcek
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
+
CIPANP: May 30, 2018Adrienne Erickcek
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 )
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
To determine the free-streaming cut-off, we need the DM temperature.
T 2
3
*|~p |2
2m
+
CIPANP: May 30, 2018Adrienne Erickcek
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 )
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
To determine the free-streaming cut-off, we need the DM temperature.
T 2
3
*|~p |2
2m
+
But what are the implications for free-streaming? It depends....
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
EMDE Microhalo Simulations
22Sheridan Green, ALE+ coming soon
EMDETRH = 30 MeV
kcut = 20kRH
EMDE
no EMDE
EMDE
no EMDE
CIPANP: May 30, 2018Adrienne Erickcek
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 )
0c3hftot(M < MRH, zf )
assumes all halos have same profile at zf
include substructure:
ftot
! btot
Sheridan Green, ALE+ coming soon
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
Including 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
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
Including 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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
The Radiation Perturbation
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
CIPANP: May 30, 2018Adrienne Erickcek
The Radiation Perturbation
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
CIPANP: May 30, 2018Adrienne Erickcek
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
radiation domination
scalar domination
radiation 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|
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
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
CIPANP: May 30, 2018Adrienne Erickcek
Estimating the Boost Factor
36
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