The Early Universe s Imprint on Dark Matter

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1 The Early Universe s Imprint on Dark Matter UNC Chapel Hill Towards Dark Matter Discovery KICP, University of Chicago April 13, 2018

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

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

2 What Happened Before BBN? 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. Carlos, Casas, Quevedo, Roulet 1993 Banks, Kaplan, Nelson 1994 Acharya, Kumar, Bobkov, Kane, Shao, Watson 2008 Acharya, Kumar, Kane,Watson 2009 Recent Summary: Kane, Sinha, Watson

3 Cosmic Timeline Big Bang Nucleosynthesis 0.07 MeV < T < 3MeV 0.08 sec < t < 4 min CMB T =0.25 ev t = 380, 000 yr Now T =2.3 4 ev t = 13.8 Gyr Inflation Radiation Domination Matter-Radiation Equality T =0.74 ev t = 57, 000 yr Matter Domination a t 1/2 a t 2/3 rad a 4 mat a 3 a e Ht = const Matter- Equality T =3.2 4 ev t =9.5Gyr 3

4 A Different View of the Gap time temperature energy inflation? cosmic microwave background generated galaxies, us 15 GeV(?) Inflation Mustafa Amin s modified version of PDG -3 GeV Set the stage for Big Bang nucleosynthesis -13 GeV today

5 Evolution of the pre-bbn Universe The Universe was once dominated by a scalar field the inflaton string moduli Fast-rolling scalar: = P =) / a 6 For V 2, oscillating scalar field matter. over many oscillations, average pressure is zero. density in scalar field evolves as a 3 V ( ) scalar field density perturbations grow as Jedamzik, Lemoine, Martin 20; a Easther, Flauger, Gilmore 20 Other massive particles could come to dominate the Universe: axinos or gravitinos hidden sector particles/mediators Eventually, the scalar/particle decays into radiation, reheating the Universe. T RH > 3 MeV Ichikawa, Kawasaki, Takahashi 2005; 2007 de Bernardis, Pagano, Melchiorri

6 Cosmic Timeline BBN 0.07 MeV < T < 3MeV 0.08 sec < t < 4 min CMB T =0.25 ev t = 380, 000 yr Now T =2.3 4 ev t = 13.8 Gyr Inflation EMDE or Kination Radiation Matter Domination Domination a t 1/2 a t 2/3 rad a 4 mat a 3 a e Ht = const Implications: Reheating T =? 1. Dark matter production 2. Early structure growth Matter- Radiation Equality T =0.74 ev t = 57, 000 yr Matter- Equality T =3.2 4 ev t =9.5Gyr 6

7 DM Origin 1: Nonthermal Radiation (1 f) rad Matter f mat a 3 Scalar Radiation Matter reheating Branching ratio determines present-day dark matter density: ρ/ρ crit, a 3/2 a 4 f 0.43(T eq /T RH ) a scale factor (a) T eq =0.75 ev We need a very small branching ratio: f< 7 7

8 DM Origin 2: Thermal Radiation Giudice, Kolb, Riotto 2001 Matter ρ/ρ initial a 3/2 a 3 T RH = 50 GeV m =5TeV scale factor (a) Scalar Radiation Matter Matter Eq. =0.25 = h vi 0.25 =2 29 cm 3 /s Ω χ h Annihilation Cross Section σv (cm 3 /s) Freeze-out: / 1 Freeze-in: m χ = 200T RH m χ = 300T RH m χ = 400T RH m χ = 500T RH freezein freezeout h vi /h vi 8

9 DM Origin 3: Nonthermal with Annihilations Radiation Gelmini, Gondolo 2006 Gelmini, Gondolo, Soldatenko, Yaguna 2006 Matter ρ/ρ initial f =0.5 Scalar Radiation Matter Matter Eq. a 3/ scale factor (a) Branching ratio can be order unity: annihilations then destroy excess DM at reheating. Freeze-out: / 1 This scenario requires a larger annihilation cross section: h vi 0.25 ' m /20 T RH h vi (3 26 cm 3 /s) 9

10 From Miracle to Mess! Lower TRH TRH= GeV 1e3 MeV 0 MeV TRH= MeV TRH=0 MeV TRH=1 GeV Ωh η=0 2 f = e-3 1e-5 1e3 Ωh 0.1 1e-3 1e-5 1e3 Ωh 2 η = 1e-6 mh 2 Increasing f /m 2 η = 1e e-3 1e-5 1e3 Ωh 2 η = 1e e-3 1e-5 1e3 Ωh 2 η = 1/ e-3 1e-5 m Neutralino Mass (GeV) Neutralino Mass (GeV) Gelmini, Gondolo, Yaguna PRD74, Neutralino Mass (GeV)Soldatenko, Neutralino Mass (GeV) (2006)

11 Probing Dark Matter Production Kination: Universe dominated by a fast rolling scalar field / a 6 faster expansion rate implies earlier freeze-out larger annihilation cross section needed to match observed abundance Mass vs. Reheat Temp. for bb Annihilation Channel Mass vs. Reheat Temp. for ττ Annihilation Channel 3 2 HESS Constraints Fermi Constraints T F = T RH BBN Constraint T F < T RH T F > T RH 3 2 HESS Constraints Fermi Constraints T F = T RH BBN Constraint T F < T RH T F > T RH T RH (GeV) T RH (GeV) M χ (GeV) -3 Kayla Redmond & ALE M χ (GeV) But an early matter-dominated era (EMDE) requires smaller annihilation cross sections! What hope do we have of probing these scenarios? 11

12 Microhalos from an EMDE Nonthermal Dark Matter: ALE & Sigurdson, Phys. Rev D 84, (2011) Nonthermal Dark Matter with Annihilations: Fan, Ozsoy, Watson, Phys. Rev. D 90, (2014) Thermal Dark Matter: ALE Phys. Rev. D 92, 3505 (2015)

13 The Dark Matter Perturbation Evolution of the Matter Density Perturbation 000 EMDE dm/ horizon entry linear growth logarithmic growth radiation domination scale factor (a) 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 13

14 The Dark Matter Perturbation The Matter Density Perturbation during Radiation Domination dm dm( 3 arh)/ superhorizon entered horizon during radiation domination standard evolution Hu & Sugiyama k/k RH entered horizon during scalar domination a RH k 2 = a hor krh 2 dm = 2 k krh ln a a RH 14

15 RMS Density Fluctuation 5 T RH = 0.1 GeV σ(m) 4 3 T RH = 1.0 GeV T RH = GeV T RH > 0 GeV Enhanced perturbation growth affects scales with R < k 1 RH Define M RH to be mass within this comoving radius. M/M M RH ' 5 M L 1 GeV T RH 3 Microhalos! 15

16 (M) Free-streaming Free-streaming will exponentially suppress power on scales smaller than the free-streaming horizon: fsh(t) = Modify transfer function: T (k) =exp 4 k 2 2k 2 fsh T 0 (k) T RH =1GeV t t RH No Cut-off k fsh = 40 k RH v a dt 3 k fsh = 20 k RH k fsh = k RH k fsh = 5 k RH T RH >0 GeV 2 Structures grown during reheating only survive if M/M L k fsh /k RH > 16

17 From Perturbations to Microhalos 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 ln M = 2 d ln d ln M differential bound fraction Key ratio: Halos with are rare. Define M (z) c (M,z) (M,z) < c by (M,z)= c M /M L c (M,z) exp 1 2 T RH =1GeV 0 2 c 2 (M,z) No Cut-off k fsh = 40 k RH k fsh = 20 k RH k fsh = k RH T RH > 0 GeV z 17

18 The Evolution of the Bound Fraction 0.3 z = 400 z = 200 df/dlnm df/dlnm z = 0 z = 50 No Cut-o k cut /k RH = 40 k cut /k RH = 20 k cut /k RH = 0.3 z = 25 z = df/dlnm M/M RH M/M RH 18

19 Independent of Reheat Temperature 0.3 T RH = GeV T RH = 1 GeV df/dlnm 0.2 T RH = 0.1 GeV No Cut-o k cut /k RH = 40 k cut /k RH = k cut /k RH = M/M RH 19

20 The Total Bound Fraction Bound Fraction with M<M RH T RH = GeV 1 GeV 0.1 GeV 0 Redshift (z) k cut = k RH k cut = 40 k RH k cut = 20 k RH z k fsh = 40k RH k fsh = k RH Std

21 The Annihilation Rate ann Volume /h vin2 / h vi m 2 2 σv /m χ 2 [GeV -4 ] h vi m 2 T RH!1 m χ = 0 GeV m χ /T RH = 0 m χ = 1 TeV T RH [GeV] TeV = GeV 4 m 2 The annihilation rate is highest for small dm masses and low reheat temperatures. The boost factor from enhanced substructure is critical for detection. 21

Towards the Boost Factor df d ln M 0.35 0.30 0.25 0.20 0.15 0. 0.05 0.00 T RH =8.

formalism indicates that formation of the microhalos is strongly hierarchical: its microhalos

22 Towards the Boost Factor df d ln M T RH =8.5 MeV z=0 z=50 z=25 z= z= 7 z= 5 z= M/M L z = 30 The Press-Schechter formalism indicates that formation of the microhalos is strongly hierarchical: its microhalos all the way down. Simulated Earth-mass microhalos z = pc 0.02 pc Standard T RH = 30 MeV M RH =3 6 M 22

23 Estimating the Boost Factor Dark matter annihilation rate: Halo filled with microhalos: J = NJ micro +4 Z R Number Z of microhalos: N = (survival prob.) M halo M 0 = h vi 2m 2 Z (1 f 0 ) 2 2 halo(r) dr df d ln M d ln M 2 (r)d 3 r h vi 2m 2 J Assume microhalo NFW profile with c = 2 at formation redshift. Anderhalden & Diemand 2013 early forming microhalos: dense cores: z f & 50 micro (r s ) > 2 halo (r) for r>1kpc assume that microhalo centers survive outside of inner kpc: reduces number of microhalos by 1%. Ishiyama 2014 assume that microhalos are stripped to r = r s : reduces J micro by <20% 23

24 Bound Fraction with M<M RH Estimating the Boost Factor II Dark matter annihilation rate: Boost Factor: ALE B(M) T RH = GeV 1 GeV 0.1 GeV 0 = h vi 2m 2 J R 2 (r)4 r 2 dr / (z f ) Redshift (z) k cut = k RH k cut = 40 k RH k cut = 20 k RH 1+B c 3 h Z z f = 400 z f = 50 2 (r)d 3 r h vi 2m 2 J f tot (M<M RH,z f ) k cut /k RH = 40 k cut /k RH = 20 k cut /k RH = M halo (M ) Boost from Microhalos 24

25 Moving Toward Constraints (1+B) σv /m χ 2 [GeV -4 ] ann Volume /h vin2 / h vi m 2 2 IGRB dsphs IGRB: B = 75, 000 dsphs: B = 20, 000 T RH [GeV] z f = 400 m χ = 0 T RH m χ = 150 T RH dsphs IGRB IGRB (S) k cut = 40k RH k cut = 20k RH h vi (cm 3 s 1 ) h vi m 2 4-year Pass 7 Limit 6-year Pass 8 Limit Median Expected 68% Containment 95% Containment Stacked dsphs Thermal Relic Cross Section (Steigman et al. 2012) DM Mass (GeV/c 2 ) Rough comparison obs vs. Fermi-LAT Collaboration 2015 (1 + B) h vi m 2 M =0.25 dsphs: total boost for halo. IGRB: EMDE boost relative to standard boost. b b 6 M 25

26 (1+B) σv /m χ 2 [GeV -4 ] Moving Toward Constraints ann Volume /h vin2 / h vi m 2 2 IGRB Two source dsphs of uncertainty: IGRB: B = 75, 000 dsphs: B = 20, 000 T RH [GeV] m χ = 0 T RH m χ = 150 T RH dsphs IGRB IGRB (S) 1. small-scale cut-off 2. do the first-generation microhalos survive? z f = 400 k cut = 40k RH k cut = 20k RH h vi (cm 3 s 1 ) 21 4-year Pass 7 Limit 22 6-year Pass 8 Limit Median Expected 23 68% Containment 95% Containment This mechanism can make 24 isolated bino 25 DM detectable. 26 Thermal Relic Cross Section (Steigman et al. 2012) ALE, Sinha, Watson h vi m 2 Stacked dsphs DM Mass (GeV/c 2 ) Rough comparison obs vs. Fermi-LAT Collaboration 2015 (1 + B) h vi m 2 M =0.25 dsphs: total boost for halo. IGRB: EMDE boost relative to standard boost. b b 6 M 25

27 Kinetic Decoupling during an EMDE δ / Φ First potential source of a small-scale cut-off: interactions between dark matter and relativistic particles m χ = 4000 GeV T RH = 5 GeV k = k RH = 9.96 k dec δ χ δ r δ φ δ χ γ = 0 Horizon Entry δ φ a Reheating δ / Φ 0 Isaac Waldstein, ALE, Cosmin Ilie, coming soon m χ = 4000 GeV T RH = 5 GeV k = k RH = 996 k dec Horizon Entry δ χ δ r δ φ δ χ γ = 0 δ φ a γ = H Reheating 0 γ = H scale factor (a) scale factor (a) Interactions do not significantly suppress the perturbations, even if the dark matter remains coupled to the relativistic particles well into the EMDE... 26

28 δ / Φ 0 Kinetic Decoupling during an EMDE First potential source of a small-scale cut-off: interactions between dark matter and relativistic particles m χ = 4000 GeV T RH = 5 GeV k = k RH = 9.96 k dec δ χ δ r δ φ γ = δ 0 8 χ δ / Φ 0 6 δ φ a δ / Φ Horizon Entry Reheating 4 γ = H Reheating 1 2 δ φ a Horizon Reheating Entry 2 Horizon Entry δ φ a 0 γ = H scale factor 0 (a) scale factor (a) scale factor (a) 8 6 m χ = 4000 GeV γ = H T RH = 5 GeV k = k RH = 996 k dec δ χ δ r δ φ δ χ γ = 0 Interactions do not significantly suppress the perturbations, even if the dark matter remains coupled to the relativistic particles well into the EMDE... m χ = 4000 GeV δ χ T RH = 5 GeV k = k RH = k δ dec r δ φ δ χ γ = 0 Isaac Waldstein, ALE, Cosmin Ilie, coming soon and even through reheating! see also Choi, Gong, Shin

29 The DM temperature Isaac Waldstein, ALE, Cosmin Ilie 2017 What about free-streaming? We need the DM temperature. T 2 3 Temperature (GeV) * ~p 2 2m + EMDE decoupling = H scale factor (a) a dt da +2T = 2 H (T T ) T T χ reheating RD fully coupled: momentum transfer rate expansion rate H ) T ' T fully decoupled: H ) T / a 2 But during an EMDE H T / T 6 quasi-decoupled: / T 6 T 4 T / T 3 / a 9/8 T / a 9/8 27

30 The DM temperature Isaac Waldstein, ALE, Cosmin Ilie 2017 What about free-streaming? We need the DM temperature. T 2 3 Temperature (GeV) * ~p 2 2m + EMDE decoupling = H scale factor (a) a dt da +2T = 2 H (T T ) T T χ reheating RD fully coupled: momentum transfer rate expansion rate H ) T fully decoupled: ' T But what are the implications for H ) T / a 2 free-streaming? It depends... But during an EMDE H T / T 6 quasi-decoupled: / T 6 T 4 T / T 3 / a 9/8 T / a 9/8 27

31 Microhalo Simulations EMDE RD EMDE Sheridan Green, ALE+ coming soon RD No EMDE z = 500! 30 EMDE T RH = 30 MeV k cut = 20k RH 28

32 Simulation Results Lots of microhalos with steep profiles and copious substructure. dn/d ln M (Mpc 3 ) EMDE RD Press-Schechter Sheth-Tormen (15 pc/h) 3 (30 pc/h) 3 (60 pc/h) 3 (120 pc/h) 3 ρ [M pc 3 h 2 ] CDM RD 13 Halo Mass (M /h) EMDE M (M ) Substructure Mass Function for 6 M /h Hosts d log ρ/d log r dn/dm [Npc 3 h 4 M 1 ] f sub > 0.5 Redshift dn dm m 1 z =30 z = r/r M/M h 29

33 Boost Factor from Simulations 1+B(M) J R 2 (r)4 r 2 dr / (z f ) 0 c 3 f tot (M<M RH,z f ) h assumes all halos have same profile at z f include substructure: 5 Predicted z e =400, f tot =0.05 z e =20, b tot =68.0 z e =30, b tot =33.9 z e =38.2, b tot =21.6 z e =113.7, b tot =1.8 f tot! b tot 1+B Sheridan Green, ALE+ coming soon 4 dn/d ln M (Mpc 3 ) M (M ) M host (M ) 30

34 Perturbations during Kination 3 k = 2400 k RH δ χ /Φ initial Φ/Φ initial Kayla Redmond, ALE coming soon 2 / a / a RH a hor / scale factor (a/a I ) r k k RH δ χ (1 a RH )/Φ initial Transfer Function Dodelson Model Kination Model (k/k RH ) / p k 31

Inflation Dark Energy Summary: Mind the Gap after Inflation Radiation domination Matter domination There is a gap in the cosmological record between inflation and the onset of Big Bang

35 Inflation Dark Energy Summary: Mind the Gap after Inflation Radiation domination Matter domination There is a gap in the cosmological record between inflation and the onset of Big Bang nucleosynthesis: 15 GeV & T & 3 GeV 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. Big Bang Nucleosynthesis (BBN) Today 32

I. Introduction 2. V. Summary and Discussion 33. References 34. Abstract

I. Introduction 2. V. Summary and Discussion 33. References 34. Abstract 2 Abstract An early matter-dominated era (EMDE) is a brief period between the end of inflation and reheating where a matter-like energy source dominates the cosmic stage. During the EMDE, sub-horizon matter