Bound on Reheating Temperature with Dark Matter [Based on the work - PowerPoint PPT Presentation

Bound on Reheating Temperature with Dark Matter [Based on the work with Tomo Takahashi] Ki -Young Choi

Contents 1. Reheating temperature and early Matter Domination 2. Dark matter in the early Matter Domination 3. Low bound on the reheating temperature 4. Discussion

Temperature of the Universe What is the available range of this initial high temperature? What is the highest temperature? What is the lowest temperature?

Inflation and Matter-Domination Inflation: vacuum-dominated Oscillation : matter-dominated Decay : radiation-dominated

Reheating During inflation, the Universe is cold. After inflation, the energy of the inflation is converted to the production of the light particles. Usually the inflaton field oscillates around vacuum and decay to produce light particles. The particles are thermalised and the Universe is heated to some temperature. We call the highest temperature when the radiation- domination starts, reheating temperature. Early matter-domination (by inflaton) before reheating is inevitable. H 2 ⇠ ρ ⇠ a − 3

Upper bound on Reheating Temperature Energy scale of the inflation constrains the highest temperature of the reheating temperature. Energy during inflation ρ ( T reh ) < V ρ ( T ) = π 2 ⇣ r ⌘ 1 / 4 30 g ∗ T 4 10 16 GeV V 1 / 4 ∼ 0 . 01 bound on tensor-to-scalar ratio T reh < 10 16 GeV

Early Matter-Domination and Reheating Reheating and early matter-domination also happen in the scenarios of Moduli, curvaton, thermal inflation, axino, gravitino, .... ◆ 1 / 4 p ✓ 90 H T reh ' Γ M P π 2 When decoupled heavy particles are very weakly interacting, they decay very late in the early Universe. Temperature ~ MeV - GeV

Reheating Temperature ◆ 1 / 4 p Matter-dom. ✓ 90 H T reh ' Γ M P Γ ' H T π 2 Rad.-dom. ρ ( T ) = π 2 30 g ∗ T 4 [From Kolb & Turner]

Low bound on Reheating Temperature 1. Big Bang Nucleosynthesis : at low-reheating temperature, neutrinos are not fully thermalised and the light element abundances are changed, as T reh & 0 . 5 − 0 . 7 MeV on the reheating temperatur for hadronic decays or T reh & 2 . 5 MeV − 4 MeV [Kwasaki, Kohri, Sugiyama, 1999, 2000] 2. BBN+CMB+LSS : precise calculation of the cosmic neutrino background and CMB T reh & 4 . 7 MeV [Salas, Lattanzi, Mangano, Miele, Pastor, Pisanti, 2015]

Big-Bang Nucleosynthesis ↔ n ↔ p + e − + ¯ T � 1 MeV ( t � 1 sec) ν e Local Thermal Equilibrium n + ν e ↔ p + e − of protons and neutrons ν e ↔ n + e + p + ¯ T ∼ 1 MeV ( t ∼ 1 sec) n + p ↔ D + γ Weak freeze-out Deuterium bottleneck p = e − ( m n − m p ) /T � 1 n T ∼ 0 . 07 MeV ( t ∼ 3 min) 6 n/p � 1 / 7 Decay of free neutrons most neutrons to He4 small D, He3 Li7 τ n ' 880 sec � 3 / 2 � mT m n − m p � 1 . 29 MeV e − ( m − µ ) /T n = g 2 π

New bound on low-reheating temperature 3. Dark matter halos : density perturbation during early matter-domination and no observation of small scale DM halos. T reh & 30 MeV [KYChoi, Tomo Takahashi, in preparation]

Early Matter Domination and Reheating ◆ 1 / 4 p ✓ 90 H T reh ' Γ M P π 2 Γ ' H T ρ ( T ) = π 2 30 g ∗ T 4 Radiation-dom. Early Matter-dom. [From Kolb & Turner]

Evolution of Density Perturbation − δ ≡ δρ ρ Inside horizon: Radiation (rel. particles) : oscillates decoupled DM (non rel. particles with vanishing pressure) : Rad-domination: logarithmically grows Matter-domination: linearly grows

− δ ≡ δρ Evolution in the Standard Model ρ non-linear growth 1 δ ∝ a δ ∝ log a 10 − 5 Radiation Matter domination domination ∝ a scale factor horizon entry rad-matter equality

− δ ≡ δρ Primordial Black Holes or UCMHs ρ non-linear growth 1 δ ∝ a If initially large δ ∝ log a 10 − 5 Radiation Matter domination domination ∝ a scale factor horizon entry rad-matter equality

Primordial Black Holes or UCMHs If primordial density perturbation is large: δ & 0 . 1 The matters and radiation collapse when they enters the horizon and make black holes (primordial black hole) No observation of primordial black hole rule out this large density perturbation. δ & 10 − 3 It does not make black hole, but can make small scale dm dominated halos (ultra compact mini halo, UCMH) No observation yet. The constraint depends on the properties of dark matter.

� UCMHs in the Galaxy 1 ⇧ ( r ) ⇤ r 2 . 25

Observation of UCMHs with WIMP WIMP dark matter Annihilation or decay of WIMPs in the UCMHs : gamma-ray, neutrino, cosmic rays. Fermi-LAT constrains strongly [Bringmann, Scott, Akrami, 2012]

UCMH Mass Fraction UCMH mass fraction in the Milky Way M 0 UCMH f ≡ Ω UCMH / Ω m = β ( R ) f χ M i � 4 π � with DM fraction where f χ ≡ Ω χ / Ω m 3 ρ χ ( a ) R 3 M i ≃ phys R =1 / ( aH ) M 0 - increase of the mass by grav. infall during MD UCMH . χ M i - probability of comoving size R can collapse to form UCMH Z δ max " # δ 2 1 χ χ β ( R ) = exp d δ χ p � 2 σ 2 χ , H ( R ) 2 πσ χ , H ( R ) δ min χ (

Probability to form UCMH [Bringmann, Scott, Akrami, 2013] - CDM mass variance at horizon entry from power spectrum Z 1 TH ( kR ) P δ ( k ) dk σ 2 ( R ) = W 2 k 0 : with minimum value of density contrast for UCMH at horizon entry δ min ( k, t k ) = χ It is roughly 0.001 at horizon entry in the standard Rad.-dom. Universe.

Constraints for UCMH with WIMP DM M 0 UCMH (M � ) 10 � 1 10 � 2 10 � 3 10 � 4 10 � 5 10 � 6 10 � 7 10 � 8 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 1 10 � 1 10 � 2 f max 10 � 3 10 � 4 Galactic sources extragalactic sources 10 � 5 Galactic di ff use 10 � 6 [Bringmann, Scott, Akrami, 2013] 10 2 10 3 10 4 10 5 10 6 10 7 10 k (Mpc � 1 ) We assume 100% annihilation of WIMPs into b ¯ b pairs, a WIMP mass of m χ = 1 TeV and an e ff ective annihi- lation cross-section of h σ v i = 3 ⇥ 10 � 26 cm 3 s � 1 . These

Constraints on Primordial Power Spectrum 10 − 1 10 − 2 10 − 2 WIMP kinetic decoupling 10 − 3 ❙ ❙ 10 − 3 10 − 4 Allowed regions 10 − 4 10 − 5 P R ( k ) P δ ( k ) Ultracompact minihalos (gamma rays, Fermi -LAT) 10 − 5 10 − 6 Ultracompact minihalos (reionisation, WMAP5 τ e ) 10 − 6 10 − 7 Primordial black holes 10 − 7 10 − 8 CMB, Lyman- α , LSS and other cosmological probes 10 − 8 10 − 9 10 − 9 10 − 10 10 − 3 10 − 2 10 − 1 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 10 19 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 1 k (Mpc − 1 ) [Bringmann, Scott, Akrami, 2013]

Observation of UCMHs M 0 UCMHs with non-WIMP dark matter UCMH f ≡ Ω UCMH / Ω m = β ( R ) f χ M i : To observe by Gravitational effects only - distortion in the macrolensed quasars [Zackrisson 2013] f . 0 . 1 - astrometric microlensing Even with S min [Li, Erickcek, Law, 2012] f eq & 0 : 009 . - pulsar timing f . 10 − 6 [Clark, Lewis, Scott, 2015]

Constraints for UCMH by Pulsar Timing [Clark, Lewis, Scott, 2015] Pulsar time can change pulsar-timing when the UCMHs are moving across the line of sight. WIMP They obtain the bound on the fraction of UCMHs for different scales. This is constraint is gravitational, so universal.

Constraints on Power Spectrum by Pulsar Timing [Clark, Lewis, Scott, 2015]

UCMHS with early MD Before reheating, the epoch matter-domination exists (early matter-domination). The perturbation which enters during early matter-domination can grow linearly and help to generate UCMHs. Non-observation of UCMHs can constrain the primordial power spectrum and the stage of early matter-domination.

− δ ≡ δρ UCMHs and early Matter-Domination ρ UCMHs 1 early matter δ ∝ a domination δ ∝ log a 10 − 5 Radiation Matter domination domination ∝ a horizon reheating scale factor rad-matter entry equality T reh

To find δ min ( k, t k ) = χ It is roughly 0.001 at horizon entry in the standard Radiation -dominated Universe. For early matter-domination, we need to make evolution from horizon entry to the deep inside until it forms the UCMHs. linear evolution collapse time of collapse � c � �� ð t c Þ lin ¼ 3 � 3 � � 2 = 3 � 1 : 686 : using linear theory � ð t c Þ � 5 2 The collapse should happen before some epoch, here we choose z = 1000, conservatively.

− δ ≡ δρ UCMHs and early MD UCMHs ρ δ ∝ a 1 early matter δ c = domination � δ max χ δ ∝ log a f δ min χ 10 − 5 Radiation Matter domination domination ∝ a horizon reheating scale factor rad-matter entry equality T reh

Growth of Density Perturbation During matter-domination epoch, Density perturbation contrast of the dominating heavy particles ◆ 2 a ✓ δ σ = − 2 Φ 0 − 2 k , 3 Φ 0 a i H ( a i ) a i where δ σ ≡ δρ σ / ρ σ ,

Decoupled Dark Matter: super-WIMP For decoupled dark matter, the evolution during early MD is same. Therefore at the time of reheating, ✓ k ◆ 2 δ χ ' � 2 for k < k dom , 3 Φ 0 k reh ◆ 2 ✓ k dom δ χ ' � 2 for k > k dom . 3 Φ 0 k reh The scale of reheating is ✓ T reh ◆ 1 / 3 ⇣ g ∗ ◆✓ 10 . 75 ⌘ 1 / 2 k reh = 0 . 011967 pc − 1 . MeV g ∗ s 10 . 75 (3) The scale of beginning early MD: k < k dom ,