Broad picture Flooded dark matter Core-Cusp Problem RH neutrino implementation Cosmology with Democratic Initial Conditions James Unwin UI Chicago GGI: Gearing up for LHC13 Work with L. Randall & J. Scholtz: [1509.08477] & forthcoming October 7, 2015 James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Motivation Democratic inflaton decay is a natural expectation. If there are many sectors it is surprising that at late time Standard Model has considerable fraction of energy and dominates entropy. Moreover, without a large injection of entropy into the Standard Model, dark sectors would typically contribute too much entropy. Ask: what is required to match the present Universe given a democratically decaying inflaton? Suppose Standard Model energy density from late decay of heavy state Φ , whereas DM comes from the redshifted primordial abundance. James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Cosmic history Democratic reheating following inflation: Credit: Jakub Scholtz for hand drawn figures! James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Cosmic history Heavy state becomes non-relativistic: James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Cosmic history Heavy state decays and repopulates the Standard Model: James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Cosmic history Dark matter becomes non-relativistic: James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Cosmic history Baryogenesis occurs (at some point): James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture Motivation Flooded dark matter Cosmic history Core-Cusp Problem Entropy injection RH neutrino implementation Entropy injection This can be seen instead in terms of entropy production: Φ decay floods the entropy and drastically reduces cosmological impact of the dark matter – “Flooded Dark Matter and S level Rise” [1509.08477]. James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model The period for which the energy density of DM redshifts relative to Φ energy density is controlled by the Φ lifetime. We derive the required Φ decay rate Γ to match the observed relic density. Denote the scale factor Φ becomes nonrelativistic by a = a 0 and define R ( i ) ≡ R ( a i ) ≡ ρ DM ( a i ) ρ Φ ( a i ) . Assuming democratic inflaton decay R ( 0 ) ≡ R ( a 0 ) ≃ 1. We might also wish to keep track of other primordial populations: SM ≡ ρ SM ( a 0 ) DS ≡ ρ DS ( a 0 ) R ( 0 ) R ( 0 ) ρ Φ ( a 0 ) ; ρ Φ ( a 0 ) . James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model The evolution of ρ tot can be described as ≃ m 4 H 2 ( a ) = ρ tot ( a ) �� a 0 � 4 � � 3 + R ( 0 ) � a 0 � 4 � a 0 � 4 � a 0 + R ( 0 ) + R ( 0 ) Φ SM DS 3 M 2 M 2 a a a a Pl Pl The decays of Φ become important when 3 H ( a Γ ) = Γ . Assume here that prior to decay Φ dominates the energy density and DM is relativistic. Then at time of Φ decay the scale factor is � a 0 � 3 ≃ Γ 2 M 2 Pl m 4 a Γ Φ and the ratio of energy densities at the time of the Φ decay � a 0 � 1 / 3 � � Γ 2 M 2 R (Γ) = R ( 0 ) ≃ R ( 0 ) Pl . m 4 a Γ Φ James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model Assuming adiabatic evolution of the Universe after Φ decays. The ratio of entropy densities does not change from a Γ to present � 4 / 3 � 4 / 3 � � s (Γ) s ( ∞ ) R (Γ) ≃ DM DM = . s (Γ) s ( ∞ ) SM SM The ratio of DM to SM entropies can be expressed in observed quantities s ( ∞ ) 2 π 4 2 π 4 45 ζ ( 3 )∆Ω DM 45 ζ ( 3 )∆ n DM m p DM = = , s ( ∞ ) n B Ω B m DM SM where ∆ = n B / s SM = 0 . 88 × 10 − 10 and m p is the proton mass. James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model Putting this together the Γ required to match the observed DM relic density: � 2 � 2 Γ ≃ m 2 ≃ m 2 � s DM � ∆Ω DM m p Φ Φ M Pl s DM M Pl Ω B m DM SM reheat temperature due to Φ decay Γ M Pl ≃ m Φ ∆Ω DM m p � T RH ≃ Ω B m DM Competition between requirement: phenomenologically high T RH and small Γ to dilute DM James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model 10 0 10 � 9 10 � 1 T NR � GeV � 10 � 3 T DM � T SM 10 � 2 10 � 3 10 3 10 � 4 10 9 10 � 5 10 � 9 10 � 6 10 � 3 10 0 10 3 m DM � GeV � As SM dof are regenerated via decays it becomes warmer than hidden sector � s SM � m DM Ω B � 1 / 3 � 1 / 3 T DM / T SM ≃ ≃ m DM ∆ m p Ω DM s DM The temperature of hidden sector colder than visible sector Model bath T NR � s SM at point DM nonrelativistic is � 1 / 3 T NR = m DM s DM James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model Successful models must satisfy the following general criteria: A. A thermal bath of Φ is generated after inflation which implies a limit on the mass m Φ ∼ ρ 1 / 4 Φ ( a 0 ) � 10 16 GeV. B. The Standard Model reheat temperature is well above BBN. C. The DM relic density matches the value observed today. D. Baryogenesis should occur (may place bounds on T RH ). James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness One field model 10 18 10 � 3 10 � 6 10 � 9 10 15 10 � 12 10 � 15 10 12 m � � GeV � 10 9 10 6 m DM � 300 eV m � � 10 16 GeV 10 3 T RH � 100 GeV T RH � 100 MeV 10 0 10 � 6 10 � 3 10 0 10 3 10 6 10 9 m DM � GeV � Defining Γ = κ 2 m Φ / 8 π we show contours of κ that give correct DM relic. James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness Two field model Consider two heavy fields: Φ DM and Φ SM associated with the DM and SM. Assume Φ DM that decays primarily to dark matter, and Φ SM is longer-lived. Hence s SM will dominate over s DM , as DM redshifts prior to Φ DM decays. This differs from one field case since the relative redshifting no longer starts right after Φ becomes nonrelativistic, but after Φ DM decays. We derive relationship between Γ Φ SM and Γ Φ DM to get the correct DM relic for the degenerate case m Φ SM = m Φ DM = m Φ , and initial conditions ρ i ( a 0 ) = R ( 0 ) m 4 Φ , ( a 0 : T ∼ m Φ ) i James Unwin Cosmology with Democratic Initial Conditions (GGI)
Broad picture One field Model Flooded dark matter Two field Model Core-Cusp Problem Baryogenesis RH neutrino implementation Maximal Baroqueness Two field model The energy densities are evolved to H ≃ Γ DM to obtain � a 0 � 3 ρ i ( a Γ DM ) = R ( 0 ) m 4 , ( i = Φ DM , Φ SM ) . Φ i a Γ DM As the DM redshifts like radiation between the first decay and the second, and this era is matter dominated, after the second field has decayed � Γ SM � 2 � 1 / 3 ρ SM ( a Γ SM ) = R ( 0 ) R ( 0 ) Φ DM + R ( 0 ) � ρ DM ( a Γ SM ) Φ DM Φ SM , R ( 0 ) R ( 0 ) Γ DM Φ SM Φ SM Given Γ Φ DM decay rate, the required Γ Φ SM for the observed relic density is 1 / 2 � 3 � R ( 0 ) R ( 0 ) � 2 � ∆Ω DM m p Φ SM Φ SM Γ SM ≃ Γ DM . Ω B R ( 0 ) R ( 0 ) Φ DM + R ( 0 ) m DM Φ DM Φ SM James Unwin Cosmology with Democratic Initial Conditions (GGI)
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