The Influence of DE on the Expansion Rate of the Universe and its Effects on DM Relic Abundance

Transcription

1 The Influence of DE on the Expansion Rate of the Universe and its Effects on DM Relic Abundance Esteban Jimenez Texas A&M University XI International Conference on Interconnections Between Particle Physics and Cosmology Based on: B. Dutta, E. Jimenez and I. Zavala. arxiv: Esteban Jimenez DE and DM PPC / 23

2 Standard Cosmology ΛCDM model Succesful explaining physical phenomena since Big Bang Nucleosynthesis (BBN) epoch at MeV temperatures: Primordial abundances of light elements, Cosmic Microwave Background, etc. Expansion history since freeze-out of DM and the precise measurement of the DM relic abundance (27%) fix the annihilation crosssection σv for a given DM mass. The physics describing the Universe s evolution from the end of inflation (reheating) to just before BBN remains relatively unconstrained. Esteban Jimenez DE and DM PPC / 23

3 Thermal Cold Dark Matter DM composed of weakly interacting particles. In thermal equilibrium during radiation dominated era. DM becomes non-relativistic and then decouples before BBN. Abundance (Y n s ) freezes out. The Boltzmann equation describes the evolution of the DM abundance. ( x dy Y dx = Γ ( ) ) 2 Yeq 1. H GR Y where Γ n σv = Ys σv and x = m/t. Esteban Jimenez DE and DM PPC / 23

4 Thermal Cold Dark Matter Γ H GR. Evolution is governed by the factor Γ H GR Y = Y eq thermal equilibrium. Γ H GR freeze out. Γ H GR Y = Y decoupled evolution H,Γ(GeV) H GR Γ 1000 GeV Γ 100 GeV T (GeV) 1 Esteban Jimenez DE and DM PPC / 23

5 Thermal Evolution of Abundance Y(x) Increasing < σ v > DM Content Ω DM = ρ 0 ρ c = ms 0Y ρ c x(m/t ) σv cm 3 /s Esteban Jimenez DE and DM PPC / 23

6 On the other hand... Fermi-LAT 1 and Planck 2 experiments have been exploring upper bounds. 1 arxiv: arxiv: Esteban Jimenez DE and DM PPC / 23

7 Predicting different annihilation cross-section Modified expansion rate prior to BBN, due to a modified gravity. Scalar-Tensor Theories are good candidates before big-bang nucleosynthesis 3. Gravitational interactions are mediated by a scalaf field and a tensor (the metric). Ivonne Zavala s talk, "String-DM/DE Larger or smaller σv for a given DM mass 3 arxiv: , , Esteban Jimenez DE and DM PPC / 23

8 Scalar-Tensor Theories of Gravity Frames of reference The metrics Two frames of references connected by g µν = C(φ)g µν + D(φ) µ φ ν φ where C(φ) is the conformal coupling and D(φ) is the disformal coupling. Jordan Frame, g µν Scalar field couples through the gravitational sector. S Mat ( g µν, Ψ m ). By construction, observables such as mass, length and time take their standard interpretation. x dỹ Ỹ d x = Γ ( ) 2 ) (Ỹeq 1 H Ỹ Esteban Jimenez DE and DM PPC / 23

9 Scalar-Tensor Theories of Gravity Frames of reference Einstein Frame, g µν Scalar field couples through the matter sector, S Mat (g µν, C(φ), D(φ) µ φ ν φ, Ψ m ) Physical quantities measured in this frame are spacetime dependent. Advantage is that the Einstein equations take the usual form, R µν 1 2 g µνr = κ 2 ( T φ µν + T µν ) There is also an equation describing the evolution of the scalar field. Solve equations in this frame, to obtain the expansion rate H and φ evolution. Then, go back to Jordan frame to find H. In this talk, I only focus on the conformal scenario (D(φ) = 0). Thus g µν = C(φ)g µν Esteban Jimenez DE and DM PPC / 23

10 Equation of State It is a frame invariant quantity: ω = p ρ = p ρ = ω During the radiation dominated era, 1 3 ω = ρ 3 p ρ = A ρ A 3 p A ρ where ρ A and p A are the contribuition of SM particles and ρ π 2 g eff ( T) T 4 /3 Esteban Jimenez DE and DM PPC / 23

11 Equation of State ω (T ) T (GeV) p = ω ρ Radiation domination, ω 1/3. Matter domination, ω = 0. Dark Energy domination, ω = 1. Esteban Jimenez DE and DM PPC / 23

12 Conformal Scenario Evolution of scalar field is dictated by, 2 3B ϕ + (1 ω) ϕ + 2(1 3 ω)α(ϕ) = 0. where N = ln a/a 0, B = 1 ϕ 2 /6, α(ϕ) = d ln C1/2 dϕ, ω = p ρ. Veff φ Esteban Jimenez DE and DM PPC / 23

13 Conformal Scenario Expansion Rate of the Universe In the plot 4 below C(ϕ) = ( e 8 ϕ ) 2 and (ϕ 0, ϕ 0 ) = (0.2, 0.99) H(GeV) H H GR T (GeV) arxiv: Esteban Jimenez DE and DM PPC / 23

14 Conformal Scenario Comparing Γ and H Esteban Jimenez DE and DM PPC / 23

15 Conformal Scenario Dark Matter Relic Abundance The Boltzmann equation becomes x dỹ Ỹ d x = Γ ( 1 H ) 2 ) (Ỹeq. Ỹ 10-7 Y(x) Y GR Ỹ Y Eq Example for a mass 1000 GeV (arxiv: ) x(m/t ) Esteban Jimenez DE and DM PPC / 23

16 Conformal Scenario Relic Abundance for 130 GeV Esteban Jimenez DE and DM PPC / 23

17 Conformal Scenario Dark Matter Annihilation Cross Section 10 σ v /10-26 (cm 3 s -1 )) Standard Conformal m(gev) arxiv: Esteban Jimenez DE and DM PPC / 23

18 Conclusions ST present a atractor mechanism to standard cosmology prior to BBN. DM annihilation cross-section larger and smaller than the one predicted by standard cosmology, consistent with the experimental bounds. Significant variation in the evolution of abundance for high masses (Presented example for 1000 GeV) Esteban Jimenez DE and DM PPC / 23

19 Scalar-Tensor Theories of Gravity Frames of reference Two frames of references connected by g µν = C(φ)g µν + D(φ) µ φ ν φ Jordan Frame, g µν Scalar field couples through the gravitational sector. As an example, the action for D = 0 is given by, S tot = 1 2κ 2 d 4 x g GR + S Mat ( g µν, Ψ m ). [ 1 C R g µν Z(φ) µ φ ν φ 2U(φ) By construction, observables such as mass, length and time take their standard interpretation. x dỹ Ỹ eq d x = Γ ( ( ) 2 Ỹ 1) H Ỹ eq ] Esteban Jimenez DE and DM PPC / 23

20 Scalar-Tensor Theories of Gravity Frames of reference Einstein Frame, g µν Scalar field couples through the matter sector. S = 1 2κ 2 d 4 x g R d 4 x g + S Mat (C(φ)g µν + D(φ) µ φ ν φ, Ψ m ). [ ] 1 2 ( φ)2 + V(φ) Physical quantities measured in this frame are spacetime dependent. ( ) R µν 1 2 g µνr = κ 2 Tµν φ + T µν Esteban Jimenez DE and DM PPC / 23

21 Scalar-Tensor Theories of Gravity Cosmological equations FRW metric g µν, ds 2 = dt 2 + a(t) 2 dx i dx i. Einstein and scalar field equations become where H = ȧ a. H 2 = κ2 3 [ρ φ + ρ], Ḣ + H 2 = κ2 6 [ρ φ + 3p φ + ρ + 3p], φ + 3H φ + V,φ + Q 0 = 0. Esteban Jimenez DE and DM PPC / 23

22 Conformal Scenario Expansion Rate of the Universe With the solution for the scalar field we find H as follows, Expansion Rate in the Jordan Frame H = C1/2 (ϕ) 1 C 1/2 (ϕ 0 ) (1 α(ϕ)ϕ ) 1 (ϕ ) 2 6(1 α(ϕ)ϕ ) α 2 (ϕ 0 ) H GR where denotes derivative w.r.t Ñ = ln ã/ã 0 Esteban Jimenez DE and DM PPC / 23

23 Parameter Constraints Solar system tests of gravity impose constraints 5. α α 0 = dα/dϕ ϕ H H GR order 1 before the onset of BBN. 5 arxiv: Esteban Jimenez DE and DM PPC / 23