Dark matter from Dark Energy-Baryonic Matter Couplings
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1 Dark matter from Dark Energy-Baryonic Matter Coulings Alejandro Avilés 1,2 1 Instituto de Ciencias Nucleares, UNAM, México 2 Instituto Nacional de Investigaciones Nucleares (ININ) México January 10, 2010 Cosmología en la Playa 2011 Puerto Vallarta
2 Outline Motivations Interactions with the Trace of the Energy Momentum Tensor Background Cosmology Cosmological Perturbations Summary and Conclusions
3 Motivations Dark Degeneracy [M. Kunz PRD 80, (2009)]: Dark comonents in the Universe are defined through 8πG Tµν dark = G µν 8πG Tµν obs Interacting models between dark energy and matter fields have been roosed in order to amelliorate the Coincidence Problem. But, this interactions give rise to long range undetected new forces. Some screening mechanism have been roosed in order to evade fifth forces and equivalence rincile tests.[khoury and Weltman PRD 69, (2004)] In some interactions the continuity equation of baryonic matter is reserved.
4 Motivations Dark Degeneracy [M. Kunz PRD 80, (2009)]: Dark comonents in the Universe are defined through 8πG Tµν dark = G µν 8πG Tµν obs Interacting models between dark energy and matter fields have been roosed in order to amelliorate the Coincidence Problem. But, this interactions give rise to long range undetected new forces. Some screening mechanism have been roosed in order to evade fifth forces and equivalence rincile tests.[khoury and Weltman PRD 69, (2004)] In some interactions the continuity equation of baryonic matter is reserved.
5 Motivations Dark Degeneracy [M. Kunz PRD 80, (2009)]: Dark comonents in the Universe are defined through 8πG Tµν dark = G µν 8πG Tµν obs Interacting models between dark energy and matter fields have been roosed in order to amelliorate the Coincidence Problem. But, this interactions give rise to long range undetected new forces. Some screening mechanism have been roosed in order to evade fifth forces and equivalence rincile tests.[khoury and Weltman PRD 69, (2004)] In some interactions the continuity equation of baryonic matter is reserved.
6 Motivations Dark Degeneracy [M. Kunz PRD 80, (2009)]: Dark comonents in the Universe are defined through 8πG Tµν dark = G µν 8πG Tµν obs Interacting models between dark energy and matter fields have been roosed in order to amelliorate the Coincidence Problem. But, this interactions give rise to long range undetected new forces. Some screening mechanism have been roosed in order to evade fifth forces and equivalence rincile tests.[khoury and Weltman PRD 69, (2004)] In some interactions the continuity equation of baryonic matter is reserved.
7 Interactions with the trace of the energy momentum tensor 1 Z S = S φ + S m + S int S int = Fermionic Field d 4 x A(φ)T g. T = g µν T µν, T µν = 2 g δ(s m + S int ) δg µν L = g ψ(iγ µ µ m)ψ + A(φ)T g g ψ(iγ µ µ e α(φ) m)ψ e α(φ) = 1 1 A(φ) Electromagnetic Field L = 1 4 F µν F µν g + A(φ)T g 1 4 F µν F µν g Perfect Fluid L = ρ g + A(φ)T g e α(φ) ρ g
8 Interactions with the trace of the energy momentum tensor 1 Z S = S φ + S m + S int S int = Fermionic Field d 4 x A(φ)T g. T = g µν T µν, T µν = 2 g δ(s m + S int ) δg µν L = g ψ(iγ µ µ m)ψ + A(φ)T g g ψ(iγ µ µ e α(φ) m)ψ e α(φ) = 1 1 A(φ) Electromagnetic Field L = 1 4 F µν F µν g + A(φ)T g 1 4 F µν F µν g Perfect Fluid L = ρ g + A(φ)T g e α(φ) ρ g
9 Interactions with the trace of the energy momentum tensor 1 Z S = S φ + S m + S int S int = Fermionic Field d 4 x A(φ)T g. T = g µν T µν, T µν = 2 g δ(s m + S int ) δg µν L = g ψ(iγ µ µ m)ψ + A(φ)T g g ψ(iγ µ µ e α(φ) m)ψ e α(φ) = 1 1 A(φ) Electromagnetic Field L = 1 4 F µν F µν g + A(φ)T g 1 4 F µν F µν g Perfect Fluid L = ρ g + A(φ)T g e α(φ) ρ g
10 Interactions with the trace of the energy momentum tensor 1 Z S = S φ + S m + S int S int = Fermionic Field d 4 x A(φ)T g. T = g µν T µν, T µν = 2 g δ(s m + S int ) δg µν L = g ψ(iγ µ µ m)ψ + A(φ)T g g ψ(iγ µ µ e α(φ) m)ψ e α(φ) = 1 1 A(φ) Electromagnetic Field L = 1 4 F µν F µν g + A(φ)T g 1 4 F µν F µν g Perfect Fluid L = ρ g + A(φ)T g e α(φ) ρ g
11 Interactions with the trace of the energy momentum tensor 1 Z S = S φ + S m + S int S int = Fermionic Field d 4 x A(φ)T g. T = g µν T µν, T µν = 2 g δ(s m + S int ) δg µν L = g ψ(iγ µ µ m)ψ + A(φ)T g g ψ(iγ µ µ e α(φ) m)ψ e α(φ) = 1 1 A(φ) Electromagnetic Field L = 1 4 F µν F µν g + A(φ)T g 1 4 F µν F µν g Perfect Fluid L = ρ g + A(φ)T g e α(φ) ρ g
12 Interactions with the trace of the energy momentum tensor 2 Action Z S = d 4 x» R g 16πG 1 2 φ,α φ,α V (φ) A(φ)T ρ, Field Equations G µν = 8πG(T φ µν + e α(φ) T b µν), φ V (φ) = α (φ)e α(φ) ρ, V ef (φ) = V (φ) + e α(φ) ρ. Conservation Equations: 1. Continuity Equation 2. Geodesic Equation Newtonian Limit µ (ρ u µ) = 0, u µ µu ν = α (φ)(g µν + u µ u ν ) µφ. d 2 X dt 2 = Φ N α(φ)
13 Interactions with the trace of the energy momentum tensor 2 Action Z S = d 4 x» R g 16πG 1 2 φ,α φ,α V (φ) e α(φ) ρ. Field Equations G µν = 8πG(T φ µν + e α(φ) T b µν), φ V (φ) = α (φ)e α(φ) ρ, V ef (φ) = V (φ) + e α(φ) ρ. Conservation Equations: 1. Continuity Equation 2. Geodesic Equation Newtonian Limit µ (ρ u µ) = 0, u µ µu ν = α (φ)(g µν + u µ u ν ) µφ. d 2 X dt 2 = Φ N α(φ)
14 Interactions with the trace of the energy momentum tensor 2 Action Z S = d 4 x» R g 16πG 1 2 φ,α φ,α V (φ) e α(φ) ρ. Field Equations G µν = 8πG(T φ µν + e α(φ) T b µν), φ V (φ) = α (φ)e α(φ) ρ, V ef (φ) = V (φ) + e α(φ) ρ. Conservation Equations: 1. Continuity Equation 2. Geodesic Equation Newtonian Limit µ (ρ u µ) = 0, u µ µu ν = α (φ)(g µν + u µ u ν ) µφ. d 2 X dt 2 = Φ N α(φ)
15 Interactions with the trace of the energy momentum tensor 2 Action Z S = d 4 x» R g 16πG 1 2 φ,α φ,α V (φ) e α(φ) ρ. Field Equations G µν = 8πG(T φ µν + e α(φ) T b µν), φ V (φ) = α (φ)e α(φ) ρ, V ef (φ) = V (φ) + e α(φ) ρ. Conservation Equations: 1. Continuity Equation 2. Geodesic Equation Newtonian Limit µ (ρ u µ) = 0, u µ µu ν = α (φ)(g µν + u µ u ν ) µφ. d 2 X dt 2 = Φ N α(φ)
16 Interactions with the trace of the energy momentum tensor 2 Action Z S = d 4 x» R g 16πG 1 2 φ,α φ,α V (φ) e α(φ) ρ. Field Equations G µν = 8πG(T φ µν + e α(φ) T b µν), φ V (φ) = α (φ)e α(φ) ρ, V ef (φ) = V (φ) + e α(φ) ρ. Conservation Equations: 1. Continuity Equation 2. Geodesic Equation Newtonian Limit µ (ρ u µ) = 0, u µ µu ν = α (φ)(g µν + u µ u ν ) µφ. d 2 X dt 2 = Φ N α(φ)
17 Background Cosmology 1 H 2 = 8πG 1 φ V (φ) + (e α(φ) 1)ρ + ρ φ + 3H φ + V (φ) + α (φ)e α(φ) ρ = 0 ρ + 3Hρ = 0 ρ dark = ρ φ + (e α(φ) 1)ρ 1 ρ dark + 3H(1 + w dark )ρ dark = 0, w dark. 1 + eα(φ) 1 ρ V (φ) 0 a 3 V (φ) = Mn+4 φ n e α(φ) = e β M P φ V (φ) = 1 2 m2 φ φ2 e α(φ) = β φ2 M 2
18 Background Cosmology 1 H 2 = 8πG 1 φ V (φ) + (e α(φ) 1)ρ + ρ φ + 3H φ + V (φ) + α (φ)e α(φ) ρ = 0 ρ + 3Hρ = 0 ρ dark = ρ φ + (e α(φ) 1)ρ 1 ρ dark + 3H(1 + w dark )ρ dark = 0, w dark. 1 + eα(φ) 1 ρ V (φ) 0 a 3 V (φ) = Mn+4 φ n e α(φ) = e β M P φ V (φ) = 1 2 m2 φ φ2 e α(φ) = β φ2 M 2
19 Background Cosmology 1 H 2 = 8πG 1 φ V (φ) + (e α(φ) 1)ρ + ρ φ + 3H φ + V (φ) + α (φ)e α(φ) ρ = 0 ρ + 3Hρ = 0 ρ dark = ρ φ + (e α(φ) 1)ρ 1 ρ dark + 3H(1 + w dark )ρ dark = 0, w dark. 1 + eα(φ) 1 ρ V (φ) 0 a 3 V (φ) = Mn+4 φ n e α(φ) = e β M P φ V (φ) = 1 2 m2 φ φ2 e α(φ) = β φ2 M 2
20 Background Cosmology 2 Ωdark β = 1 β = 0.2 β = ΛCDM β = 0.04 β M 2 G a a
21 Suernovae Ia Fit UNION 2 [R. Amanullah et al. (SCP), Astrohys. J. 716, 712 (2010).] Union2 data 0.40 Union Μ C z z = 1 a 1 «dl µ = 5 log Mc Z z d L (z) = (1 + z) 0 dz H(z ) C 2 C 1 = eα(φ) 1 V (φ) ρ, today C 2 = e α(φ) 1. today
22 Cosmological Perturbations Scalar erturbations on longitudinal gauge ds 2 = (1 + 2Ψ)dt 2 + a 2 (t)(1 2Φ)δ ij dx i dx j Perturbed variables ρ( x, t) = ρ 0 (t)(1 + δ( x, t)) φ( x, t) = φ 0 (t) + δφ( x, t) u µ ( x, t) = u µ a v µ ( x, t)
23 Cosmological Perturbations Scalar erturbations on longitudinal gauge ds 2 = (1 + 2Ψ)dt 2 + a 2 (t)(1 2Φ)δ ij dx i dx j Perturbed variables ρ( x, t) = ρ 0 (t)(1 + δ( x, t)) φ( x, t) = φ 0 (t) + δφ( x, t) u µ ( x, t) = u µ a v µ ( x, t)
24 Cosmological Perturbations Scalar erturbations on longitudinal gauge ds 2 = (1 + 2Ψ)dt 2 + a 2 (t)(1 2Φ)δ ij dx i dx j Perturbed variables ρ( x, t) = ρ 0 (t)(1 + δ( x, t)) φ( x, t) = φ 0 (t) + δφ( x, t) u µ ( x, t) = u µ a v µ ( x, t)
25 Cosmological Perturbations Φ M Φ M c s c s m Φ t
26 Conclusions Interactions between dark energy and baryonic matter could be an alternative to some of the dark matter in the Universe. Coulings to the trace of the energy momentum tensor are suitable for this urose: The interaction to the electromagnetic field and to relativistic matter become zero. The continuity equation of matter is reserved. The numerical analysis shows that these models are caable of reroducing the observed background cosmology. Also, that linear erturbations have an accetable behavior.
27 Thank you A.A. and Jorge L. Cervantes-Cota. To be ublished in PRD arxiv:
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