The Dark Degeneracy: The Dark Fluid and Interacting Cosmic Components Jorge Cervantes In collaboration with Alejandro Avilés National Nuclear Research Institute (ININ), Mexico Cosmology at the Beach, 2012 Standard Model of Cosmology 2 2 2 i i Homogeneus and isotropic (and flat) spacetime:d s = −dt + a (t)δij dx dx . 2 2 a_ 8πG H ≡ = (ρT ) a 3 a¨ 4πG a = − (ρT + 3PT ) a 3 where ρT = ργ + ρν + ρb + ρdm + ρde, which comply with ρ_rel + 4Hρrel = 0; ρ_nonrel + 3Hρnonrel = 0; ρde = const: ··· 2 Two main properties are relevant: clustering dark matter( cs = 0) and accelerating dark energy (PT < −1=3). Standard Model of Cosmology 2 2 2 i i Homogeneus and isotropic (and flat) spacetime:d s = −dt + a (t)δij dx dx . 2 2 a_ 8πG H ≡ = (ρT ) a 3 a¨ 4πG a = − (ρT + 3PT ) a 3 where ρT = ργ + ρν + ρb + ρdm + ρde, which comply with ρ_rel + 4Hρrel = 0; ρ_nonrel + 3Hρnonrel = 0; ρde = const: ··· 2 Two main properties are relevant: clustering dark matter( cs = 0) and accelerating dark energy (PT < −1=3). Standard Model of Cosmology 2 2 2 i i Homogeneus and isotropic (and flat) spacetime:d s = −dt + a (t)δij dx dx . 2 2 a_ 8πG H ≡ = (ρT ) a 3 a¨ 4πG a = − (ρT + 3PT ) a 3 where ρT = ργ + ρν + ρb + ρdm + ρde, which comply with ρ_rel + 4Hρrel = 0; ρ_nonrel + 3Hρnonrel = 0; ρde = const: ··· 2 Two main properties are relevant: clustering dark matter( cs = 0) and accelerating dark energy (PT < −1=3). Standard Model of Cosmology 2 2 2 i i Homogeneus and isotropic (and flat) spacetime:d s = −dt + a (t)δij dx dx . 2 2 a_ 8πG H ≡ = (ρT ) a 3 a¨ 4πG a = − (ρT + 3PT ) a 3 where ρT = ργ + ρν + ρb + ρdm + ρde, which comply with ρ_rel + 4Hρrel = 0; ρ_nonrel + 3Hρnonrel = 0; ρde = const: ··· 2 Two main properties are relevant: clustering dark matter( cs = 0) and accelerating dark energy (PT < −1=3). Supernova Cosmology Project Knop et al. (2003) ΩΜ , ΩΛ 0.25,0.75 0.25, 0 24 1, 0 22 Supernova Cosmology Project B m 20 effective 18 Calan/Tololo & CfA 16 14 1.0 0.5 ΩΜ , ΩΛ 0.25,0.75 0.0 0.25, 0 0.5 1, 0 mag. residual from empty cosmology 1.0 0.0 0.2 0.4 0.6 0.8 1.0 redshift z Dark fluids or dark geometry? Dark Fluid Components 1 obs dark Gµν = T + T 8πG µν µν Any selection of the dark energy-momentum tensor is arbitrary. Dark Geometry 1 dark obs (Gµν + G ) = T 8πG µν µν Any selection of the dark Einstein tensor is arbitrary. ··· A popular choice (historical reasons!): dark dm de Tµν = Tµν + Tµν with: dm Tµν = ρuµuν a perfect fluid of CDM; de Tµν = Λ gµν the cosmological constant; a very successful model , but there are many possibilities. Dark fluids or dark geometry? Dark Fluid Components 1 obs dark Gµν = T + T 8πG µν µν Any selection of the dark energy-momentum tensor is arbitrary. Dark Geometry 1 dark obs (Gµν + G ) = T 8πG µν µν Any selection of the dark Einstein tensor is arbitrary. ··· A popular choice (historical reasons!): dark dm de Tµν = Tµν + Tµν with: dm Tµν = ρuµuν a perfect fluid of CDM; de Tµν = Λ gµν the cosmological constant; a very successful model , but there are many possibilities. Dark fluids or dark geometry? Dark Fluid Components 1 obs dark Gµν = T + T 8πG µν µν Any selection of the dark energy-momentum tensor is arbitrary. Dark Geometry 1 dark obs (Gµν + G ) = T 8πG µν µν Any selection of the dark Einstein tensor is arbitrary. ··· A popular choice (historical reasons!): dark dm de Tµν = Tµν + Tµν with: dm Tµν = ρuµuν a perfect fluid of CDM; de Tµν = Λ gµν the cosmological constant; a very successful model , but there are many possibilities. Dark fluids or dark geometry? Dark Fluid Components 1 obs dark Gµν = T + T 8πG µν µν Any selection of the dark energy-momentum tensor is arbitrary. Dark Geometry 1 dark obs (Gµν + G ) = T 8πG µν µν Any selection of the dark Einstein tensor is arbitrary. ··· A popular choice (historical reasons!): dark dm de Tµν = Tµν + Tµν with: dm Tµν = ρuµuν a perfect fluid of CDM; de Tµν = Λ gµν the cosmological constant; a very successful model , but there are many possibilities. Alternative models to ΛCDM I k-essence I phantom energy I strings’s motived models: ghost condensates, UV corrections to curvature, conformal anomalies. I Non-minimal couplings f (φ)R I dm-de interacting models I Chameleons I Galileons, etc, etc ...and more I MOND I backreaction of perturbations α I Chaplygin gas, p = 1/ρ I Brane worlds: RS, DPG, Gauss Bonnet I Loop Quantum Cosmology I Infrared corrections to curvatures: f(R) I Cosmic voids, archipelago. ...Let’s look at a possible model. Alternative models to ΛCDM I k-essence I phantom energy I strings’s motived models: ghost condensates, UV corrections to curvature, conformal anomalies. I Non-minimal couplings f (φ)R I dm-de interacting models I Chameleons I Galileons, etc, etc ...and more I MOND I backreaction of perturbations α I Chaplygin gas, p = 1/ρ I Brane worlds: RS, DPG, Gauss Bonnet I Loop Quantum Cosmology I Infrared corrections to curvatures: f(R) I Cosmic voids, archipelago. ...Let’s look at a possible model. Alternative models to ΛCDM I k-essence I phantom energy I strings’s motived models: ghost condensates, UV corrections to curvature, conformal anomalies. I Non-minimal couplings f (φ)R I dm-de interacting models I Chameleons I Galileons, etc, etc ...and more I MOND I backreaction of perturbations α I Chaplygin gas, p = 1/ρ I Brane worlds: RS, DPG, Gauss Bonnet I Loop Quantum Cosmology I Infrared corrections to curvatures: f(R) I Cosmic voids, archipelago. ...Let’s look at a possible model. Dark matter from scalar field-baryonic couplings Plethora of couplings: Conformal, trace, non-minimal... Z 4 p R 1 ,α S = d x −g − φ φ,α − V (φ) + S + Sm; 16πG 2 int p with Lint = −gA(φ)T . 2 δ(S + Sm) T = − p int gµν : −g δgµν (φ) α(φ) (m) Gµν = 8πG(Tµν + e Tµν ) dm z}|{ φ int b α(φ) Tµν = Tµν + Tµν +Tµν ; T = e ρ | {z } dark Tµν and 0 0 α(φ) φ − V (φ) = α (φ)e ρ, Dark matter from scalar field-baryonic couplings Plethora of couplings: Conformal, trace, non-minimal... Z 4 p R 1 ,α S = d x −g − φ φ,α − V (φ) + S + Sm; 16πG 2 int p with Lint = −gA(φ)T . 2 δ(S + Sm) T = − p int gµν : −g δgµν (φ) α(φ) (m) Gµν = 8πG(Tµν + e Tµν ) dm z}|{ φ int b α(φ) Tµν = Tµν + Tµν +Tµν ; T = e ρ | {z } dark Tµν and 0 0 α(φ) φ − V (φ) = α (φ)e ρ, Dark matter from scalar field-baryonic couplings Plethora of couplings: Conformal, trace, non-minimal... Z 4 p R 1 ,α S = d x −g − φ φ,α − V (φ) + S + Sm; 16πG 2 int p with Lint = −gA(φ)T . 2 δ(S + Sm) T = − p int gµν : −g δgµν (φ) α(φ) (m) Gµν = 8πG(Tµν + e Tµν ) dm z}|{ φ int b α(φ) Tµν = Tµν + Tµν +Tµν ; T = e ρ | {z } dark Tµν and 0 0 α(φ) φ − V (φ) = α (φ)e ρ, Dark matter from scalar field-baryonic couplings Plethora of couplings: Conformal, trace, non-minimal... Z 4 p R 1 ,α S = d x −g − φ φ,α − V (φ) + S + Sm; 16πG 2 int p with Lint = −gA(φ)T . 2 δ(S + Sm) T = − p int gµν : −g δgµν (φ) α(φ) (m) Gµν = 8πG(Tµν + e Tµν ) dm z}|{ φ int b α(φ) Tµν = Tµν + Tµν +Tµν ; T = e ρ | {z } dark Tµν and 0 0 α(φ) φ − V (φ) = α (φ)e ρ, Background 2 8πG 1 _ 2 α(φ) I H = 3 2 φ + V (φ)+(e − 1)ρ + ρ ¨ _ 0 0 α(φ) 0 −3 I φ + 3Hφ + V (φ) + α (φ)e ρba = 0 1 V (φ) = 1 m2 φ2; eα = 1 + 1 φ2 wdark = − (in slow roll) 2 φ 2 α(φ)− 1+ e 1 ρ0a−3 V (φ) b (0) α(φ)− Ω C = e 1 ρ ≈ DM ≈ 0:3; 1 V (φ) (0) Ω z=0 DE (0) Ω C = eα(φ) − 1 ≈ DM ≈ 4:7 2 (0) Ω z=0 b Background 2 8πG 1 _ 2 α(φ) I H = φ + V (φ)+(e − 1)ρ + ρ V (φ) = 1 m2 φ2; eα = 1 + 1 φ2 3 2 2 φ 2 ¨ _ 0 0 α(φ) 0 −3 I φ + 3Hφ + V (φ) + α (φ)e ρba = 0 1.0 1 wdark = − (in slow roll) eα(φ)−1 1+ ρ0a−3 0.5 V (φ) b (0) dark 0.0 α(φ)− Ω w C = e 1 ρ ≈ DM ≈ 0:3; 1 V (φ) (0) -0.5 Ω z=0 DE (0) Ω α(φ) -1.0 C = e − 1 ≈ DM ≈ 4:7 0.0 0.5 1.0 1.5 2.0 2 (0) Ω a z=0 b Union2 0.40 Union2 data 44 0.35 42 1 0.30 40 m C 38 0.25 36 34 0.20 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 4.2 4.4 4.6 4.8 5.0 5.2 z C2 Linear Perturbations b = 0.01 -0.002 200 -0.003 150 -0.004 Y -0.005 d 100 -0.006 50 -0.007 0.00 0.02 0.04 0.06 0.08 0.10 0 0.00 0.02 0.04 0.06 0.08 0.10 mf t 0.0002 φ_ δφ_ − φ_ 2Ψ − m2 φ δφ 0.0001 2 0 0 φ 0 c = s φ 2 s 0.0000 φ_ δφ_ − φ_ 2Ψ + m2 φ δφ + 1 φ2(δ + 0 δφ) c 0 0 0 φ 2 0 1+ 1 φ 2 -0.0001 2 0 -0.0002 0.00 0.02 0.04 0.06 0.08 0.10 (A.