Dark matter from Dark Energy-Baryonic Matter...

Dark matter from Dark Energy-Baryonic Matter Couplings

Alejandro Avilés 1,2

1Instituto de Ciencias Nucleares, UNAM, México

2Instituto Nacional de Investigaciones Nucleares (ININ) México

January 10, 2010Cosmología en la Playa 2011

Puerto Vallarta

Outline

I Motivations

I Interactions with the Trace of the Energy Momentum Tensor

I Background Cosmology

I Cosmological Perturbations

I Summary and Conclusions

Motivations

I Dark Degeneracy [M. Kunz PRD 80 , 123001 (2009)]: Dark components inthe Universe are defined through

8πG T darkµν = Gµν − 8πG T obs

I Interacting models between dark energy and matter fields havebeen proposed in order to amelliorate the Coincidence Problem.

I But, this interactions give rise to long range undetected new forces.I Some screening mechanism have been proposed in order to evade fifth forces and

equivalence principle tests.[Khoury and Weltman PRD 69 , 044026 (2004)]

I In some interactions the continuity equation of baryonic matter ispreserved.

Motivations

Interactions with the trace of the energy momentum tensor 1

S = Sφ + Sm + Sint Sint =

Zd4x A(φ)T

p−g.

T = gµνTµν , Tµν = −2√−g

δ(Sm + Sint)

δgµν

I Fermionic Field

L = −p−g ψ(iγµ∂µ −m)ψ + A(φ)T

−→ −p−g ψ(iγµ∂µ − eα(φ)m)ψ

eα(φ) =1

1− A(φ)

I Electromagnetic Field

L = −14

FµνFµνp−g + A(φ)T

p−g −→ −

FµνFµνp−g

I Perfect Fluid

L = −ρp−g + A(φ)T

p−g −→ −eα(φ)ρ

Zd4x A(φ)T

p−g.

δ(Sm + Sint)

δgµν

I Fermionic Field

eα(φ) =1

1− A(φ)

L = −14

p−g −→ −

FµνFµνp−g

I Perfect Fluid

Zd4x A(φ)T

p−g.

δ(Sm + Sint)

δgµν

I Fermionic Field

eα(φ) =1

1− A(φ)

L = −14

p−g −→ −

FµνFµνp−g

I Perfect Fluid

Zd4x A(φ)T

p−g.

δ(Sm + Sint)

δgµν

I Fermionic Field

eα(φ) =1

1− A(φ)

L = −14

p−g −→ −

FµνFµνp−g

I Perfect Fluid

Zd4x A(φ)T

p−g.

δ(Sm + Sint)

δgµν

I Fermionic Field

eα(φ) =1

1− A(φ)

L = −14

p−g −→ −

FµνFµνp−g

I Perfect Fluid

I Action

p−g»

R16πG

−12φ,αφ,α − V (φ)− A(φ)T − ρ

I Field EquationsGµν = 8πG(Tφµν + eα(φ)T b

µν),

φ− V ′(φ) = α′(φ)eα(φ)ρ,

Vef (φ) = V (φ) + eα(φ)ρ.

I Conservation Equations:

1. Continuity Equation∇µ(ρ uµ) = 0,

2. Geodesic Equationuµ∇µuν = −α′(φ)(gµν + uµuν)∂µφ.

I Newtonian Limitd2~Xdt2

= −∇ΦN −∇α(φ)

I Action

p−g»

R16πG

−12φ,αφ,α − V (φ)− eα(φ)ρ

µν),

φ− V ′(φ) = α′(φ)eα(φ)ρ,

= −∇ΦN −∇α(φ)

I Action

p−g»

R16πG

µν),

φ− V ′(φ) = α′(φ)eα(φ)ρ,

= −∇ΦN −∇α(φ)

I Action

p−g»

R16πG

µν),

φ− V ′(φ) = α′(φ)eα(φ)ρ,

= −∇ΦN −∇α(φ)

I Action

p−g»

R16πG

µν),

φ− V ′(φ) = α′(φ)eα(φ)ρ,

= −∇ΦN −∇α(φ)

Background Cosmology 1

I H2 = 8πG3

“12 φ

2 + V (φ) + (eα(φ) − 1)ρ+ ρ”

I φ+ 3Hφ+ V ′(φ) + α′(φ)eα(φ)ρ = 0I ρ+ 3Hρ = 0

ρdark = ρφ + (eα(φ) − 1)ρ

ρdark + 3H(1 + wdark )ρdark = 0, wdark ≈ −1

1 + eα(φ)−1V (φ)

ρ0a−3.

I V (φ) = Mn+4

I eα(φ) = e− β

I V (φ) = 12 m2

I eα(φ) = 1 + 12β

I H2 = 8πG3

“12 φ

2 + V (φ) + (eα(φ) − 1)ρ+ ρ”

1 + eα(φ)−1V (φ)

ρ0a−3.

I V (φ) = Mn+4

I eα(φ) = e− β

I V (φ) = 12 m2

I eα(φ) = 1 + 12β

I H2 = 8πG3

“12 φ

2 + V (φ) + (eα(φ) − 1)ρ+ ρ”

1 + eα(φ)−1V (φ)

ρ0a−3.

I V (φ) = Mn+4

I eα(φ) = e− β

I V (φ) = 12 m2

I eα(φ) = 1 + 12β

0.0 0.5 1.0 1.5 2.0-1.0

rkI ——– β = 1I · · · · · · β = 0.2I ——– β = 0.04I - - - - - ΛCDM

β = 0.04 ⇒β

M2p' G

0.00 0.02 0.04 0.06 0.08 0.100.0

Β = 0.01

0.00 0.05 0.10 0.150.0

Β = 0.04

Supernovae Ia Fit

UNION 2 [R. Amanullah et al. (SCP), Astrophys. J. 716, 712 (2010).]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Union2 data

z =1a− 1

µ = 5 log10

«+ 25

dL(z) = (1 + z)

H(z′)

4.2 4.4 4.6 4.8 5.0 5.20.20

Union2

C1 =eα(φ) − 1

V (φ)ρ

C2 = eα(φ) − 1

Cosmological Perturbations

I Scalar perturbations on longitudinal gauge

ds2 = −(1 + 2Ψ)dt2 + a2(t)(1− 2Φ)δij dx i dx j

I Perturbed variables

ρ(~x , t) = ρ0(t)(1 + δ(~x , t))

φ(~x , t) = φ0(t) + δφ(~x , t)

uµ(~x , t) = uµ0 +1a

vµ(~x , t)

ρ(~x , t) = ρ0(t)(1 + δ(~x , t))

φ(~x , t) = φ0(t) + δφ(~x , t)

uµ(~x , t) = uµ0 +1a

vµ(~x , t)

ρ(~x , t) = ρ0(t)(1 + δ(~x , t))

φ(~x , t) = φ0(t) + δφ(~x , t)

uµ(~x , t) = uµ0 +1a

vµ(~x , t)

Cosmological Perturbations 2

0.00 0.02 0.04 0.06 0.08 0.100.0

1.0∆

Β = 0.01

0.00 0.02 0.04 0.06 0.08 0.10

-0.002

-0.001

0.00 0.02 0.04 0.06 0.08 0.10

-0.0002

-0.0001

0.0000

0.0001

0.0002

0.00 0.02 0.04 0.06 0.08 0.10-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

0.00 0.05 0.10 0.150.0

∆∆

Β = 0.04

0.00 0.05 0.10 0.15

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.00 0.05 0.10 0.15

-0.0003

-0.0002

-0.0001

0.0000

0.0001

0.0002

0.0003

0.00 0.05 0.10 0.15

-0.006

-0.005

-0.004

-0.003

-0.002

Conclusions

I Interactions between dark energy and baryonic matter could bean alternative to some of the dark matter in the Universe.

I Couplings to the trace of the energy momentum tensor aresuitable for this purpose:

I The interaction to the electromagnetic field and to relativistic matter become zero.I The continuity equation of matter is preserved.

I The numerical analysis shows that these models are capable ofreproducing the observed background cosmology. Also, thatlinear perturbations have an acceptable behavior.

Thank you

A.A. and Jorge L. Cervantes-Cota. To be published in PRDarXiv: 1012.3203

Dark matter from Dark Energy-Baryonic Matter...

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