dark matter from dark energy-baryonic matter...
TRANSCRIPT
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
µν
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
I Dark Degeneracy [M. Kunz PRD 80 , 123001 (2009)]: Dark components inthe Universe are defined through
8πG T darkµν = Gµν − 8πG T obs
µν
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
I Dark Degeneracy [M. Kunz PRD 80 , 123001 (2009)]: Dark components inthe Universe are defined through
8πG T darkµν = Gµν − 8πG T obs
µν
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
I Dark Degeneracy [M. Kunz PRD 80 , 123001 (2009)]: Dark components inthe Universe are defined through
8πG T darkµν = Gµν − 8πG T obs
µν
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.
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
−→ −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 −→ −
14
FµνFµνp−g
I Perfect Fluid
L = −ρp−g + A(φ)T
p−g −→ −eα(φ)ρ
p−g
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
−→ −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 −→ −
14
FµνFµνp−g
I Perfect Fluid
L = −ρp−g + A(φ)T
p−g −→ −eα(φ)ρ
p−g
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
−→ −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 −→ −
14
FµνFµνp−g
I Perfect Fluid
L = −ρp−g + A(φ)T
p−g −→ −eα(φ)ρ
p−g
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
−→ −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 −→ −
14
FµνFµνp−g
I Perfect Fluid
L = −ρp−g + A(φ)T
p−g −→ −eα(φ)ρ
p−g
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
−→ −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 −→ −
14
FµνFµνp−g
I Perfect Fluid
L = −ρp−g + A(φ)T
p−g −→ −eα(φ)ρ
p−g
Interactions with the trace of the energy momentum tensor 2
I Action
S =
Zd4x
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)
Interactions with the trace of the energy momentum tensor 2
I Action
S =
Zd4x
p−g»
R16πG
−12φ,αφ,α − V (φ)− eα(φ)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)
Interactions with the trace of the energy momentum tensor 2
I Action
S =
Zd4x
p−g»
R16πG
−12φ,αφ,α − V (φ)− eα(φ)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)
Interactions with the trace of the energy momentum tensor 2
I Action
S =
Zd4x
p−g»
R16πG
−12φ,αφ,α − V (φ)− eα(φ)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)
Interactions with the trace of the energy momentum tensor 2
I Action
S =
Zd4x
p−g»
R16πG
−12φ,αφ,α − V (φ)− eα(φ)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)
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
φn
I eα(φ) = e− β
MPφ
I V (φ) = 12 m2
φφ2
I eα(φ) = 1 + 12β
φ2
M2p
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
φn
I eα(φ) = e− β
MPφ
I V (φ) = 12 m2
φφ2
I eα(φ) = 1 + 12β
φ2
M2p
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
φn
I eα(φ) = e− β
MPφ
I V (φ) = 12 m2
φφ2
I eα(φ) = 1 + 12β
φ2
M2p
Background Cosmology 2
0.0 0.5 1.0 1.5 2.0-1.0
-0.5
0.0
0.5
1.0
a
Ωda
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
0.5
1.0
1.5
mΦ t
a
Β = 0.01
0.00 0.05 0.10 0.150.0
0.5
1.0
1.5
mΦ t
a
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
34
36
38
40
42
44
z
Μ
Union2 data
z =1a− 1
µ = 5 log10
„dL
Mpc
«+ 25
dL(z) = (1 + z)
Z z
0
dz′
H(z′)
4.2 4.4 4.6 4.8 5.0 5.20.20
0.25
0.30
0.35
0.40
C2
C1
Union2
C1 =eα(φ) − 1
V (φ)ρ
˛˛
today
,
C2 = eα(φ) − 1
˛˛
today
.
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)
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)
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)
Cosmological Perturbations 2
0.00 0.02 0.04 0.06 0.08 0.100.0
0.2
0.4
0.6
0.8
1.0∆
∆0
Β = 0.01
.
0.00 0.02 0.04 0.06 0.08 0.10
-0.002
-0.001
0.000
0.001
0.002
∆Φ
Mp
.
0.00 0.02 0.04 0.06 0.08 0.10
-0.0002
-0.0001
0.0000
0.0001
0.0002
c s2
.
0.00 0.02 0.04 0.06 0.08 0.10-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
mΦ t
Y
0.00 0.05 0.10 0.150.0
0.2
0.4
0.6
0.8
1.0
∆∆
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
∆Φ
Mp
.
0.00 0.05 0.10 0.15
-0.0003
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
c s2
.
0.00 0.05 0.10 0.15
-0.006
-0.005
-0.004
-0.003
-0.002
mΦ t
Y
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