Disformal Dark Energy · Disformal Dark Energy Disformal Quintessence Conclusions Disformal Dark...
Transcript of Disformal Dark Energy · Disformal Dark Energy Disformal Quintessence Conclusions Disformal Dark...
Disformal Dark EnergyDisformal Quintessence
Conclusions
Disformal Dark Energyand Disformal Quintessence
Miguel Zumalacarregui
Institute of Cosmos Sciences, University of Barcelona
with T. Koivisto, D. Mota and P. Ruiz-Lapuente
5th Iberian Cosmology Meeting, Porto, March 2010
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Outline
1 Disformal Dark EnergyDisformal TransformationsField Theories from Disformal Relation
2 Disformal QuintessenceLinear PerturbationsParameter Constraints
3 Conclusions
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]
∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]
∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]
∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]
∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]
∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0
can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0 can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Introduction
Universe’s expansion accelerates (CMB, SNe, BAO...)
Λ, exotic matter, modifications of gravity, inhomogeneities...
Scalar Fields - Quintessence
Lφ =√−g[gµνφ,µφ,ν+V (φ)
]∼√−gΛ
Can track matter density: ρφ ∝ ρm
If φ ≈ 0 can accelerate the universe: ρφ ≈ constant
Need slow down mechanism!
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure:
g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Disformal Transformations
Conformal transformation: gµν → A(x)gµν
Disformal Transformations
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Most general relation that respects covariance and causality,
Only introduces a scalar d.o.f. φ(x)
Modifies causal structure: g00 ∝ 1− B
Aφ2
⇒ Can slow down the time flow
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation I
Disformal Prescription
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Replace gµν → gµν in some sector of the Lagrangian
Simplest example: Λ living in a disformal metric (A = 1)
√−g Λ =
√−g [1 +B(∂φ)2]1/2 Λ
is a Chaplygin gas.
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation I
Disformal Prescription
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Replace gµν → gµν in some sector of the Lagrangian
Simplest example: Λ living in a disformal metric (A = 1)
√−g Λ =
√−g [1 +B(∂φ)2]1/2 Λ
is a Chaplygin gas.
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation I
Disformal Prescription
gµν = A(φ)gµν +B(φ)φ,µφ,ν
Replace gµν → gµν in some sector of the Lagrangian
Simplest example: Λ living in a disformal metric (A = 1)
√−g Λ =
√−g [1 +B(∂φ)2]1/2 Λ
is a Chaplygin gas.
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate
-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
IntroductionDisformal TransformationsField Theories from Disformal Relation
Field Theories from the Disformal Relation II
ε B(φ) V (φ) Model
0 0 Λ Cosmological constant1 0 V (φ) Quintessence-1 0 V (φ) Phantom quintessence
0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”
1 > 0 V (φ) Disformal quintessence-1 ? ? Disformal phantom ?
Lφ = −√−g[ε
2gµνφ,µφ,ν + V (φ)
]; gµν = A(φ)gµν +B(φ)φ,µφ,ν
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Disformal Quintessence
Scalar in purely disformal metric: gµν = gµν +B(φ)φ,µφ,ν
L =√−g R−
√−g[
12gµνφ,µφ,ν + V (φ)
]+ Lm
Disformal Features negligible at early times
V (φ) = exp[−αφ/Mp]
Tracking solutions
B(φ) = exp[β(φ+ φx)/Mp]
Transition if β > α
φx → transition time → Ωφ
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Disformal Quintessence
Scalar in purely disformal metric: gµν = gµν +B(φ)φ,µφ,ν
L =√−g R−
√−g[
12gµνφ,µφ,ν + V (φ)
]+ Lm
Disformal Features negligible at early times
V (φ) = exp[−αφ/Mp]
Tracking solutions
B(φ) = exp[β(φ+ φx)/Mp]
Transition if β > α
φx → transition time → Ωφ
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Disformal Quintessence
Scalar in purely disformal metric: gµν = gµν +B(φ)φ,µφ,ν
L =√−g R−
√−g[
12gµνφ,µφ,ν + V (φ)
]+ Lm
Disformal Features negligible at early times
V (φ) = exp[−αφ/Mp]
Tracking solutions
B(φ) = exp[β(φ+ φx)/Mp]
Transition if β > α
φx → transition time → Ωφ
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Disformal Quintessence
Scalar in purely disformal metric: gµν = gµν +B(φ)φ,µφ,ν
L =√−g R−
√−g[
12gµνφ,µφ,ν + V (φ)
]+ Lm
Disformal Features negligible at early times
V (φ) = exp[−αφ/Mp]
Tracking solutions
B(φ) = exp[β(φ+ φx)/Mp]
Transition if β > α
φx → transition time → Ωφ
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Background Dynamics
Early dark energy:
Ωφ ∝ α−2
Acceleration:
w0 + 1 ∼ α/β
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12 14
Ωφ
z
β = 12 α
α=10α=5
Λ-limit
high α: Negligible amount of early DE
high β/α: Fast transition to wφ ≈ −1
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Background Dynamics
Early dark energy:
Ωφ ∝ α−2
Acceleration:
w0 + 1 ∼ α/β -1
-0.8
-0.6
-0.4
-0.2
0
0 2 4 6 8 10 12 14
wφ
z
α = 10
β=80αβ=12αβ=3α
Λ-limit
high α: Negligible amount of early DE
high β/α: Fast transition to wφ ≈ −1
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Background Dynamics
Early dark energy:
Ωφ ∝ α−2
Acceleration:
w0 + 1 ∼ α/β -1
-0.8
-0.6
-0.4
-0.2
0
0 2 4 6 8 10 12 14
wφ
z
α = 10
β=80αβ=12αβ=3α
Λ-limit
high α: Negligible amount of early DE
high β/α: Fast transition to wφ ≈ −1
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Linear Perturbations
Equations involved, different from Λ in
Expansion Effects
Early dark energy: H2 ∝ ρm + ρφ ⇒ reduces matter growth
Acceleration: Dilutes linear structure, ↓ wφ ⇒↑ acc. time
DE perturbations → speed of sound c2s ≈ 1− δg00
Before transition: c2s ≈ 1
Transition: 0 < c2s < 1, but DE perturbations well supressed
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Linear Perturbations
Equations involved, different from Λ in
Expansion Effects
Early dark energy: H2 ∝ ρm + ρφ ⇒ reduces matter growth
Acceleration: Dilutes linear structure, ↓ wφ ⇒↑ acc. time
DE perturbations → speed of sound c2s ≈ 1− δg00
Before transition: c2s ≈ 1
Transition: 0 < c2s < 1, but DE perturbations well supressed
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Linear Perturbations
Equations involved, different from Λ in
Expansion Effects
Early dark energy: H2 ∝ ρm + ρφ ⇒ reduces matter growth
Acceleration: Dilutes linear structure, ↓ wφ ⇒↑ acc. time
DE perturbations → speed of sound c2s ≈ 1− δg00
Before transition: c2s ≈ 1
Transition: 0 < c2s < 1, but DE perturbations well supressed
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the CMB
α = 10
l(l+
1)/2
π C
l
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.01
0.1
1
10 100 1000
l
6= normalisation
Angular shift
ISW effect (small)
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the CMB
α = 10
l(l+
1)/2
π C
l
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.01
0.1
1
10 100 1000
l
6= normalisation
Angular shift
ISW effect (small)
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the CMB
α = 10
l(l+
1)/2
π C
l
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.01
0.1
1
10 100 1000
l
6= normalisation
Angular shift
ISW effect (small)
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the CMB
α = 10
l(l+
1)/2
π C
l
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.01
0.1
1
10 100 1000
l
6= normalisation
Angular shift
ISW effect (small)
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the Matter Power
β = 12α
P(k
)
Λ α = 10α = 5
0.1
1
0.0001 0.001 0.01 0.1 1
dev.
%
k/h [Mpc-1]
Early DE (α):
Higher H(z) reduces growth
Acceleration (β/α):
Longer structure wash out
Constraints from LSS
Less CDM power than ΛUnknown galaxy bias factorcan compensate
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the Matter Power
α = 10
P(k
)
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.1
1
0.0001 0.001 0.01 0.1 1
dev.
%
k/h [Mpc-1]
Early DE (α):
Higher H(z) reduces growth
Acceleration (β/α):
Longer structure wash out
Constraints from LSS
Less CDM power than ΛUnknown galaxy bias factorcan compensate
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the Matter Power
α = 10
P(k
)
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.1
1
0.0001 0.001 0.01 0.1 1
dev.
%
k/h [Mpc-1]
Early DE (α):
Higher H(z) reduces growth
Acceleration (β/α):
Longer structure wash out
Constraints from LSS
Less CDM power than Λ
Unknown galaxy bias factorcan compensate
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Effects on the Matter Power
α = 10
P(k
)
Λ β = 80 αβ = 12 αβ = 3 α
β = 1.5 α
0.1
1
0.0001 0.001 0.01 0.1 1
dev.
%
k/h [Mpc-1]
Early DE (α):
Higher H(z) reduces growth
Acceleration (β/α):
Longer structure wash out
Constraints from LSS
Less CDM power than ΛUnknown galaxy bias factorcan compensate
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints I
MCMC: vary α, β/α + 6 parameters
Data from:
- WMAP7- SNe- BAO- LRG
Luminous red galaxies: Best galaxy bias in range [1, 3]
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints I
MCMC: vary α, β/α + 6 parameters
Data from:
- WMAP7- SNe- BAO- LRG
Luminous red galaxies: Best galaxy bias in range [1, 3]
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints II
Filled: Full Data / Lines: BAO+SNe
Excluded Region
α & 10 β/α & 7
Significant early DE (∼ 3%)
Slow transition / high wφ
LSS important → bias
Allowed Region
Compatible with Λ limit
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints II
Filled: Full Data / Lines: BAO+SNe
Excluded Region
α & 10 β/α & 7
Significant early DE (∼ 3%)
Slow transition / high wφ
LSS important → bias
Allowed Region
Compatible with Λ limit
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints II
Filled: Full Data / Lines: BAO+SNe
Excluded Region
α & 10 β/α & 7
Significant early DE (∼ 3%)
Slow transition / high wφ
LSS important → bias
Allowed Region
Compatible with Λ limit
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints II
Filled: Full Data / Lines: BAO+SNe
Excluded Region
α & 10 β/α & 7
Significant early DE (∼ 3%)
Slow transition / high wφ
LSS important → bias
Allowed Region
Compatible with Λ limit
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Background DynamicsLinear PerturbationsParameter Constraints
Observational Constraints II
Filled: Full Data / Lines: BAO+SNe
Excluded Region
α & 10 β/α & 7
Significant early DE (∼ 3%)
Slow transition / high wφ
LSS important → bias
Allowed Region
Compatible with Λ limit
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy
Disformal Dark EnergyDisformal Quintessence
Conclusions
Conclusions
Disformal prescription recovers many scalar field DE models
Simple mechanism to induce a slow roll phase
Disformal Quintessence is a good Λ imitator
Tracking solutions
Needs choice of φx → Ωde
To Do:
Disformal couplings for matter/radiation/gravity
Miguel Zumalacarregui Disformal Dark Energy