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

Conclusions

Outline

1 Disformal Dark EnergyDisformal TransformationsField Theories from Disformal Relation

2 Disformal QuintessenceLinear PerturbationsParameter Constraints

3 Conclusions

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!

Conclusions

Introduction

∼√−gΛ

If φ ≈ 0

Conclusions

Introduction

∼√−gΛ

If φ ≈ 0

Conclusions

Introduction

∼√−gΛ

If φ ≈ 0

Conclusions

Introduction

∼√−gΛ

If φ ≈ 0

Conclusions

Introduction

]∼√−gΛ

If φ ≈ 0

Conclusions

Introduction

]∼√−gΛ

If φ ≈ 0 can accelerate the universe: ρφ ≈ constant

Conclusions

Introduction

]∼√−gΛ

If φ ≈ 0 can accelerate the universe: ρφ ≈ constant

Conclusions

Disformal Transformations

Conformal transformation: gµν → A(x)gµν

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

⇒ Can slow down the time flow

Conclusions

Modifies causal structure:

g00 ∝ 1− B

Conclusions

Field Theories from the Disformal Relation I

Disformal Prescription

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.

Conclusions

√−g Λ =

√−g [1 +B(∂φ)2]1/2 Λ

is a Chaplygin gas.

Conclusions

√−g Λ =

√−g [1 +B(∂φ)2]1/2 Λ

is a Chaplygin gas.

Conclusions

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

Conclusions

Lφ = −√−g[ε

Conclusions

Lφ = −√−g[ε

Conclusions

0 > 0 Λ Chaplygin gas0 1 V (φ) Tachyon condensate

-1 A(φ) 0 “K-essence”-1 eβφ 0 “Dilatonic ghost”

Lφ = −√−g[ε

Conclusions

Lφ = −√−g[ε

Conclusions

Lφ = −√−g[ε

Conclusions

Lφ = −√−g[ε

Conclusions

Background DynamicsLinear PerturbationsParameter Constraints

Disformal Quintessence

Scalar in purely disformal metric: gµν = gµν +B(φ)φ,µφ,ν

L =√−g R−

√−g[

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

Conclusions

L =√−g R−

√−g[

Tracking solutions

Conclusions

L =√−g R−

√−g[

Tracking solutions

Conclusions

L =√−g R−

√−g[

Tracking solutions

Conclusions

Background Dynamics

Early dark energy:

Ωφ ∝ α−2

Acceleration:

w0 + 1 ∼ α/β

0 2 4 6 8 10 12 14

β = 12 α

α=10α=5

Λ-limit

high α: Negligible amount of early DE

high β/α: Fast transition to wφ ≈ −1

Conclusions

Background Dynamics

Early dark energy:

Ωφ ∝ α−2

Acceleration:

w0 + 1 ∼ α/β -1

0 2 4 6 8 10 12 14

α = 10

β=80αβ=12αβ=3α

Λ-limit

Conclusions

Background Dynamics

Early dark energy:

Ωφ ∝ α−2

Acceleration:

w0 + 1 ∼ α/β -1

0 2 4 6 8 10 12 14

α = 10

β=80αβ=12αβ=3α

Λ-limit

Conclusions

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

Conclusions

Expansion Effects

Conclusions

Expansion Effects

Conclusions

Effects on the CMB

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

10 100 1000

6= normalisation

Angular shift

ISW effect (small)

Conclusions

Effects on the CMB

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

10 100 1000

6= normalisation

Angular shift

ISW effect (small)

Conclusions

Effects on the CMB

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

10 100 1000

6= normalisation

Angular shift

ISW effect (small)

Conclusions

Effects on the CMB

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

10 100 1000

6= normalisation

Angular shift

ISW effect (small)

Conclusions

Effects on the Matter Power

β = 12α

Λ α = 10α = 5

0.0001 0.001 0.01 0.1 1

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

Conclusions

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

0.0001 0.001 0.01 0.1 1

k/h [Mpc-1]

Early DE (α):

Conclusions

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

0.0001 0.001 0.01 0.1 1

k/h [Mpc-1]

Early DE (α):

Less CDM power than Λ

Unknown galaxy bias factorcan compensate

Conclusions

α = 10

Λ β = 80 αβ = 12 αβ = 3 α

β = 1.5 α

0.0001 0.001 0.01 0.1 1

k/h [Mpc-1]

Early DE (α):

Conclusions

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]

Conclusions

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]

Conclusions

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

Conclusions

Excluded Region

α & 10 β/α & 7

Allowed Region

Conclusions

Excluded Region

α & 10 β/α & 7

Allowed Region

Conclusions

Excluded Region

α & 10 β/α & 7

Allowed Region

Conclusions

Excluded Region

α & 10 β/α & 7

Allowed Region

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

Conclusions

Tracking solutions

To Do:

Conclusions

Tracking solutions

To Do:

Conclusions

Tracking solutions

To Do:

Conclusions

Tracking solutions

To Do:

Conclusions

Tracking solutions

To Do:

disformal dark energy · disformal dark energy disformal quintessence conclusions disformal dark...

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