Voids of dark energyIrit MaorIrit Maor

Case Western Reserve UniversityCase Western Reserve University

With Sourish DuttaWith Sourish DuttaPRD 75, gr-qc/0612027PRD 75, gr-qc/0612027

Irit MaorIrit MaorCase Western Reserve UniversityCase Western Reserve University

With Sourish DuttaWith Sourish DuttaPRD 75, gr-qc/0612027PRD 75, gr-qc/0612027

MAY 8, 2007MAY 8, 2007

CCAPP, OSUCCAPP, OSU

MAY 8, 2007MAY 8, 2007

CCAPP, OSUCCAPP, OSU

A very quick summary:A very quick summary:A very quick summary:A very quick summary:

The universe is accelerating. The universe is accelerating. [kinematics][kinematics]

We do not know why.We do not know why. [dynamics][dynamics]

Cosmological constant?Cosmological constant?

120 orders of magnitude!120 orders of magnitude!

The universe is accelerating. The universe is accelerating. [kinematics][kinematics]

We do not know why.We do not know why. [dynamics][dynamics]

Cosmological constant?Cosmological constant?

120 orders of magnitude!120 orders of magnitude!

wmap3:wmap3: w= ¡ 1:062+0:128¡ 0:079

“wmap does not need quintessence ” (Page)

“wmap does not need quintessence ” (Page)

Motivation for the cosmological Motivation for the cosmological constantconstant

Motivation for the cosmological Motivation for the cosmological constantconstant

Bludman, 0702085Bludman, 0702085

But: “CMB needs something else”But: “CMB needs something else”But: “CMB needs something else”But: “CMB needs something else”

Many degeneracies for w(z).Many degeneracies for w(z). Maor et al, 0007297Maor et al, 0007297

Upadhye et al, 0411803Upadhye et al, 0411803

Which parameters?Which parameters? Liddle, 0401198Liddle, 0401198

Which priors?Which priors? Maor et al, 0112526Maor et al, 0112526

Which data sets?Which data sets? Bridle et al, 0303180Bridle et al, 0303180

Many degeneracies for w(z).Many degeneracies for w(z). Maor et al, 0007297Maor et al, 0007297

Upadhye et al, 0411803Upadhye et al, 0411803

Which parameters?Which parameters? Liddle, 0401198Liddle, 0401198

Which priors?Which priors? Maor et al, 0112526Maor et al, 0112526

Which data sets?Which data sets? Bridle et al, 0303180Bridle et al, 0303180

Motivation for dynamical dark energyMotivation for dynamical dark energyMotivation for dynamical dark energyMotivation for dynamical dark energy

A mild generalization of the old standard cosmological A mild generalization of the old standard cosmological model. model.

Scalar fields are not a new concept, “inspired” by Scalar fields are not a new concept, “inspired” by fundamental theories.fundamental theories.

Hopes for dynamical fine tuning.Hopes for dynamical fine tuning.

Probably an ok description of more complicated scenarios.Probably an ok description of more complicated scenarios.

A mild generalization of the old standard cosmological A mild generalization of the old standard cosmological model. model.

Scalar fields are not a new concept, “inspired” by Scalar fields are not a new concept, “inspired” by fundamental theories.fundamental theories.

Hopes for dynamical fine tuning.Hopes for dynamical fine tuning.

Probably an ok description of more complicated scenarios.Probably an ok description of more complicated scenarios.

w=w(z) 6= ¡ 1

..but:..but:..but:..but:

tracker, k-essence, phantom, coupled, …your tracker, k-essence, phantom, coupled, …your favourite DDE modelfavourite DDE model

fine tuning not solved!fine tuning not solved!

tracker, k-essence, phantom, coupled, …your tracker, k-essence, phantom, coupled, …your favourite DDE modelfavourite DDE model

fine tuning not solved!fine tuning not solved!

Other alternativesOther alternativesOther alternativesOther alternatives

SN are wrong SN are wrong

Xtra dimensions (Xtra dimensions ( effective w(z) or coupled effective w(z) or coupled DDE)DDE)

your favourite theory of gravity (your favourite theory of gravity ( same as above) same as above)

super horizon modessuper horizon modes

SN are wrong SN are wrong

Xtra dimensions (Xtra dimensions ( effective w(z) or coupled effective w(z) or coupled DDE)DDE)

your favourite theory of gravity (your favourite theory of gravity ( same as above) same as above)

super horizon modessuper horizon modes

The background:The background:The background:The background:BAOBAOClustersClustersCMBCMBISWISWSNSNSZSZWLWL……

BAOBAOClustersClustersCMBCMBISWISWSNSNSZSZWLWL……

#% for

maybe #% for

w0dwdz

Background measurements will have a very hard time differentiating between CC and DDE.

All focus on w(z).

Null experiments, how far?

Background measurements will have a very hard time differentiating between CC and DDE.

All focus on w(z).

Null experiments, how far?

Looking for the dark stuffLooking for the dark stuffLooking for the dark stuffLooking for the dark stuff

Solar systemSolar system

Extrapolation from the cosmic to the solar scale.Extrapolation from the cosmic to the solar scale.

Clear signature of dark gravity!Clear signature of dark gravity!

Solar systemSolar system

Extrapolation from the cosmic to the solar scale.Extrapolation from the cosmic to the solar scale.

Clear signature of dark gravity!Clear signature of dark gravity!

Looking for the dark stuffLooking for the dark stuffLooking for the dark stuffLooking for the dark stuff

PerturbationsPerturbations

Does DDE cluster on scales less than ~100 Mpc?Does DDE cluster on scales less than ~100 Mpc?

(yes)(yes)

A thorough understanding of the behaviour of A thorough understanding of the behaviour of perturbations is needed.perturbations is needed.

If it clusters, it is not the cosmological constant!!If it clusters, it is not the cosmological constant!!

PerturbationsPerturbations

Does DDE cluster on scales less than ~100 Mpc?Does DDE cluster on scales less than ~100 Mpc?

(yes)(yes)

A thorough understanding of the behaviour of A thorough understanding of the behaviour of perturbations is needed.perturbations is needed.

If it clusters, it is not the cosmological constant!!If it clusters, it is not the cosmological constant!!

Looking for the dark stuffLooking for the dark stuffLooking for the dark stuffLooking for the dark stuff

Non linear regimeNon linear regime

how does the DDE behave?how does the DDE behave?

model sensitivity vs generality?model sensitivity vs generality?

Non linear regimeNon linear regime

how does the DDE behave?how does the DDE behave?

model sensitivity vs generality?model sensitivity vs generality?

In progress, with DuttaIn progress, with Dutta

Implications of inhomogeneities?Implications of inhomogeneities?Implications of inhomogeneities?Implications of inhomogeneities?

Large Scale, CMBLarge Scale, CMBLarge Scale, CMBLarge Scale, CMB

Weller and Lewis, 0307104Weller and Lewis, 0307104

Smaller scale inhomogeneitiesSmaller scale inhomogeneitiesSmaller scale inhomogeneitiesSmaller scale inhomogeneities

Takada, 0606533Takada, 0606533

Maor and Lahav, 0505308Maor and Lahav, 0505308

Nunes et al, 0506043Nunes et al, 0506043

Calculate, instead of parameterize, the Calculate, instead of parameterize, the clustering properties of DDE.clustering properties of DDE.

Calculate, instead of parameterize, the Calculate, instead of parameterize, the clustering properties of DDE.clustering properties of DDE.

L = LG +Lm +LÁ

Standard gravitational actionStandard gravitational action

Standard pressureless fluidStandard pressureless fluid

Standard gravitational actionStandard gravitational action

Standard pressureless fluidStandard pressureless fluid

LGLm

LÁ = 12 (@¹ Á)

2 ¡ V(Á)

V(Á) = 12m2Á2

mH 0

¼1

Linear perturbationLinear perturbationLinear perturbationLinear perturbation

(Synchronous gauge)(Synchronous gauge)

ds2 =dt2 ¡ a2(t)£(1+2³(t;r)) dr2+((1+2Ã(t;r)) r2d­ 2

¤

»´ _³ +2 _Ã

½m(t;r) ! ½m(t) +±½(t;r)

Á(t;r) ! Á(t) +±Á(t;r)

V(Á+±Á) = V(Á) +±V(Á;±Á)

The equationsThe equationsThe equationsThe equations

Zeroth order:Zeroth order: standard FRW evolution of the standard FRW evolution of the background.background.

First order:First order: equations for the perturbation equations for the perturbation variables, which after a Fourier transformation variables, which after a Fourier transformation are ODE’s.are ODE’s.

Zeroth order:Zeroth order: standard FRW evolution of the standard FRW evolution of the background.background.

First order:First order: equations for the perturbation equations for the perturbation variables, which after a Fourier transformation variables, which after a Fourier transformation are ODE’s.are ODE’s.

Initial conditionsInitial conditionsInitial conditionsInitial conditions

Matter:Matter: gaussian, with width well within the gaussian, with width well within the horizon.horizon.

Scalar field:Scalar field: homogeneous IC, with no kinetic homogeneous IC, with no kinetic energy (w=-1). energy (w=-1).

Metric:Metric: by the constraints equations. by the constraints equations.

Results are insensitive to ICResults are insensitive to IC

Matter:Matter: gaussian, with width well within the gaussian, with width well within the horizon.horizon.

Scalar field:Scalar field: homogeneous IC, with no kinetic homogeneous IC, with no kinetic energy (w=-1). energy (w=-1).

Metric:Metric: by the constraints equations. by the constraints equations.

Results are insensitive to ICResults are insensitive to IC

ResultsResultsResultsResults

Anti-correlation between matter and DE perturbationsAnti-correlation between matter and DE perturbations

ResultsResultsResultsResults

Amplitude grows fast!Amplitude grows fast!

ResultsResultsResultsResults

“cross-over”“cross-over”

Equation of StateEquation of StateEquation of StateEquation of State

Background EOSBackground EOS

Linear correction to EOSLinear correction to EOS

First order corrected EOSFirst order corrected EOS

±w= 1½0

¡±p¡ w0±½

¢w0 =

p0½0

=12_Á2¡ V

12_Á2+V

w1 =w0+±w

Equation of stateEquation of stateEquation of stateEquation of state

Spatial profile of the equation of stateSpatial profile of the equation of state

Why a void?Why a void?

Void formationVoid formationVoid formationVoid formation

Energy density correction:

PE correction < 0PE correction < 0 KE correction > 0KE correction > 0

KE correction quickly dominates void KE correction quickly dominates void

±½Á =m2Á±Á+ _Á±_Á

Acceleration slows, but doesn’t change sign.Acceleration slows, but doesn’t change sign.

Á> 0 _Á< 0±Á< 0

±K E >0

±_Á< 0

±PE < 0

ConclusionsConclusionsConclusionsConclusions

DDE develops voids [ripples].

Our results are generic for slow-roll DDE.

Possible interesting dynamics in the non-linear regime.

Observables?

DDE develops voids [ripples].

Our results are generic for slow-roll DDE.

Possible interesting dynamics in the non-linear regime.

Observables?