voids of dark energy irit maor case western reserve university with sourish dutta prd 75,...
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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?