Signature of dark energy perturbations in cluster counts

L. Raul AbramoPhysics Institute

Univ. of São Paulo

work with R. Batista (USP) - see also his talk!

R. Rosenfeld (IFT) - should have seen his talk!& L. Liberato (IFT)

arXiv: 0902.3226+ 0707.2882 (JCAP), 0710.2368 (PRD), 0806.3461 (PRD)

Outline

Dark energy, if not Λ, must fluctuate ⇒ imprint on CMB & LSS

- P(k): linear pert. theory- Halos: nonlinear evolution (“IR v. UV”)

Use a generalized spherical collapse model (top-hat profile) and Press-Schechter to compute the mass function Observations: assumed hypothetical SZ and WL cluster

surveys with very simple ansatz for limiting mass Forecasts: Fisher matrix in 7-parameter space

Q: is it possible (will it ever be possible) to detect the influence of dark energy perturbations on number counts of galaxy clusters? Order of magnitude?

Clusters & Cosmology:Bahcal, Fan & Cen ‘97

Haiman, Mohr & Holder ‘00Battye & Weller ’03

etc. etc. etc.....

Top-hat spherical collapse model

EoS of DE (background): Pressure perturbations of DE: effective sound speed

Exact same equations found in Pseudo-New. approach + top-hat

Matter (CDM + baryons):

t

Gunn & Gott ‘72

R.A. et al. ‘07 - ‘08

⇒ in collapsed regions, effective equation of state changes Nunes & Mota ’06R.A. et al. ‘08

tc ⇒ zc

+ pressure ⇒

Fosalba & Gaztanaga ‘98 Percival ‘01

Mota & van de Bruck ‘04Mota ‘08

Hu ’02and others

Influence of DE pressure on growth of structureR.A., Batista, Liberato & Rosenfeld ‘07 Linear regime:

w>-1 w<-1

- matter, homog DE- matter, inhom. DE

... DE inhomogeneity

Nonlinear regime:w>-1 w<-1

Press-Schechter (1974)...

Viana & Liddle ‘96

Deviates at most by ~40% from Jenkins et al. (2001) near our fiducial cosmologies, for masses of interest

linearly extrapolated density contrast @ zc:spherical collapse equations

δnl

δl~1.7

~147

virializ.

linear growth function

Sensitivity to ceff2 only through the mass function

Log10 M (h-1 MO)

(dn/

dMce

-dn/

dM0)

/dnd

M0

z=0

z=0.25

z=0.5

z=0

z=0.25

z=0.5

ceff2

Hypothetical surveys: “SZ-like” and “WL-like” selection functions

WL/present

SZ/present

WL/near future

SZ/near futureWL/future

SZ/future

Binning:✴ 3, 5 and 8 mass bins for p, nf and f surveys ✴ 10, 15 and 25 redshift bins for p, nf and f surveys

14.5

14.0

13.5

Sky areas: 4.000 deg2 (p), 18.000 deg2 (nf), 30.000 deg2 (f)

SZ (p) : 7.300 clusters (~SPT/DES ???)WL (p) : 4.600

SZ (nf): 60.000WL (nf): 280.000 (~LSST)

SZ (f): 106

WL (f): 1.5x106210.5 1.5

Limiting mass:

Statistics: Fisher matrix Only Poisson (shot) noise

Fisher matrix:

Unmarginalized 68% C.L. limits on θa :

Marginalized 68% C.L. limits on θa :

θa : 7-parameter space

Fiducial values (DDE): (0.72, 0.25, 0.05, 0.76, -1.1, 0.5, )

00.5

-0.75

sensitivity to sound speed ~ |1+w|ΛCDM: perturbations are nil, so NO sensitivity to sound speed!

Near best-fit: SNLS, Wang ’08, Vikhlinin ‘08

Results: SZ, fiducial ceff2=0 SZ surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=0

ceff2ceff

2

Ωm Ωm

Black: clusters only

COSMOpriors

ceff2 priors

ceff2 prior

+ COSMO priors

“COSMO” set of priors: WMAP (R) + BAO (A) + HST + BBN Weak prior on ceff2: σ(ceff2)=1

present (p) future (f)near future (nf) All 68% C.L. limits, marginalized

Ωm

ceff2

COSMOprior

Results: WL, fiducial ceff2=0

WL surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=0

ceff2ceff

2

Ωm Ωm

clusters only

COSMOprior

ceff2 priors

ceff2 prior

+ COSMO priors

present (p) future (f)near future (nf)Ωm

ceff2

COSMOprior

ceff2: How much of a nuisance?Ωm , σ8

WL surveys w0=-1.1, wa=0.5, ceff2=0

σ8

Ωm

ceff2 prior

near future (nf)

Ωm

future (f)

COSMOpriors

ceff2 pr. +COSMO pr.

no ceff2

no ceff2

+ COSMOpriors

σ8

present

Fiducial Ωm=0.25 , σ8=0.76

Ωm

σ8

SZ and WL surveys w0=-1.1, wa=0.5, ceff2=0

wa

ceff2 prior

WL, near future

COSMO priorsceff

2 prior+COSMO priors

no ceff2

no ceff2

+ COSMO priors

SZ, present

clusters only, no priors

ceff2: How much of a nuisance?w0 , wa

wa

w0w0

Results: SZ, fiducial ceff2=+0.5 SZ surveys (only nf and f) w0=-1.1, wa=0.5,

ceff2=+0.5

ceff2ceff

2

Ωm Ωm

clusters only

COSMOprior

ceff2 prior

ceff2 prior

+ COSMOprior

“COSMO” set of priors: WMAP (shift) + BAO + HST + BBN Weak prior on ceff2: σ(ceff2)=1

near future (nf) future (f)

ceff2: How much of a nuisance?

SZ surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5

σ8

ΩmRed: clusters+ceff

2 prior

near future (nf)

Ωm

future (f)

Blue: clusters+ COSMO priors

Green: clusters+ceff2

+ COSMO priorsBrown: no ceff

2

Orange: no ceff2 + COSMO priors

σ8

ceff2: How much of a nuisance?

WL surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5

σ8

Ωm

ceff2 prior

near future (nf)

Ωm

future (f)

COSMOprior

ceff2 prior

+ COSMO

no ceff2no ceff

2 + COSMO

σ8

clusters only

Moreover...

Mota & van de Bruck ’04Supergravity scalar field DE model (Brax & Martin)

Pressure in collapsed region depends on model of DE (scalar field, K-essence, ...) - sound speed sq. in collapsed regions need not be same as linear theory sound speed

collapcollapsese

Inside halos, ceff2 can be positive or negative, in principle (?)

Effective sound speed is just proxy for pressure in halos:

But take care: on large scales/linear theory, “ceff2“ negative probably absurd - and ruled

out

Takada ’06

Dedeo, Caldwell & Steinhardt ‘03Weller & Lewis ‘03

Bean & Doré ‘04 ...

Torres-Rodriguez, Cress & Moodley ’07 -’08

Results: SZ, ceff2=-0.75 SZ surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=-

0.75

ceff2ceff

2

Ωm Ωm

clusters only

ceff2 prior

present (p, SPT-like) near future (nf)

Ωm

ceff2

future (f)

COSMO prior (+ceff

2 pr.)

Results: WL, ceff2=-0.75 WL surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=-

0.75

ceff2ceff

2

Ωm Ωm

ceff2 prior

present (p, SPT-like) near future (nf)

Ωm

ceff2

future (f)

COSMO prior (+ceff

2 pr.)

clusters only

Conclusions

Although our numbers should be taken with a , dark energy perturbations may have a measurable impact on nonlinear structure formation - but only if DDE far from ΛCDM Would be fantastic to have a solid theory of nonlinear

structure formation in the presence of dark energy perturbations. THEN we could realistically forecast the sensitivity of

number counts (as well as many other observables in nonlinear regime) to the clustering properties of dark energy

To learn about the nature of dark energy, we must study its perturbations (linear and nonlinear).

Results: WL, fiducial ceff2=+0.5

WL surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5

ceff2ceff

2

Ωm Ωm

Black: clusters only

Blue: clusters+COSMO priors

Red: clusters+ceff

2 priors

Green: clusters+ceff

2 + COSMO priors

near future (nf) future (f)

SZ surveys w0=-1.1, wa=0.5, ceff2=0

σ8

Ωm

ceff2 prior

near future (nf)

Ωm

future (f)

COSMO priorsceff

2 prior+COSMO priors

no ceff2

no ceff2

+ COSMOpriors

σ8

present

Fiducial Ωm=0.25 , σ8=0.76

clusters only, no priors

σ8

Ωm

ceff2: How much of a nuisance?Ωm , σ8

ceff2 negative: how much of a nuisance?

SZ surveys w0=-1.1, wa=0.5, ceff2=-0.75

σ8

Ωm

ceff2 prior

near future (nf)

Ωm

future (f)

COSMOprior

no ceff2

no ceff2

+ COSMOprior

σ8

present

Fiducial Ωm=0.25 , σ8=0.76

σ8

Ωm

ceff2 negative: how much of a nuisance?

WL surveys w0=-1.1, wa=0.5, ceff2=-0.75

σ8

Ωm

ceff2 prior

near future (nf)

Ωm

future (f)

COSMOprior

no ceff2

no ceff2

+ COSMOprior

σ8

present

Fiducial Ωm=0.25 , σ8=0.76

Ωm

σ8

Comparing GR with Pseudo-Newtonian approach (linear theory)

Pseudo-NewtonianGR

ExactExact

w=-0.8k=0.25 h Mpc-1