Signature of dark energy perturbations in cluster counts
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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)
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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.....
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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
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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
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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
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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
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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:
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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
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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
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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
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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
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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
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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)
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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
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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
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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:
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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
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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.)
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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
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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).
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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)
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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
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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
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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
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Comparing GR with Pseudo-Newtonian approach (linear theory)
Pseudo-NewtonianGR
ExactExact
w=-0.8k=0.25 h Mpc-1