Signature of dark energy perturbations in cluster counts

1. Signature of dark energy perturbations in cluster counts L. Raul Abramo Physics 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)

2. 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? Dark energy, if not Λ, mustfluctuate ⇒ imprint on CMB & LSS - P(k): linear pert. theory - Halos: nonlinear evolution (“IR v. UV”) Clusters & Cosmology: Bahcal, Fan & Cen ‘97 Haiman, Mohr & Holder ‘00 Battye & Weller ’03 etc. etc. etc..... Outline • 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

3. Top-hat spherical collapse model Gunn & Gott ‘72 tc⇒ zc t Fosalba & Gaztanaga ‘98 Percival ‘01 Mota & van de Bruck ‘04 Mota ‘08 + pressure ⇒ R.A. et al. ‘07 - ‘08 • Matter (CDM + baryons): • EoS of DE (background): • Pressure perturbations of DE: effective sound speed Hu ’02 and others ⇒ in collapsed regions, effective equation of state changes Nunes & Mota ’06 R.A. et al. ‘08 • Exact same equations found in Pseudo-New. approach + top-hat

4. Influence of DE pressure on growth of structure • Linear regime: R.A., Batista, Liberato & Rosenfeld ‘07 w>-1 w<-1 - matter, homog DE - matter, inhom. DE ... DE inhomogeneity • Nonlinear regime: w>-1 w<-1

5. Press-Schechter (1974)... linearly extrapolated density contrast @ zc: spherical collapse equations linear growth function δnl virializ. ~147 δl ~1.7 Viana & Liddle ‘96 • Deviates at most by ~40% from Jenkins et al. (2001) near our fiducial cosmologies, for masses of interest

6. Sensitivity to ceff2only through the mass function z=0.5 z=0.25 z=0 ceff2 (dn/dMce-dn/dM0)/dndM0 z=0 z=0.25 z=0.5 Log10 M (h-1 MO)

7. Hypothetical surveys: “SZ-like” and “WL-like” selection functions Limiting mass: SZ (p) : 7.300 clusters (~SPT/DES ???) WL (p) : 4.600 SZ (nf): 60.000 WL (nf): 280.000 (~LSST) SZ (f): 106 WL (f): 1.5x106 WL/present 14.5 WL/near future SZ/present WL/future SZ/near future 14.0 SZ/future 13.5 0.5 1 1.5 2 • Sky areas: 4.000 deg2 (p), 18.000 deg2 (nf), 30.000 deg2 (f) • 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

8. 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 0 0.5 -0.75 • Fiducial values (DDE):(0.72, 0.25, 0.05, 0.76, -1.1, 0.5, ) Near best-fit: SNLS, Wang ’08, Vikhlinin ‘08 sensitivity to sound speed ~ |1+w| ΛCDM: perturbations are nil, so NO sensitivity to sound speed!

9. Results: SZ, fiducial ceff2=0 • SZ surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=0 • “COSMO” set of priors: WMAP (R) + BAO (A) + HST + BBN • Weak prior on ceff2: σ(ceff2)=1 • All 68% C.L. limits, marginalized present (p) near future (nf) future (f) Ωm Ωm Ωm Black: clusters only ceff2 priors ceff2 prior + COSMO priors COSMO prior COSMO priors ceff2 ceff2 ceff2

10. Results: WL, fiducial ceff2=0 • WL surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=0 present (p) near future (nf) future (f) Ωm Ωm Ωm clusters only ceff2 priors COSMO prior ceff2 prior + COSMO priors COSMO prior ceff2 ceff2 ceff2

11. ceff2: How much of a nuisance? Ωm , σ8 • WL surveys w0=-1.1, wa=0.5, ceff2=0 • Fiducial Ωm=0.25 , σ8=0.76 present near future (nf) future (f) Ωm Ωm Ωm ceff2 prior no ceff2 ceff2 pr. +COSMO pr. COSMO priors no ceff2 + COSMO priors σ8 σ8 σ8

12. ceff2: How much of a nuisance? w0 , wa • SZ and WL surveys w0=-1.1, wa=0.5, ceff2=0 wa wa WL, near future SZ, present clusters only, no priors no ceff2 ceff2 prior COSMO priors ceff2 prior +COSMO priors no ceff2 + COSMO priors w0 w0

13. Results: SZ, fiducial ceff2=+0.5 • SZ surveys (only nf and f) w0=-1.1, wa=0.5, ceff2=+0.5 • “COSMO” set of priors: WMAP (shift) + BAO + HST + BBN • Weak prior on ceff2: σ(ceff2)=1 near future (nf) future (f) clusters only ceff2 prior ceff2 prior + COSMO prior Ωm Ωm COSMO prior ceff2 ceff2

14. ceff2: How much of a nuisance? • SZ surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5 Red: clusters+ceff2 prior Ωm Ωm Blue: clusters + COSMO priors Green: clusters+ceff2 + COSMO priors Brown: no ceff2 Orange: no ceff2 + COSMO priors σ8 σ8 near future (nf) future (f)

15. ceff2: How much of a nuisance? • WL surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5 clusters only Ωm Ωm ceff2 prior ceff2 prior + COSMO COSMO prior no ceff2 + COSMO no ceff2 σ8 σ8 near future (nf) future (f)

16. Moreover... Effective sound speed is just proxy for pressure in halos: • 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 • Inside halos, ceff2 can be positive or negative, in principle (?) Mota & van de Bruck ’04 Supergravity scalar field DE model (Brax & Martin) collapse

17. But take care: on large scales/linear theory, “ceff2“ negative probably absurd - and ruled out Dedeo, Caldwell & Steinhardt ‘03 Weller & Lewis ‘03 Bean & Doré ‘04 ... Takada ’06 Torres-Rodriguez, Cress & Moodley ’07 -’08

18. Results: SZ, ceff2=-0.75 • SZ surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=-0.75 Ωm Ωm Ωm clusters only ceff2 prior COSMO prior (+ceff2 pr.) ceff2 ceff2 ceff2 present (p, SPT-like) near future (nf) future (f)

19. Results: WL, ceff2=-0.75 • WL surveys (p, nf and f) w0=-1.1, wa=0.5, ceff2=-0.75 Ωm Ωm Ωm clusters only ceff2 prior COSMO prior (+ceff2 pr.) ceff2 ceff2 ceff2 present (p, SPT-like) near future (nf) future (f)

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

21. Results: WL, fiducial ceff2=+0.5 • WL surveys (nf and f) w0=-1.1, wa=0.5, ceff2=+0.5 near future (nf) future (f) Black: clusters only Red: clusters +ceff2 priors Ωm Ωm Blue: clusters+COSMO priors Green: clusters +ceff2 + COSMO priors ceff2 ceff2

22. ceff2: How much of a nuisance? Ωm , σ8 • SZ surveys w0=-1.1, wa=0.5, ceff2=0 • Fiducial Ωm=0.25 , σ8=0.76 present near future (nf) future (f) Ωm Ωm Ωm clusters only, no priors ceff2 prior no ceff2 COSMO priors ceff2 prior +COSMO priors no ceff2 + COSMO priors σ8 σ8 σ8

23. ceff2 negative: how much of a nuisance? • SZ surveys w0=-1.1, wa=0.5, ceff2=-0.75 • Fiducial Ωm=0.25 , σ8=0.76 Ωm Ωm Ωm ceff2 prior no ceff2 no ceff2 + COSMO prior COSMO prior σ8 σ8 σ8 present near future (nf) future (f)

24. ceff2 negative: how much of a nuisance? • WL surveys w0=-1.1, wa=0.5, ceff2=-0.75 • Fiducial Ωm=0.25 , σ8=0.76 Ωm Ωm Ωm ceff2 prior no ceff2 no ceff2 + COSMO prior COSMO prior σ8 σ8 σ8 present near future (nf) future (f)

25. Comparing GR with Pseudo-Newtonian approach (linear theory) GR Pseudo-Newtonian Exact Exact w=-0.8 k=0.25 h Mpc-1