Cosmology with the largest galaxy cluster surveys: Going beyond Fisher matrix forecasts

We make the first detailed MCMC likelihood study of cosmological constraints that are expected from some of the largest, ongoing and proposed, cluster surveys in different wave-bands and compare the estimates to the prevalent Fisher matrix forecasts. Mock catalogs of cluster counts expected from the surveys -- eROSITA, WFXT, RCS2, DES and Planck, along with a mock dataset of follow-up mass calibrations are analyzed for this purpose. A fair agreement between MCMC and Fisher results is found only in the case of minimal models. However, for many cases, the marginalized constraints obtained from Fisher and MCMC methods can differ by factors of 30-100%. The discrepancy can be alarmingly large for a time dependent dark energy equation of state, w(a); the Fisher methods are seen to under-estimate the constraints by as much as a factor of 4--5. Typically, Fisher estimates become more and more inappropriate as we move away from LCDM, to a constant-w dark energy to varying-w dark energy cosmologies. Fisher analysis, also, predicts incorrect parameter degeneracies. From the point of mass-calibration uncertainties, a high value of unknown scatter about the mean mass-observable relation, and its redshift dependence, is seen to have large degeneracies with the cosmological parameters sigma_8 and w(a) and can degrade the cosmological constraints considerably. We find that the addition of mass-calibrated cluster datasets can improve dark energy and sigma_8 constraints by factors of 2--3 from what can be obtained compared to CMB+SNe+BAO only. Since, details of future cluster surveys are still being planned, we emphasize that optimal survey design must be done using MCMC analysis rather than Fisher forecasting. [abridged]Comment: 26 pages, 13 figures, 7 tables, accepted for publication in JCA

On Weighted Multivariate Sign Functions

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.Comment: Keywords: Multivariate sign, Principal component analysis, Data depth, Sufficient dimension reductio

The hybrid SZ power spectrum: Combining cluster counts and SZ fluctuations to probe gas physics

Sunyaev-Zeldovich (SZ) effect from a cosmological distribution of clusters carry information on the underlying cosmology as well as the cluster gas physics. In order to study either cosmology or clusters one needs to break the degeneracies between the two. We present a toy model showing how complementary informations from SZ power spectrum and the SZ flux counts, both obtained from upcoming SZ cluster surveys, can be used to mitigate the strong cosmological influence (especially that of sigma_8) on the SZ fluctuations. Once the strong dependence of the cluster SZ power spectrum on sigma_8 is diluted, the cluster power spectrum can be used as a tool in studying cluster gas structure and evolution. The method relies on the ability to write the Poisson contribution to the SZ power spectrum in terms the observed SZ flux counts. We test the toy model by applying the idea to simulations of SZ surveys.Comment: 12 pages. 11 plots. MNRAS submitte

Precision cosmology with a combination of wide and deep Sunyaev-Zeldovich cluster surveys

We show the advantages of a wedding cake design for Sunyaev-Zel'dovich cluster surveys. We show that by dividing up a cluster survey into a wide and a deep survey, one can essentially recover the cosmological information that would be diluted in a single survey of the same duration due to the uncertainties in our understanding of cluster physics. The parameter degeneracy directions of the deep and wide surveys are slightly different, and combining them breaks these degeneracies effectively. A variable depth survey with a few thousand clusters is as effective at constraining cosmological parameters as a single depth survey with a much larger cluster sample.Comment: 4 figures, 1 table; revised versio