### [1006.1950] Probability of the most massive cluster under n

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**June 28 2010**This is a very nice calculation demonstrating how the level of primordial non-Gaussianity can be constrained by evaluating the probability that the most massive cluster in a surveyed cosmological volume has a mass in a given range. The paper is closely related to the recent work by Holz & Perlmutter (2010), but extends the calculation to non-Gaussian initial conditions.

The authors show how the local primordial non-Gaussianity parameter, fNL, is degenerate with [tex]\sigma_8[/tex] and use the cluster XMM2235 discovered by Jee et al. (2009) to constrain these 2 parameters. The marginal constraint on fNL thus obtained is 449 +/- 286, although the posterior distribution is highly skewed towards positive fNL (their fig. 4).

The authors make the interesting point that constraints on fNL from massive cluster abundances probe much smaller scales than fNL constraints from the CMB or large-scale halo bias. Combining fNL constraints from these different measurements therefore allows a test of the scale-dependence of fNL.

It would be interesting to know what constraints on fNL could be achieved from observing the most massive cluster in a full-sky survey. From Holz & Perlmutter (2010), the most massive cluster for LCDM in an all-sky survey should have a mass [tex]2\times 10^{15} < M < 10^{16}[/tex] [tex]M_{\odot}[/tex] and would be found at [tex]z[/tex] ~ 0.2. XMM2235 on the other hand has a mass of [tex]6.4\times 10^{14}[/tex] [tex]M_{\odot}[/tex] and is at z = 1.4. From fig. 4 of LoVerde et al. (2007) it looks like the mass functions at these two scales and redshifts (for a nonzero fNL) would differ by < 10%. That is, it looks like the redshift evolution of the mass function for nonzero fNL models partially compensates for probing a higher mass object (which will be found at lower redshift in LCDM). But, maybe the larger survey volume would help increase the sensitivity to fNL?

The authors show how the local primordial non-Gaussianity parameter, fNL, is degenerate with [tex]\sigma_8[/tex] and use the cluster XMM2235 discovered by Jee et al. (2009) to constrain these 2 parameters. The marginal constraint on fNL thus obtained is 449 +/- 286, although the posterior distribution is highly skewed towards positive fNL (their fig. 4).

The authors make the interesting point that constraints on fNL from massive cluster abundances probe much smaller scales than fNL constraints from the CMB or large-scale halo bias. Combining fNL constraints from these different measurements therefore allows a test of the scale-dependence of fNL.

It would be interesting to know what constraints on fNL could be achieved from observing the most massive cluster in a full-sky survey. From Holz & Perlmutter (2010), the most massive cluster for LCDM in an all-sky survey should have a mass [tex]2\times 10^{15} < M < 10^{16}[/tex] [tex]M_{\odot}[/tex] and would be found at [tex]z[/tex] ~ 0.2. XMM2235 on the other hand has a mass of [tex]6.4\times 10^{14}[/tex] [tex]M_{\odot}[/tex] and is at z = 1.4. From fig. 4 of LoVerde et al. (2007) it looks like the mass functions at these two scales and redshifts (for a nonzero fNL) would differ by < 10%. That is, it looks like the redshift evolution of the mass function for nonzero fNL models partially compensates for probing a higher mass object (which will be found at lower redshift in LCDM). But, maybe the larger survey volume would help increase the sensitivity to fNL?