Primordial non-Gaussianity and Dark Energy constraints from Cluster Surveys

TL;DR

This work investigates whether primordial non-Gaussianity, modeled by a local form with parameter $f_{NL}$, biases dark energy constraints from galaxy-cluster counts. Using an ideal SZ-like survey akin to SPT-DES, the authors implement non-Gaussian mass-function models (EPS-based with $F_{NG}=n_{EPS}/n_{PS}$, calibrated against Gaussian N-body results) and perform a Poisson-likelihood analysis across redshift and mass, considering both a constant equation of state $w$ and a time-varying case $w(a)=w_0+(1-a)w_a$. They show that including redshift information largely preserves dark energy constraints under current and near-future CMB priors on $f_{NL}$, though degeneracies with $ sigma_8$ remain, especially when only a single mass bin is used. Expanding to multiple mass bins mitigates these degeneracies and enables cluster data to constrain $f_{NL}$ at a level competitive with galaxy bispectrum probes, providing a robust cross-check for CMB measurements. The study highlights the importance of accounting for non-Gaussianity in cluster analyses while acknowledging neglected systematics, such as mass-observable relations and theoretical uncertainties in the mass function, which could affect real-world applicability.

Abstract

Galaxy cluster surveys will be a powerful probe of dark energy. At the same time, cluster abundance is sensitive to any non-Gaussianity of the primordial density field. It is therefore possible that non-Gaussian initial conditions might be misinterpreted as a sign of dark energy or at least degrade the expected constraints on dark energy parameters. To address this issue, we perform a likelihood analysis of an ideal cluster survey similar in size and depth to the upcoming South Pole Telescope/Dark Energy Survey (SPT-DES). We analyze a model in which the strength of the non-Gaussianity is parameterized by the constant fNL; this model has been used extensively to derive Cosmic Microwave Background (CMB) anisotropy constraints on non-Gaussianity, allowing us to make contact with those works. We find that the constraining power of the cluster survey on dark energy observables is not significantly diminished by non-Gaussianity provided that cluster redshift information is included in the analysis. We also find that even an ideal cluster survey is unlikely to improve significantly current and future CMB constraints on non-Gaussianity. However, when all systematics are under control, it could constitute a valuable cross check to CMB observations.

Figures (4)

• Figure 1: Uncertainty on the mass function $n(M,z)$ due to non-Gaussianity expressed as the ratio between the non-Gaussian to the Gaussian mass function at four different redshifts ($0$, $0.5$, $1$ and $1.5$) for different values of $f\!_{N\!L}$. The inner continuous lines corresponds to the (2-$\sigma$) limits $-27<f\!_{N\!L}<121$ derived from the WMAP (first year) constraints on $f\!_{N\!L}$ by Creminelli:2005hu while the outer continuous lines corresponds to the limits $-243<f\!_{N\!L}<337$ from the expected SDSS galaxy bispectrum constraints Scoccimarro:2003wn computed with the EPS approach, Eq. (\ref{['nEPS']}). The dashed lines, almost coincident with the continuous ones, correspond to the same limits computed by means of the MVJ formula, Eq. (\ref{['nMVJ']}).
• Figure 2: Cluster counts per unit redshift (upper panels) and comoving cluster density (lower panels) as a function of redshift for different values of the non-Gaussian parameter $f\!_{N\!L}$ ($f\!_{N\!L}=\mp 100$, continuous lines), of the dark energy equation of state parameter $w$ ($w=-1.1$ and $-0.9$, short-dashed lines) and of $\sigma_8$ ($\sigma_8=0.85$ and $0.95$, long-dashed lines) compared to the fiducial case (dotted line) with $\sigma_8=0.9$, $w=-1$ and $f\!_{N\!L}=0$. Assumes the mass limit $M_{lim}=1.75\times 10^{14}\, h^{-1} \, {\rm M}_{\odot}$.
• Figure 3: The mass function $n(M,z)$ as a function of the mass $M$ at $z=0$ (upper panels) and $z=1$ (lower panels) for different values of the non-Gaussian parameter $f\!_{N\!L}$ (continuous lines), of the dark energy equation of state parameter $w_0$ (short-dashed lines) and of $\sigma_8$ (long-dashed lines) compared to the fiducial case (dotted line) with $\sigma_8=0.9$, $w=-1$ and $f\!_{N\!L}=0$.
• Figure 4: Forecast marginalized likelihoods and $95\%$ C.L. contour plots from the cluster survey for the 4-parameter ($\Omega_m$, $\sigma_8$, $w$ and $f\!_{N\!L}$) model. In each contour plot, the other two parameters are marginalized over; in each likelihood plot, the other three parameters are marginalized over. We assume a fiducial $\Lambda$CDM model with $\sigma_8=0.9$ and use one mass bin defined by $M>M_{lim}=1.75\times 10^{14}\, h^{-1} \, {\rm M}_{\odot}$.