Cosmological parameter inference from galaxy clustering: The effect of the posterior distribution of the power spectrum

TL;DR

This paper examines how the choice of posterior distribution shape affects cosmological parameter inference from galaxy survey power spectra, highlighting potential biases and proposing more efficient modeling approaches.

Contribution

It demonstrates that Gaussian posteriors can bias parameter estimates and introduces alternative posterior forms that reduce computational complexity.

Findings

Gaussian posteriors underestimate $f_{NL}$ by 0.4 for Euclid-like data.

Underestimation of $f_{NL}$ is 19.1 for SDSS-III DR9 data.

Alternative posterior forms absorb covariance dependence, simplifying analysis.

Abstract

We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution $\mathcal{P}_R$ we expect for a Gaussian density field $\delta_k$, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with $\mathcal{P}_R$, both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by $f_\mathrm{NL}$. Marginalising over a Gaussian posterior distribution $\mathcal{P}_f$ with fixed covariance matrix yields a posterior mean value of $f_\mathrm{NL}$ which, for a data set with the characteristics of Euclid, will be underestimated by $\triangle f_\mathrm{NL}=0.4$, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by $\triangle f_\mathrm{NL}=19.1$. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.