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

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 $△f_{\mathrm{NL}}=0.4$, 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 $△f_{\mathrm{NL}}=19.1$. 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.

9 pages, 7 figures

References in corpus (7)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Primordial non-gaussianity, statistics of collapsed objects, and the Integrated Sachs-Wolfe effect
• The BigBOSS Experiment
• Constraining primordial non-Gaussianity via a multitracer technique with surveys by Euclid and Square Kilometre Array
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Likelihood methods for the combined analysis of CMB temperature and polarisation power spectra
• Non-local bias in the halo bispectrum with primordial non-Gaussianity

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• Matter trispectrum: theoretical modelling and comparison to N-body simulations
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