Optimal Binning of the Primordial Power Spectrum

Abstract

The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. In this paper we will investigate the best scales the primordial power spectrum can be probed, in accordance with the knowledge about other cosmological parameters such as ${\Omega }_b$, ${\Omega }_c$, ${\Omega }_{\Lambda }$, $h$ and $\tau$. The aim is to find the most informative way of measuring the primordial power spectrum at different length scales, using different types of surveys and the information they provide for the desired cosmological parameters. We will find the optimal binning of the primordial power spectrum for this purpose, by making use of the Fisher matrix formalism. We will then find a statistically orthogonal basis for a set of cosmological parameters, mentioned above, and a set of bins of the primordial power spectrum to investigate the correlation between the two sets. For this purpose we make use of principal component analysis and Hermitian square root of the Fisher matrix. The surveys used in this project are Planck and SDSS(BRG), but the formalism can easily be extended to any windowed measurements of the perturbation spectrum.

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