Binning of the primordial power spectrum and optimal galaxy survey design

Abstract

The power spectrum describes the fluctuations in the Universe and encodes much of the cosmological information. Hence measuring different types of power spectra is of great importance in cosmology today. In this thesis we try to constrain two of these power spectra, the primordial power spectrum and the galaxy power spectrum. First we analyse the binning of the primordial power spectrum. 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. We will investigate which scales the primordial power spectrum can best be probed, in accordance with the knowledge about other cosmological parameters. The aim is to find the most informative way of measuring the primordial power spectrum at different length scales, using different types of surveys, such as Planck and SDSS (Bright Red Galaxy). For this we make use of the Fisher matrix formalism, principal component analysis and Hermitian square root of the Fisher matrix. This method of binning of the primordial power spectrum is then applied to the reconstruction of this power spectrum from WMAP and simulated Planck data. Here a new method for the reconstructing, directly from observations of the Cosmic Microwave Background (CMB), is introduced. Finally, we investigate the optimal observing strategy for measuring galaxy/matter power spectrum. These power spectra are of great importance in cosmology. Measuring this spectrum will enable us to measure other cosmological parameters. If we are only interested in the large scale power spectrum then we might gain more by sparsely observing a larger patch of sky, for the same observing time, rather than observing a smaller contiguous area. We will investigate the advantages and disadvantages of this strategy using Bayesian Experimental Design.