Binning of the primordial power spectrum and optimal galaxy survey design

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

True cosmic microwave background power spectrum estimation

International audienceAims. The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost the entire statistical information of CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. We aim to recover the true underlying CMB power spectrum from the one realization that we have without knowing the cosmological parameters. Methods. The sparsity of the CMB power spectrum is rst investigated in two dictionaries; discrete cosine transform (DCT) and wavelet transform (WT). The CMB power spectrum can be recovered with very few coe cients in these two dictionaries and hence is very compressible. Results. We studied the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we developed a technique that estimates the true underlying CMB power spectrum from data, i.e., without a need to know the cosmological parameters. Conclusions. This smooth estimated spectrum can be used to simulate CMB maps with similar properties as the true CMB simulations with the correct cosmological parameters. This allows us to perform Monte Carlo simulations in a given project without having to know the cosmological parameters. The developed IDL code, TOUSI, for theoretical power spectrum using sparse estimation, will be released with the next version of ISAP

Optimal 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. 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

Reconstruction of the Primordial Power Spectrum by Direct Inversion

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters.Comment: 23 pages, 9 figure

Binning of the primordial power spectrum and optimal galaxy survey design

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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo