Seminarium Teorii Oddziaływań Elementarnych

The primordial power spectrum (PPS) is important both for cosmological parameter estimation and for distinguishing betweeen models of inflation. Given the uncertainty in the physics behind inflation, a model-independent approach to estimating the PPS is essential. In general cosmological observables sensitive to primordial perturbations are given by a convolution of the PPS with a smoothing kernel. Since the deconvolution problem is ill-conditioned, a regularisation scheme must be employed to control error propagation. Here we demonstrate that Tikhonov regularisation can be used to reconstruct the PPS from multiple cosmological data sets. A significant advantage of our method is that both the uncertainty and the resolution of the estimated PPS is precisely quantified. The amount of regularisation is governed by a parameter whose value must be chosen correctly for an optimal inversion. The performance of several regularisation parameter selection methods is investigated using Monte Carlo simulations. We apply our inversion procedure to data from WMAP, the Sloan Digital Sky Survey and several small scale CMB experiments.