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.