The Large Scale Anisotropy of the Cosmic Microwave Background Radiation

Although the predicted moments of the distribution of the cosmic microwave background radiation in an inflationary universe have previously been calculated, the sensitivity of these moments to small changes in the conditions required by inflation had not been explored. In this thesis, formulae are presented for calculating the moments of the background radiation due to an arbitrary perturbation in the gravitational field of the early universe. It is found that only scalar (energy density) and tensor (gravitational wave) perturbations are important for this effect. Then numerical calculations are performed; first, to confirm the previous inflationary calculations which require a critical cosmological density and a Harrison-Zel'dovich scale invariant spectrum or perturbations, and second, to compute the values of the moments in universe with non-critical energy densities and different spectra (k('(+OR-)1)). In all cases we keep the assumption that the perturbations are caused by some random process which follows a Gaussian distribution, as this seems to be a reasonable feature of inflation to keep even in non-inflationary universes. The previously predicted values of the inflation induced moments are confirmed, which imply that (epsilon)(,H) < 4 x 10('-6) and the values of the quadrupole to dipole ratio must be two orders of magnitude smaller than the current upper bound, unless gravitational waves are present. If this latter possibility is true then the moments higher than dipole must follow the 1-dependence predicted for gravitational wave perturbations. The values of the moments were found to be sensitive enough to distinguish a k('+1) or a k('-1) spectrum from a Harrison-Zel'dovich spectrum in a critical density universe, (but not in a universe which had only a few tenths of the critical density). The moments higher than dipole for a Harrison-Zel'dovich spectrum were not very sensitive to differences in the energy density but the quadrupole-to-dipole ratio was. We find that the values of the multipole moments are indeed a good test of the inflationary model. In the event that an alternative model is found to inflation, the equations presented here are general enough to be used to calculate moments from this alternative model.