Investigations into cosmology and astronomy.

The thesis begins with a short review of tensor analysis and general relativity. Only those equations which have direct application to cosmology are considered in any detail. The analyses throughout this thesis are based on the metric for homogeneous and isotropic space-times, defined by the Robertson-Ilalker line element. The classification of relativistic world-models containing both matter and radiation is considered in some detail. The properties of some model parameters are determined as a function of the temperature of the radiation field which is assumed to be Planckian. Some attention is also given to the problems of event and particle horizons in uniform world-models. Data derived from radio source observations are used extensively in an attempt to solve the cosmological problem. The distribution of source angular diameters with redshift and the variation of source average spectral index with redshift (or luminosity) both provide useful information on the evolutionary properties of the universe. The radio source counts of the recent 5C survey are examined for their cosmological implications. The analysis provides important evidence on the epoch corresponding to galaxy formation and the variation with time (or more directly with expansion parameter) of source luminosity or density in co-ordinate volume. Arguments are given supporting a rapidly expanding evolutionary universe in which the matter density is somewhat greater than usually accepted values. The effect of free-free absorption by intergalactic ionized hydrogen on the low frequency spectra of radio galaxies is examined for the steady-state, adiabatic and constant temperature universes. Using thermodynamic principles, a differential equation is derived which determines the temperature path of the intergalactic gas in evolutionary universes. The gas is assumed to be heated by cosmic rays and plasma waves, and cooled by radiative losses and expansion of co-ordinates. An integral equation is obtained for the extragalactic background intensity when intergalactic absorption is present. The radio background spectrum is determined for the steady-state, \adiabatic\" and constant temperature models of the universe. In each case the theoretical spectrum is compared with the observed background spectrum. The extragalactic component of the sky brightness is calculated by using the differential equation describing the thermal history of the intergalactic gas and the cosmological parameters derived from the source counts. The calculations include the separate cases of source luminosity evolution and source density evolution. The diffuse X-ray flux is described in terms of Compton radiation from cosmic ray electrons in intergalactic space. The electrons are assumed to be ejected from radio galaxies in a time which is small compared with the characteristic time of evolution of the universe. Normalisation of the derived X-ray spectra yield estimates for the intergalactic cosmic ray energy density. Finally a mathematical treatment is given which describes the consequences of the introduction of a general vector field into Einstein's field equations. The theory is applicable to universes of arbitrary intrinsic curvature. Some tentative conclusions are drawn concerning possible annihilation of matter."