Quasi-steady state cosmology: analytical solutions of field equations and their relationship to observations

Abstract

We solve the cosmological equations obtained by Hoyle, Burbidge and Narlikar (1995a) from a Machian theory of gravity in the case where the universe satisfies the Weyl postulate and the cosmological principle. The equations in effect are the Einstein equations of general relativity together with a negative cosmological constant and a trace-free zero rest-mass scalar field. We find a wide range of solutions for spatial sections of zero, positive and negative curvature. The solution for the quasi-steady state cosmology used by Hoyle, Burbidge and Narlikar (1994 a,b) is shown to be an approximation to the simplest of the above solutions. We apply the simplest solution to work out the redshift-magnitude relation and the radio source count. We show that there are marginal differences from the results obtained by Hoyle et al (1994a), although the present exact solution provides a better rationale for the parameters of the model.