Naidoo, Ramsamy.

### Abstract:

In this thesis we utilise a form for the Hubble constant first proposed by Berman
(1983) to study a variety of cosmological models. In particular we investigate the
Robertson-Walker spacetimes, the Bianchi I spacetime, and the scalar-tensor theory
of gravitation of Lau and Prokhovnik (1986). The Einstein field equations with variable
cosmological constant and gravitational constant are discussed and the Friedmann
models are reviewed. The relationship between observation and the Friedmann
models is reviewed. We present a number of new solutions to the Einstein
field equations with variable cosmological constant and gravitational constant in the
Robertson-Walker spacetimes for the assumed form of the Hubble parameter. We explicitly
find forms for the scale factor, cosmological constant, gravitational constant,
energy density and pressure in each case. Some of the models have an equation of
state for an ideal gas. The gravitational constant may be increasing in certain regions
of spacetime. The Bianchi I spacetime, which is homogeneous and anisotropic,
is shown to be consistent with the Berman (1983) law by defining a function which
reduces to the scale factor of Robertson-Walker. We illustrate that the scalar-tensor
theory of Lau and Prokhovnik (1986) also admits solutions consistent with the Hubble
variation proposed by Berman. This demonstrates that this approach is useful
in seeking solutions to the Einstein field equations in general relativity and alternate
theories of gravity.