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Recently, there has been a considerable interest in scale-invariant theory of gravitation.
The reason behind this is that both elementary particles and astrophysics and
cosmology appear to be describable in scale-invariant terms at least to a first approximation. As
concerned with the elementary particles, there are three main scale-invariant theories of
gravity proposed by Dirac (1973 and 1974), Hoyle and Narlikar (1974) and Canuto et al. (1977a and 1977b), respectively. Later, these theories are reviewed by Wesson (1980, 1981a and
1981b) who proposed a simple formulation of scale-invariant theory of gravitation incorporating
a gauge function where xi are coordinates in the four-dimensional space-time.
The tensor field is identified with Riemannian metric
tensor gij. gij can be interpreted as
a gravitational potential tensor, which determines the interaction between matter
and gravitation. The scale-invariant theory formulated by Wesson (1980, 1981a and 1981b) is
so far the best theory to describe all the interactions between matter and gravitation.
There has been a considerable interest in spatially homogeneous and anisotropic
Bianchi cosmological models. The existence of such models allows a theoretical discussion of
many important aspects (Ryan and Shapely, 1975).
Recently, Mohanty and Mishra (2003) have studied the feasibility of Bianchi type VIII
and IX space-times with a time dependent gauge function and a matter field in the form
of perfect fluid. In that paper, they have constructed a radiating model of the universe for
the feasible Bianchi type VIII space-time. Moreover, Mishra (2003a and 2003b) has
constructed the static and non-static plane symmetric cosmological models in this theory with a
time dependent gauge function.
In this paper, the Bianchi type II cosmological model in Wesson's scale invariant theory
of gravitation is investigated, when the source of the matter field is that of a perfect fluid.
The field equations of scale invariant theory are presented in the next section. |
