## Conformal symmetries : solutions in two classes of cosmological models.

##### Abstract

In this thesis we study the conformal symmetries in two locally rotationally symmetric
spacetimes and the homothetic symmetries of a Bianchi I spacetime. The
conformal Killing equation in a class AIa spacetime (MacCallum 1980), with a G4
of motions, is integrated to obtain the general solution subject to integrability conditions.
These conditions are comprehensively analysed to determine the restrictions
on the metric functions. The Killing vectors are contained in the general conformal
solution. The homothetic vector is obtained and the explicit functional dependence
of the metric functions determined. The class AIa spacetime does not admit a nontrivial
special conformal factor. We also integrate the conformal Killing equation
in the anisotropic locally rotationally symmetric spacetime of class A3 (MacCallum
1980), with a G4 of motions, to obtain the general conformal Killing vector and the
conformal factor subject to integrability conditions. The Killing vectors are obtained
as a special case from the general conformal solution. The homothetic vector is found
for a nonzero constant conformal factor. The explicit functional form of the metric
functions is determined for the existence of this homothetic vector. The spatially
homogeneous and anisotropic A3 spacetime also does not admit a nontrivial special
conformal vector. In the Bianchi I spacetime, with a G3 of motions, the conformal
Killing equation is integrated for a constant conformal factor to generate the homothetic
symmetries. The integrability conditions are solved to determine the functional
dependence of the three time-dependent metric functions.