Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

New solutions of Bianchi models in scalar-tensor theories 157
where and a column sum is given by where
V or IX and
For the Bianchi type V model one has the additional constraint:
implying that and are inverse proportional functions,
note that the mean Hubble parameter,
is for this Bianchi type model FRW models are obtained if
whereby the flat model corresponds to the Bianchi I
curvature term, the open to Bianchi V, and closed model to Bianchi IX.
Additionally, the continuity equation yields:
being a dimensional constant depending on the fluid present. The
vacuum case is attained when
The system of ordinary differential equations, Eqs. (1-12), can be
recast in the following set:
and
where and we have written the Hubble rates as follows
(similar to the Bianchi type I model deduced in Ref. [14]):