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

98 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
The corresponding scale factors are
for and
for and
5. CONCLUSIONS
For spaces, perfect fluid solutions imply that given and
the numerical value of is determined by the amount of “matter”
present while also its sign depends on In other words, when space
is non flat one can not freely choose the sign, or the degree of coupling
between the tensor and the scalar modes. Note the fact that in such
spaces these fluids expand in the same way, that is, expansion ignores the
particular nature of “matter”. Even more disturbing is the possibility
that this evolution turns out to be the only kind of expansion which
can be given in terms of polynomial, transcendental, or other fairly well
known functions which may furthermore be also time invertible. For
the open space, a linear expansion is known to give a Milne
Universe where space–time is, actually, flat Minkowski space. However,
a linear expansion in is not a Milne solution.
Acknowledgments
This work was supported by CONACyT Grant No. 5–3672–E9312
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