Sandro D. P. Vitenti, Nelson Pinto-Neto
It has been shown that a contracting universe with a dust-like ($w \approx
0$) fluid may provide an almost scale invariant spectrum for the gravitational
scalar perturbations. As the universe contracts, the amplitude of such
perturbations are amplified. The gauge invariant variable $\Phi$ develops a
growing mode which becomes much larger than the constant one around the bounce
phase. The constant mode have its amplitude fixed by COBE normalization, thus
the amplitude of the growing mode can become much larger than one. In this
paper, we first show that this is a general feature of bouncing models, since
we expect that General Relativity should be valid in all scales away from the
bounce. However, in the Newtonian gauge, the variable $\Phi$ gives the value of
the metric perturbation $\phi$, raising doubts on the validity of the linear
perturbative regime at the bounce. In order to address this issue, we obtain a
set of necessary conditions for the perturbative series to be valid along the
whole history of the model, and we show that there is a gauge in which all
these conditions are satisfied, for a set of models, if the constant mode is
fixed by COBE normalization. As a by-product of this analysis, we point out
that there are sets of solutions for the perturbation variables where some
gauge fixing conditions are not well defined, turning these gauges prohibited
for those solutions.
View original:
http://arxiv.org/abs/1111.0888
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