Large Adiabatic Scalar Perturbations in a Regular Bouncing Universe
  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 has its amplitude fixed by Cosmic Background Explorer
(COBE) normalization, thus the amplitude of the growing mode can become much
larger than 1. 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.
