  By considering a simplified but exact model for realizing the ekpyrotic
scenario, we clarify various assumptions that have been used in the literature.
In particular, we discuss the new ekpyrotic prescription for passing the
perturbations through the singularity which we show to provide a spectrum
depending on a non physical normalization function. We also show that this
prescription does not reproduce the exact result for a sharp transition. Then,
more generally, we demonstrate that, in the only case where a bounce can be
obtained in Einstein General Relativity without facing singularities and/or
violation of the standard energy conditions, the bounce cannot be made
arbitrarily short. This contrasts with the standard (inflationary) situation
where the transition between two eras with different values of the equation of
state can be considered as instantaneous. We then argue that the usually
conserved quantities are not constant on a typical bounce time scale. Finally,
we also examine the case of a test scalar field (or gravitational waves) where
similar results are obtained. We conclude that the full dynamical equations of
the underlying theory should be solved in a non singular case before any
conclusion can be drawn.
