Comments on "Growth of Covariant Perturbations in the Contracting Phase of a Bouncing Universe" by A. Kumar

Understand

A recent paper by Kumar (2012) (hereafter K12) claimed that in a contracting model, described by perturbations around a collapsing Friedmann model containing dust or radiation, the perturbations can grow in such a way that the linearity conditions would become invalid.

• This conclusion is not correct due to the following facts: first, it is claimed that the linearity conditions are not satisfied, but nowhere in K12 the amplitudes of the perturbations were in fact estimated.
• Therefore, without such estimates, the only possible conclusion from this work is the well known fact that the perturbations indeed grow during contraction, which, per se, does not imply that the linearity conditions become invalid.
• Second, some evaluations of the linearity conditions are incorrect because third other terms, instead of the appropriate second order ones, are mistakenly compared with first order terms, yielding artificially fast growing conditions.