Comment on perturbations during a regular bounce

We point out an inconsistency of a method used in the literature, first advocated by P. Peter and N. Pinto-Neto in [Phys. Rev. D 66, 063509 (2002)], for studying adiabatic scalar perturbations in a regular bouncing universe (in four dimensions). The method under scrutiny consists of splitting the Bardeen potential into two pieces with independent evolutions, in order to avoid a singular behavior at the boundaries of the region where the null energy condition (NEC) is violated. However, we argue that this method violates energy-momentum conservation. We then introduce a novel method which provides two independent solutions for the Bardeen potential around the boundaries, even in the case of adiabatic perturbations. The two solutions are well behaved and not divergent