Reply to "Bouncing Universes and their perturbations: remarks on a toy   model"
  In this web note, we reply to a recent paper, gr-qc/0404126, confirming a previous work of ours in which a cosmological bouncing phase was shown to have the ability of modifying the spectrum of primordial perturbations (PRD 68, 103517 2003), but challenging its physical conditions of validity. Explicitly, Ref. gr-qc/0404126, besides pretending our Taylor series expansion of the scale factor close to the bounce amounts to choosing a family of polynomial scale factors, also claims that the bounce affects the spectrum only if the mass scale of the scalar field driving the dynamics is of the order of the Planck mass. We show that these objections are either misleading or incorrect since the minimum size of the Universe a_0 (value of the scale factor at the bounce) is either not physically specified, as required in a closed Universe, or implicitly assumed to be the Planck mass. We calculate this mass and obtain that, unsurprisingly, for a reasonable value of a_0, i.e. much larger than the Planck length, the scalar field mass is smaller than the Planck mass. 
Jerome Martin and Patrick Peter