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Assuming that curvature perturbations and gravitational waves originallyarise from vacuum fluctuations in a matter-dominated phase of contraction, westudy the dynamics of the cosmological perturbations evolving through anonsingular bouncing phase described by a generic single scalar fieldLagrangian minimally coupled to Einstein gravity. In order for such a model tobe consistent with the current upper limits on the tensor-to-scalar ratio,there must be an enhancement of the curvature fluctuations during the bouncephase. We show that, while it remains possible to enlarge the amplitude ofcurvature perturbations due to the nontrivial background evolution, this growthis very limited because of the conservation of curvature perturbations onsuper-Hubble scales. We further perform a general analysis of the evolution ofprimordial non-Gaussianities through the bounce phase. By studying the generalform of the bispectrum we show that the non-Gaussianity parameter$f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhancedduring the bounce phase if the curvature fluctuations grow. Hence, in suchnonsingular bounce models with matter given by a single scalar field, thereappears to be a tension between obtaining a small enough tensor-to-scalar ratioand not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upperbounds. This conclusion may be considered as a "no-go" theorem that rules outany single field matter bounce cosmology starting with vacuum initialconditions for the fluctuations.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Evolution of cosmological perturbations and the production of  non-Gaussianities through a nonsingular bounce: Indications for a no-go  theorem in single field matter bounce cosmologies