Abstract. Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. We find that the model can be completely described in terms of a single parameter, viz. the ratio of the scale associated with the bounce to the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.
The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In the literature, the enhanced power spectrum was calculated from the inflationary potential. However, in this paper, we show that a potential of multi scalar fields can be reconstructed from a given power spectrum which is made of a scale-invariant one on large scales and the other with a peak on small scales. In this reconstructed potential, the slow-roll of the second field in the curved trajectory is responsible for the generation of a peak in the power spectrum on small scales through the isocurvature perturbation. With multi scalar fields, the reconstructed potential may not be unique and we can find different potentials from a given power spectrum.
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