Matter bounce cosmology with a generalized single field: non-Gaussianity and an extended no-go theorem

TL;DR

This paper explores a generalized matter bounce cosmology with a $k$-essence scalar field, analyzing how sound speed affects non-Gaussianities and tensor-to-scalar ratios, and extends a no-go theorem for single field models.

Contribution

It extends the matter bounce scenario to include arbitrary sound speeds, analyzing non-Gaussianities and tensor ratios, and proposes an extended no-go theorem for single field models.

Findings

Small sound speed enhances curvature perturbation and suppresses tensor-to-scalar ratio.

Large non-Gaussianities arise at small sound speeds, conflicting with observations.

Certain sound speeds produce new bispectrum shapes and scaling behaviors.

Abstract

We extend the matter bounce scenario to a more general theory in which the background dynamics and cosmological perturbations are generated by a $k$-essence scalar field with an arbitrary sound speed. When the sound speed is small, the curvature perturbation is enhanced, and the tensor-to-scalar ratio, which is excessively large in the original model, can be sufficiently suppressed to be consistent with observational bounds. Then, we study the primordial three-point correlation function generated during the matter-dominated contraction stage and find that it only depends on the sound speed parameter. Similar to the canonical case, the shape of the bispectrum is mainly dominated by a local form, though for some specific sound speed values a new shape emerges and the scaling behaviour changes. Meanwhile, a small sound speed also results in a large amplitude of non-Gaussianities, which is disfavored by current observations. As a result, it does not seem possible to suppress the tensor-to-scalar ratio without amplifying the production of non-Gaussianities beyond current observational constraints (and vice versa). This suggests an extension of the previously conjectured no-go theorem in single field nonsingular matter bounce cosmologies, which rules out a large class of models. However, the non-Gaussianity results remain as a distinguishable signature of matter bounce cosmology and have the potential to be detected by observations in the near future.