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