Viable tensor-to-scalar ratio in a symmetric matter bounce
  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. If we consider the scale associated with the bounce to be of the
order of the Planck scale, the model is completely described in terms of only
one parameter, viz 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.
