Two Field Matter Bounce Cosmology
  We re-examine the non-singular Matter Bounce scenario first developed in
[arXiv:1206.2382], which starts with a matter-dominated period of contraction
and transitions into an Ekpyrotic phase of contraction. We consider both matter
fields, the first of which plays the role of regular matter, and the second of
which is responsible for the non-singular bounce. Since the dominant matter
field is massive, the induced curvature fluctuations are initially not
scale-invariant, whereas the fluctuations of the second scalar field (which are
initially entropy fluctuations) are scale-invariant. We study the transfer of
the initial entropy perturbations into curvature fluctuations in the
matter-dominated phase of contraction and show that the latter become nearly
scale invariant on large scales but are blue tilted on small scales. We study
the evolution of both curvature and entropy fluctuations through the bounce,
and show that both have a scale-invariant spectrum which is blue-tilted on
small scales. However, we find that the entropy fluctuations have an amplitude
that is much smaller than that of the curvature perturbations, due to
gravitational amplification of curvature perturbations during the bounce phase.
