Ekpyrotic bounce driven by Kalb-Ramond field
  We propose an ekpyrotic bounce scenario driven by a second rank antisymmetric
Kalb-Ramond field, where the universe initially contracts through an ekpyrotic
stage having a non-singular bouncing like behaviour, and consequently, it
smoothly transits to an expanding phase. In particular, the KR field has an
interaction with a scalaron field (coming from higher curvature d.o.f) by a
linear coupling. The interaction energy density between the KR and the scalaron
grows faster than $a^{-6}$ during the contraction phase -- which has negligible
effects at the distant past, however as the universe continues to contract,
this interaction energy density gradually grows and plays a significant role to
trigger a non-singular bounce at a minimum value of the scale factor. The
existence of the ekpyrotic phase justifies the resolution of the BKL
instability, where the anisotropic energy density gets diluted compared to that
of the bouncing agent. The bounce being symmetric and ekpyrotic, the energy
density of the bouncing agent rapidly decreases after the bounce during the
expanding phase of the universe, and consequently the standard Big-Bang
cosmology gets recovered. We find that the comoving Hubble radius diverges at
the distant past, which leads to the generation era of the primordial
perturbation modes at the deep contracting phase far away from the bounce. In
effect, the curvature perturbation gets a blue tilted spectrum over the large
scale modes -- not consistent with the Planck data. To circumvent this problem,
we propose an extended scenario where the ekpyrotic phase is preceded by a
quasi-matter dominated pre-ekpyrotic phase, and re-investigate the perturbation
power spectrum. As a result, the primordial curvature perturbation, at scales
that cross the horizon during the pre-ekpyrotic stage, turns out to be nearly
scale invariant that is indeed consistent with the recent Planck data.
