  One of the important open questions in high-energy physics is to understand
the lack of evidence of Kalb-Ramond (KR) field, in particular in the present
day cosmology. In this paper we aim to address this issue by showing that a
bounce scenario in the evolution of the Universe strongly advocates their
elusiveness, even if their energy density was very large to start with. We
consider the Kalb-Ramond field and its effects in the context of generalized
teleparallel gravity in (3+1) dimensions. Teleparallel gravity is a description
of gravitation in which the tetrads are the dynamical degrees of freedom, and
the torsion arising from fields with spin are accommodated naturally as field
strength tensors. In order to describe the coupling prescription, we address
the correct generalization of the Fock-Ivanenko derivative operator for an
n-form tensor field. By varying with respect to the tetrads, this rank-2 field
is shown to source the teleparallel equivalent of Einstein's equations. We
study the possibility of reproducing two well-known cosmological bounce
scenarios, namely, symmetric bounce and matter bounce in four-dimensional
spacetime with with the Friedmann-Lemaitre-Robertson-Walker metric and observe
that the solution requires the KR field energy density to be localized near the
bounce. The crucial result in our work is that this feature also naturally
explains the lack of cosmological evidence of the rank-2 field in the present
day Universe for the matter-bounce scenario. Thus, among the bouncing
cosmologies, latter is favored over the former.
