  In the present paper, we explore the possible effects of a second rank
antisymmetric tensor field, known as Kalb-Ramond (KR) field, on cosmological
particle production as well as on quantum entanglement for a massive scalar
field propagating in a four dimensional FRW spacetime evolves through a
symmetric bounce. For this purpose, the scalar field is considered to be
coupled with the KR field and also with the Ricci scalar via the term $\sim \xi
R\Phi^2$ (with $\xi$ be the coupling). The presence of KR field spoils the
conformal symmetry of a massless scalar field even for $\xi = 1/6$ in four
dimensional context, which has interesting consequences on particle production
and consequently on quantum entanglement as we will discuss. In particular, the
presence of KR field in a FRW bouncing universe allows a greater particle
production and consequently the upper bound of the entanglement entropy becomes
larger in comparison to the case when the KR field is absent. This may provide
an interesting testbed for the existence of Kalb-Ramond field in our universe.
