  One of the surprising aspects of the present Universe, is the absence of any
noticeable observable effects of higher-rank anti-symmetric tensor fields, such
as space-time torsion, in any natural phenomena. Here we address the possible
explanation of torsion, which may often be identified with the field strength
tensor of the second rank antisymmetric Kalb-Ramond field. Within the framework
of f(R) gravity, we explore the cosmological evolution of the scalar degrees of
freedom associated with higher curvature term in a general higher curvature
model $f (R) = R +\alpha_n R^n$. We show that while the values of different
cosmological parameters follow acceptable values in the framework of standard
cosmology at different epochs for different forms of higher curvature gravity
(i.e. different values of n ), only for Starobinsky model (n = 2), the Kalb
Ramond field gets naturally suppressed with cosmological evolution. In
contrast, for other models (n both positive and negative), despite their
agreement with standard cosmology, the scalar field associated with the higher
derivative degree of freedom induces an enhancement in Kalb-Ramond field and
thereby contradicts the observation. The result does not change even if we
include the Cosmological Constant. Thus our result reveals that among different
$f(R)$ models, Starobinsky model successfully explains the suppression of
space-time torsion along with a consistent cosmological evolution.
