  The recent measurements of temperature and polarization of Cosmic Microwave
Background (CMB) have improved our understanding of the Universe and are in
remarkable agreement with the $\Lambda$CDM cosmological model. However, scale
dependent features like power suppression in the angular power spectrum and
Cosmic Hemispherical Asymmetry (CHA) in the temperature field of CMB at large
angular scales, hinting at possible departure from the $\Lambda$CDM model
persist in the CMB data. In this paper we present a physical mechanism linked
to possible initial inhomogeneities in the inflationary scalar field that could
generate CHA in both scalar and tensor sector within the frame work of single
field inflationary model with an initial fast-roll phase. The modulation
amplitude of CHA in both scalar and tensor perturbations are related and depend
upon the initial shape of the inflaton potential. By using the observed value
of CHA and obeying the isotropy of the temperature field of CMB, we obtain the
theoretical upper bound on the amplitude of CHA for tensor perturbations within
the framework of single field initial fast roll inflation models. The bound
indicates that a maximum of $0.05\%$ modulation in tensor sector is possible
and hence within the measurability of future mission, tensor perturbations
should be statistically isotropic.
