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The recent measurements of temperature and polarization of Cosmic MicrowaveBackground (CMB) have improved our understanding of the Universe and are inremarkable agreement with the $\Lambda$CDM cosmological model. However, scaledependent features like power suppression in the angular power spectrum andCosmic Hemispherical Asymmetry (CHA) in the temperature field of CMB at largeangular scales, hinting at possible departure from the $\Lambda$CDM modelpersist in the CMB data. In this paper we present a physical mechanism linkedto possible initial inhomogeneities in the inflationary scalar field that couldgenerate CHA in both scalar and tensor sector within the frame work of singlefield inflationary model with an initial fast-roll phase. The modulationamplitude of CHA in both scalar and tensor perturbations are related and dependupon the initial shape of the inflaton potential. By using the observed valueof CHA and obeying the isotropy of the temperature field of CMB, we obtain thetheoretical upper bound on the amplitude of CHA for tensor perturbations withinthe framework of single field initial fast roll inflation models. The boundindicates that a maximum of $0.05\%$ modulation in tensor sector is possibleand hence within the measurability of future mission, tensor perturbationsshould be statistically isotropic.

Unified origin of hemispherical asymmetry in scalar and tensor perturbations