Unified origin of hemispherical asymmetry in scalar and tensor perturbations

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.