CMB Hemispherical Power Asymmetry from Early Phase of Inflation

Abstract: We investigate the hemispherical power asymmetry observed in the CMBR by attributing it to an early inhomogeneous phase of cosmic expansion. Unlike the conventional assumption of a perfectly isotropic and homogeneous pre-inflationary Universe, we introduce a small inhomogeneous perturbation, treated within a perturbative framework. Our analysis builds on previously developed empirical models of inhomogeneous primordial power spectrum models based on dipole modulation. Using in-in formalism, we compute two-point correlations directly from the metric and demonstrate that, at leading order, this introduces a direction-dependent power spectrum that breaks rotational symmetry and naturally selects a preferred direction, relating observed violation of the cosmological principle to inflationary power spectra arising from scalar field fluctuations. Additionally, we find that this framework produces correlations between multipoles separated by $\Delta l=1$, leading to distinctive signatures in the multipole space. Furthermore, we constrain the parameters of the inhomogeneous perturbation using observed PR4 \texttt{Commander} CMB data.