PERTURBATIVE CORRECTIONS TO THE POWER SPECTRUM OF PRIMORDIAL CURVATURE PERTURBATIONS DUE TO INFLATION WITH SPATIAL CURVATURE - Raihan Mohammad, Hammam
In this work, the corrections to the inflationary power spectrum of primordial curvature perturbations arising from small initial spatial curvature prior to inflation are calculated. The universe is described by the Friedman-LemaîtreRobertson-Walker (FLRW) model with nonzero spatial curvature and is undergoing single-field slow-roll inflation. Specifically, the investigation is focused on spatial curvature that is of the same order as the slow-roll parameter before inflation. This assumption enables the implementation of the sub-curvature approximation, where the wavelength of the modes of interest are much smaller than the curvature length scale. Additional terms proportional to the spatial curvature arises on the second-order action of perturbations due to the presence of small spatial curvature. The small spatial curvature assumption also allows the contribution of these additional terms to the power spectrum to be evaluated perturbatively around the usual quadratic free part of the action in flat space. The perturbative method employed in this work is the in-in formalism, which has been previously applied to the calculation of higher-order correlation functions of primordial perturbations. The mode function is normalized using the Bunch-Davies boundary condition. It is found that the corrections are proportional to the spatial curvature for the short-wavelength modes. However, these corrections can be enhanced when the largest observable scale is comparable to the curvature scale