Correction to the Inflationary Power Spectrum from Spatial Curvature

Hammam Raihan Mohammad; Getbogi Hikmawan; Freddy Permana Zen

Hammam Raihan Mohammad Theoretical High Energy Physics Group, Department of Physics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
Getbogi Hikmawan Theoretical High Energy Physics Group, Department of Physics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
Freddy Permana Zen Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia

Keywords: cosmic microwave background, cosmological perturbation theory, inflation, power spectrum, spatial curvature

Abstract

In this work, we calculate the corrections to the inflationary power spectrum of primordial curvature perturbations arising from small initial spatial curvature prior to inflation. The universe is described by the Friedman-Lemaître-Robertson-Walker (FLRW) model with spatial curvature and undergoing single-field slow-roll inflation. The presence of spatial curvature introduces additional terms to the second-order action of perturbations, which are proportional to the spatial curvature. We specifically focus our investigation on spatial curvature that is of the same order as the slow-roll parameter. The contribution of these additional terms to the power spectrum is evaluated perturbatively around the usual free part of the action in flat space. The Bunch-Davies boundary condition is applied to normalize the mode function. We find 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.

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