Analytical approximations for curved primordial power spectra

Abstract

We extend the work of Contaldi et al. and derive analytical approximations for primordial power spectra arising from models of inflation which include primordial spatial curvature. These analytical templates are independent of any specific inflationary potential and therefore illustrate and provide insight into the generic effects and predictions of primordial curvature, manifesting as cut-offs and oscillations at low multipoles and agreeing with numerical calculations. We identify through our analytical approximation that the effects of curvature can be mathematically attributed to shifts in the wavevectors participating dynamically.

arXiv comment11 pages, 2 figures, supplementary material available at https://doi.org/10.5281/zenodo.4024321. v1: As submitted to PRD. v2: As published in PRD (with only minor additions between v1 and v2). v3: Erratum correction in equations (25) and (26) and update to Figure 2. Displayed in erratum_diff_v2_v3.pdf in additional source files

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