Analytical approximations for curved primordial power spectra

Abstract

We extend the work of Contaldi et al. [J. Cosmol. Astropart. Phys. 07 (2003) 002.] 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 cutoffs 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 wave vectors participating dynamically.