Second order general slow-roll power spectrum

Abstract

Recent combined results from the Wilkinson microwave anisotropy probe (WMAP) and Sloan digital sky survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.