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 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.
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Choe et al. (2004) studied this question.
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