Amplitude of Perturbations from Inflation

Abstract

The observed power spectrum of the cosmic microwave background (CMB) is consistent with inflationary cosmology, which predicts a nearly scale-invariant power spectrum of quantum fluctuations of the inflaton field as they exit the Hubble horizon during inflation. Here we report a very significant correction (of several orders of magnitude) to the predicted amplitude of the power spectrum. This correction does not alter the near scale-invariance of the spectrum, but is crucial for testing predictions of the Hubble parameter during inflation against the observed amplitude of the CMB power spectrum. This novel correction appears because, as we show, the subtractions that renormalize the short-wavelength ultraviolet divergences of the inflaton two-point function have a significant effect on the amplitude of that two-point function at the longer wavelengths characteristic of the Hubble horizon. Earlier conclusions in the literature that certain theories (such as grand unified theories) implied perturbations that were too large by several orders of magnitude will have to be reconsidered in light of the present result.