  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.
