Abstract
We study the generation of primordial perturbations in a (single-field) slow-roll inflationary Universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a nonzero variance . However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize . This can (and should) be achieved by proper renormalization in an expanding Universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the cosmic microwave background anisotropies is significantly altered. We find a nontrivial change in the consistency condition that relates the tensor-to-scalar ratio to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, , is now compatible with a nonzero ratio , which is forbidden by the standard prediction (). The influence of relic gravitational waves on the cosmic microwave background may soon come within the range of planned measurements, offering a nontrivial test of the new predictions.
- Received 18 November 2009
DOI:https://doi.org/10.1103/PhysRevD.81.043514
©2010 American Physical Society