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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 Δ2(k,t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize Δ2(k,t). 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 r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, nt=0, is now compatible with a nonzero ratio r0.12±0.06, which is forbidden by the standard prediction (r=-8nt). 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. © 2010 The American Physical Society.

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Physical Review D - Particles, Fields, Gravitation and Cosmology