Revising the Predictions of Inflation for the Cosmic Microwave Background Anisotropies

We point out that, if quantum field renormalization is taken into account and the counterterms are evaluated at the Hubble-radius crossing time or few $e$-foldings after it, the predictions of slow-roll inflation for both the scalar and the tensorial power spectrum change significantly. This leads to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio with spectral indices. A reexamination of the potentials ${\varphi }^{\mathbf{2}}$ and ${\varphi }^{\mathbf{4}}$ shows that both are compatible with five-year WMAP data. Only when the counterterms are evaluated at much larger times beyond the end of inflation does one recover the standard predictions. The alternative predictions presented here may soon come within the range of measurement of near-future experiments.

Figure 1

Plot of $r$ versus $n_s$. The contours show the 68% and 95% C.L. derived from WMAP5 (in combination with baryon acoustic oscillations $\mathrm{BAO}+\mathrm{SN}$) [3]. We consider $V(\varphi )=m^2{\varphi }^2$ (solid line) and $V(\varphi )=\lambda {\varphi }^4$ (dashed line). The symbols show the prediction from each of this models in terms of the number $N$ of $e$-folds. The top part corresponds to the prediction of our formulas, while the bottom one corresponds to the standard prediction.