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Generically,the classical evolution of the inflaton has a brief fast rollstage that precedes the slow roll regime. The fast roll stage leads to a purelyattractive potential for the curvature and tensor perturbations (this potentialis purely repulsive in slowroll). This attractive potential depresses the CMBquadrupole moment for the curvature and B-mode spectra. A single newcosmological parameter emerges: the comoving wavenumber k_1 characteristicscale of this attractive potential.k_1 happens to exit the horizon precisely atthe transition from fast to slowroll.The fastroll stage dynamically modifiesthe initial power spectrum by a transfer function D(k). We compute D(k) bysolving the inflaton evolution equations. D(k) suppresses the primordial powerfor k < k_1 and enjoys the scaling property D(k) = Psi(k/k_1) where Psi(x) isan universal function. We perform a MCMC analysis of the WMAP/SDSS dataincluding the fast-roll stage and find k_1 = 0.266/Gpc. The quadrupole mode k_Q= 0.242/Gpc exits the horizon 1/10 of an efold before k_1. We compare thefastroll fit with a fit with a sharp lower cutoff on the primordial power.Fastroll provides a slightly better fit than a sharp cutoff for the TT,TE andEE modes.Moreover, our fits provide non-zero lower bounds for r, while for theother cosmological parameters we essentially get those of the LCDM model. Thefact that k_Q exits the horizon before the slowroll stage implies an upperbound in the total number of efolds N_{tot} during inflation.Combining thiswith estimates during the radiation dominated era we obtain N_{tot} ~ 66, withthe bounds 62 < N_{tot} < 82.We repeated the analysis with theWMAP-5/ACBAR-2007/SDSS data confirming the overall picture.

The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data