CMB quadrupole depression produced by early fast-roll inflation: Monte Carlo Markov chains analysis of WMAP and SDSS data

Generically, the classical evolution of the inflaton has a brief fast-roll stage that precedes the slow-roll regime. The fast-roll stage leads to a purely attractive potential in the wave equations of curvature and tensor perturbations (while the potential is purely repulsive in the slow-roll stage). This attractive potential leads to a depression of the CMB quadrupole moment for the curvature and B-mode angular power spectra. A single new parameter emerges in this way in the early universe model: the comoving wave number k₁ characteristic scale of this attractive potential. This mode k₁ happens to exit the horizon precisely at the transition from the fast-roll to the slow-roll stage. The fast-roll stage dynamically modifies the initial power spectrum by a transfer function $D(k)$. We compute $D(k)$ by solving the inflaton evolution equations. $D(k)$ effectively suppresses the primordial power for k<k₁ and possesses the scaling property D(k)=Ψ(k/k₁) where Ψ(x) is a universal function. We perform a Monte Carlo Markov chain analysis of the WMAP and SDSS data including the fast-roll stage and find the value k₁=0.266 Gpc^-1. The quadrupole mode kQ=0.242 Gpc^-1 exits the horizon earlier than k₁, about one-tenth of an e-fold before the end of fast roll. We compare the fast-roll fit with a fit without fast roll but including a sharp lower cutoff on the primordial power. Fast roll provides a slightly better fit than a sharp cutoff for the temperature--temperature, temperature--E modes, and E modes--E modes. Moreover, our fits provide nonzero lower bounds for r, while the values of the other cosmological parameters are essentially those of the pure ΛCDM model. We display the real space two point CTT(θ) correlator. The fact that kQ exits the horizon before the slow-roll stage implies an upper bound in the total number of e-folds Nₜₒₜ during inflation. Combining this with estimates during the radiation dominated era we obtain Nₜₒₜ~66, with the bounds 62<Nₜₒₜ<82. We repeated the same analysis with the WMAP-5, ACBAR-2007, and SDSS data confirming the overall picture.