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

TL;DR

This paper investigates how an early fast-roll stage in inflation can suppress the CMB quadrupole, using a new parameter and MCMC analysis of WMAP and SDSS data to refine inflationary models.

Contribution

It introduces a new cosmological parameter k_1 representing the scale of the fast-roll stage and demonstrates its effect on the primordial power spectrum and CMB quadrupole suppression.

Findings

Fast-roll stage suppresses power for k < k_1

Best-fit k_1 = 0.266/Gpc from data

Total inflation e-folds estimated around 66

Abstract

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 for the curvature and tensor perturbations (this potential is purely repulsive in slowroll). This attractive potential depresses the CMB quadrupole moment for the curvature and B-mode spectra. A single new cosmological parameter emerges: the comoving wavenumber k_1 characteristic scale of this attractive potential.k_1 happens to exit the horizon precisely at the transition from fast to slowroll.The fastroll 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) suppresses the primordial power for k < k_1 and enjoys the scaling property D(k) = Psi(k/k_1) where Psi(x) is an universal function. We perform a MCMC analysis of the WMAP/SDSS data including 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 the fastroll 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 and EE modes.Moreover, our fits provide non-zero lower bounds for r, while for the other cosmological parameters we essentially get those of the LCDM model. The fact that k_Q exits the horizon before the slowroll stage implies an upper bound in the total number of efolds N_{tot} during inflation.Combining this with estimates during the radiation dominated era we obtain N_{tot} ~ 66, with the bounds 62 < N_{tot} < 82.We repeated the analysis with the WMAP-5/ACBAR-2007/SDSS data confirming the overall picture.