The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis

TL;DR

This paper develops an effective Ginsburg-Landau theory of inflation, analyzes CMB+LSS data with MCMC, and finds that slow-roll inflation with a double-well potential fits observations well, predicting a tensor-to-scalar ratio within reach of future experiments.

Contribution

It introduces a systematic 1/N expansion for inflation, combines it with data analysis to constrain inflation parameters, and demonstrates the smallness of quantum corrections validating the effective theory.

Findings

The spectral index n_s ~ 0.964 and tensor-to-scalar ratio r ~ 0.051 are most probable.

A lower bound for r is established as 0.023 at 95% confidence level.

Quantum loop corrections are negligible, supporting the effective theory approach.

Abstract

Inflation is part of the Standard Model of the Universe supported by CMB and large scale structure LSS datasets. This review presents new developments of inflation in three main chapters. (I): The effective theory of inflation a la Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal form making explicit the inflation energy scale M, the Planck mass and the inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings are naturally small as powers of (M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV is completely determined by the scalar adiabatic fluctuations amplitude. (II): A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including WMAP5) with our analytic theoretical results yields: a lower bound for r (new inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation potential is a double well, even function of the field yielding as most probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of forthcoming CMB observations. Slow-roll inflation is generically preceded by a short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE modes well reproducing the quadrupole suppression and fixes the total number of efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates the effective theory of inflation. We show how powerful is the GL theory of inflation in predicting observables.