The Effective Theory of Inflation and the Dark Matter Status in the Standard Model of the Universe

TL;DR

This paper develops an effective inflation theory with a polynomial potential, analyzes CMB and LSS data to constrain inflation parameters, and investigates dark matter properties, concluding keV-scale dark matter is consistent with structure formation.

Contribution

It introduces a systematic 1/N expansion for inflation, provides analytic and MCMC analysis of data, and derives dark matter particle mass and decoupling parameters independently of particle physics models.

Findings

Lower bound for tensor-to-scalar ratio r > 0.023

Preferred inflation potential is a double well with n_s ≈ 0.964 and r ≈ 0.051

Dark matter particle mass is at the keV scale

Abstract

We present here the effective theory of inflation `a la Ginsburg-Landau in which the inflaton potential is a polynomial. The slow-roll expansion becomes a systematic 1/N expansion where N ~ 60. The spectral index and the ratio of tensor/scalar fluctuations are n_s - 1 = O(1/N), r = O(1/N) while the running turns to be d n_s/d \ln k = O(1/N^2) and can be neglected. The energy scale of inflation M ~ 0.7 10^{16} GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov Chains (MCMC) analysis of the available CMB+LSS data showed: (a) the spontaneous breaking of the phi -> - phi symmetry of the inflaton potential. (b) a lower bound for r: r > 0.023 (95% CL) and r > 0.046 (68% CL). (c) The preferred inflation potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: n_s = 0.964, r = 0.051. This value for r is within reach of forthcoming CMB observations. We investigate the DM properties using cosmological theory and the galaxy observations. Our DM analysis is independent of the particle physics model for DM and it is based on the DM phase-space density rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM particle mass m and for the number of ultrarelativistic degrees of freedom g_d (hence the temperature) at decoupling. We find that m turns to be at the keV scale. The keV scale DM is non-relativistic during structure formation, reproduces the small and large scale structure but it cannot be responsible of the e^+ and pbar excess in cosmic rays which can be explained by astrophysical mechanisms (Abridged).