Cosmological constraints on general, single field inflation

TL;DR

This paper develops a comprehensive framework using Hubble flow parameters to compare general single field inflation models with cosmological data, emphasizing the importance of precise calculations of primordial spectra and sound speed effects.

Contribution

It introduces an extended hierarchy of Hubble flow parameters including sound speed evolution and demonstrates the necessity of full numerical integration for accurate predictions.

Findings

Accurate primordial spectra require full flow equation integration.

The approximation r ≈ 16 c_s ε can deviate significantly, especially when c_s ≠ 1.

Constraints on inflationary parameters are derived using MCMC with observational data.

Abstract

Inflation is now an accepted paradigm in standard cosmology, with its predictions consistent with observations of the cosmic microwave background. It lacks, however, a firm physical theory, with many possible theoretical origins beyond the simplest, canonical, slow-roll inflation, including Dirac-Born-Infeld inflation and k-inflation. We discuss how a hierarchy of Hubble flow parameters, extended to include the evolution of the inflationary sound speed, can be applied to compare a general, single field inflationary action with cosmological observational data. We show that it is important to calculate the precise scalar and tensor primordial power spectra by integrating the full flow and perturbation equations, since values of observables can deviate appreciably from those obtained using typical second-order Taylor expanded approximations in flow parameters. As part of this, we find that a commonly applied approximation for the tensor to scalar ratio, r \approx 16 c_s\epsilon, becomes poor (deviating by as much as 50%) as c_s deviates from 1 and hence the Taylor expansion including next-to-leading order contribution terms involving c_s is required. By integrating the full flow equations, we use a Monte-Carlo-Markov-Chain approach to impose constraints on the parameter space of general single field inflation, and reconstruct the properties of such an underlying theory in light of recent cosmic microwave background and large-scale structure observations.