Constraining Inflation

TL;DR

This paper introduces a new framework for analyzing inflationary models using slow roll reconstruction derived from the Hamilton-Jacobi formulation, providing simplified equations, a classification scheme, and forecasts for observational constraints.

Contribution

It presents a novel classification scheme for inflation models based on potential parameters and explores the detectability of slow roll parameters with future cosmological data.

Findings

Low inflationary scales simplify Hamilton-Jacobi equations.

Minimal running of spectral index is undetectable with current CMB experiments.

High redshift 21 cm data could test second order inflationary consistency conditions.

Abstract

Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of inflationary dynamics. It automatically includes information from sub-leading terms in slow roll, and facilitatesthe inclusion of priors based on the duration on inflation. We show that at low inflationary scales the Hamilton-Jacobi equations simplify considerably. We provide a new classification scheme for inflationary models, based solely on the number of parameters needed to specify the potential, and provide forecasts for likely bounds on the slow roll parameters from future datasets. A minimal running of the spectral index, induced solely by the first two slow roll parameters (\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic Microwave Background experiments. However, we show that the ability to detect this signal increases with the lever arm in comoving wavenumber, and we conjecture that high redshift 21 cm data may allow tests of second order consistency conditions on inflation. Finally, we point out that the second order corrections to the spectral index are correlated with the inflationary scale, and thus the amplitude of the CMB B-mode.