Reconstructing a general inflationary action

TL;DR

This paper explores how to reconstruct the entire inflationary action from observational data, moving beyond specific models like potential or DBI inflation, using a flow equation formalism applicable to general single-field theories.

Contribution

It introduces a formalism for reconstructing the full inflationary Lagrangian from observational constraints, applicable to a wide class of single-field inflation models.

Findings

Constraints on the inflationary action from scalar and tensor spectra.

Flow equation formalism for general L(X,φ) Lagrangians.

Reduction to canonical and DBI inflation in specific gauges.

Abstract

If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories, then observations need not be simply applied to reconstructing the inflaton potential, V(\phi), or a specific kinetic term, as in DBI inflation, but rather to reconstruct the inflationary action in its entirety. We discuss the constraints that can be placed on a general single field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian, L(X,\phi), with X={1/2}\partial_\mu\phi\partial^\mu\phi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge \partial L/\partial X = c_s^{-1}.