Reconstructing a general inflationary action

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 $V(\ensuremath{\phi})$ or a specific kinetic term, as in Dirac-Born-Infeld 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. The analytic form of the action that is consistent with data turns out to be surprisingly simple and easy to categorize. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian $\mathcal{L}(X,\ensuremath{\phi})$, with $X=\frac{1}{2}{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}{\ensuremath{\partial}}^{\ensuremath{\mu}}\ensuremath{\phi}$, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge ${\mathcal{L}}_{X}={c}_{s}^{\ensuremath{-}1}$.