Reconstructing a general inflationary action

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 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 L(X,phi), with X=1/2 partial derivative(mu)phi partial derivative(mu)phi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge L-X=c(s)(-1).