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 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}. 
Rachel Bean, Daniel J.H. Chung, and Ghazal Geshnizjani