Reconstruction of inflation models

In this paper, we reconstruct viable inflationary models by starting from spectral index and tensor-to-scalar ratio from Planck observations. We analyze three different kinds of models: scalar field theories, fluid cosmology, and f (R)-modified gravity. We recover the well-known R-2 inflation in Jordan-frame and Einstein-frame representation, the massive scalar inflaton models and two models of inhomogeneous fluid. A model of R-2 correction to Einstein's gravity plus a cosmological constant with an exact solution for early-time acceleration is reconstructed.