  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 Jodan 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.
