Abstract
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.