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We describe in this paper the observables of inflationary models, inparticular the spectrum index of torsion scalar perturbations, thetensor-to-scalar ratio, and the running of the spectral index, in the frameworkof perfect fluid models and F(T) gravity theories through the reconstructionmethods. Then, our results on the perfect fluid and F(T) gravity theories ofinflation are compared with recent cosmological observations such as the Plancksatellite and BICEP2 experiment. Ours studies prove that the perfect fluid andF(T) gravity models can reproduce the inflationary universe consistent aboveall with the Planck data. We have reconstructed several models and consideredothers which give the best fit values compatible with the spectral index ofcurvature perturbations, the tensor-to-scalar ratio, and the running of thespectral index within the allowed ranges suggested by the Planck and BICEP2results.

Perfect fluid and F(T) gravity descriptions of inflationary universe and comparison with obervational data