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

We describe in this paper the observables of inflationary models, in particular the spectrum index of torsion scalar perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and F(T)$F(T)$ gravity theories through the reconstruction methods. Then, our results on the perfect fluid and F(T)$F(T)$ gravity theories of inflation are compared with recent cosmological observations such as the Planck satellite and BICEP2 experiment. Our studies prove that the perfect fluid and F(T)$F(T)$ gravity models can reproduce the inflationary Universe consistent above all with the Planck data. We have reconstructed several models and considered others which give the best fit values compatible with the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index within the allowed ranges suggested by the Planck and BICEP2 results. By taking the trace-anomaly into consideration, we have shown that the reconstructed models F(T)$F(T)$ can not describe a finite de Sitter inflation without an additional constant n$n$ that we related to cosmological constant.