We study inflation, perturbations, non-gaussinity and late-time cosmological dynamics of a tachyon field both minimally and non-minimally coupled to gravity. By analyzing the parameters space of the model, the viability of the model in confrontation with recent observational data is considered. In a dynamical system technique, we study the phase space dynamics of both minimally and non-minimally coupled tachyon field. We find the fixed points (lines in our setup) and explore their stability. Also, we perform a statefinder diagnostic to both cases and show that the trajectories of the state finder pairs reach a stable state which is corresponding to a ΛCDM scenario.PACS numbers: 98.80. Cq , 95.36.+x

Motivated by α-attractor models, in this paper we consider a Gauss-Bonnet inflation with an E-model-type of potential. We consider the Gauss-Bonnet coupling function to be the same as the E-model potential. In the small α limit we obtain an attractor at r = 0 as expected, and in the large α limit we recover the Gauss-Bonnet model with potential and coupling function of the form φ 2n . We study perturbations and non-Gaussianity in this setup and we find some constraints on the model's parameters in comparison with PLANCK data sets. We study also the reheating epoch after inflation in this setup. For this purpose, we seek the number of e-folds and temperature during reheating epoch. These quantities depend on the model's parameter and the effective equation of state of the dominating energy density in the reheating era. We find some observational constraints on these parameters.PACS numbers: 04.50. Kd , 98.80.Cq , 98.80.Es

We study cosmological inflation on a warped DGP braneworld where inflaton field is nonminimally coupled to induced gravity on the brane. We present a detailed calculation of the perturbations and inflation parameters both in Jordan and Einstein frame. We analyze the parameters space of the model fully to justify about the viability of the model in confrontation with recent observational data. We compare the results obtained in these two frames also in order to judge which frame gives more acceptable results in comparison with observational data.PACS numbers: 98.80. Cq,

We consider two non-canonical scalar fields (tachyon and DBI) with E-model type of the potential. We study cosmological inflation in these models to find possible α-attractors. We show that similar to the canonical scalar field case, in both tachyon and DBI models there is a value of the scalar spectral index in small α limit which is just a function of the e-folds number. However, the value of ns in DBI model is somewhat different from the other ones. We also compare the results with Planck2015 TT, TE, EE+lowP data. The reheating phase after inflation is studied in these models which gives some more constraints on the model's parameters. PACS: 98.80.Cq , 98.80.Es