Reconstruction of logamediate and exponential inflationary models using generalized induced gravity scenario

Abstract

This manuscript explores the dynamics of an inflationary model using two known exact solutions, i.e., logamediate and exponential expansion. To achieve this, the framework of generalized induced gravity non-minimally coupled to Ricci scalar is taken under consideration. Using slow-roll approximation and a generalized form of coupling function, we find the possible forms of potential needed to produce inflation in the model and conduct the mathematical analysis of cosmological perturbations. In both of the eras, we constraint the involved model parameters by comparing the $r-n_{s}$ trajectories with Planck 2015 astrophysical data. Also, we reconstruct these inflationary models assuming as attractors the scalar spectral index and tensor-scalar ratio as a function of number of e-foldings.