After Planck 2013, a broad class of inflationary models called α -attractors was developed which has universal observational predictions. For small values of the parameter α, the models have good consistency with the recent CMB data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, ns, and tenso-to-scalar ratio, r, and then using BICEP2/Keck 2015 and Planck 2015 data we impose constraints on α -attractors. Then, we study the reheating in α-attractors. The reheating temperature, Tre, and the number of e-folds during reheating, Nre, are calculated as functions of ns. Using these results, we determine the range of free parameter of two classes of α -attractors which satisfy the constraints of recent CMB data.

The metric of some Lorentzian wormholes in the background of the FRW universe is obtained. It is shown that for a de Sitter space-time the new solution is supported by Phantom Energy. The wave equation for a scalar field in such backgrounds is separable. The form of the potential for the Schrödinger type one dimensional wave equation is found.

In this work we introduce a new plateau-like inflationary model including a quadratic scalar potential coupled non-minimally to gravity. This potential has a dominant constant energy density at early times which can realize successful inflation. It also includes an infinitesimal non-zero term V0 responsible for explaining dark energy which causing the universe to expand accelerating at the late time. We show that this model predicts small tensor-to-scalar ratio of the order of r ≈ 0.01 which is fully consistent with Planck constraints. Using the lower and upper bounds on reheating temperature, we provide additional constraints on the non-minimal coupling parameter ξ of the model. We also study the preheating stage predicted by this kind of potentials using numerical calculations. * Electronic address: eshaghi249@gmail.com † Electronic address: m.zarei@cc.iut.ac.ir ‡ Electronic address: n˙riazi@sbu.ac.ir § Electronic address: akiasat@sci.ui.ac.ir