A Non-minimally Coupled Potential for Inflation and Dark Energy after Planck 2015: A Comprehensive Study

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 $V_0$ 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 $r\approx 0.01$ 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 $\xi$ of the model. We also study the preheating stage predicted by this kind of potentials using numerical calculations.