Reheating and Inflationary dynamics driven by an inverse tangent potential

Abstract

In this work, we study the early universe inflation and the post-inflation reheating era employing an inverse tangent potential of the form $V=V_0 \cdot[tan^{-1}(\frac{\kappa \phi}{m_p})]^2$, where $\kappa$ is a free parameter of the potential and $m_p$ is the reduced Planck mass. We derive the slow roll parameters, the number of e-folds(N), the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the tensor spectral index $n_T$ for the inverse tangent potential. We examine the inflationary observables using the data of the Planck-2018 and recent ACT collaboration and obtain constraints on the potential parameter $\kappa$. We also employ a reheating analysis by invoking the conservation of entropy between today and the time when reheating starts. We obtain bounds on the reheating temperature $T_{re}$ and the number of e-folds of the reheating $N_{re}$ using the spectral-index $n_s$ constraints from Planck 2018 and the ACT results. We show that this inverse-tangent potential can act as an alternative to the standard inflationary potentials like Starobinsky which are excluded at $2\sigma$ level by the recent sixth data release (DR6) of the Atacama Cosmology Telescope (ACT) collaboration.