Reheating and Inflationary dynamics driven by an inverse tangent potential

TL;DR

The study investigates whether an inverse tangent inflaton potential $V = V_0 [\tan^{-1}(\kappa \phi/m_p)]^2$ can drive successful slow-roll inflation and a viable reheating phase. By deriving the slow-roll parameters and observables ($n_s$, $r$, $\alpha_s$) and constraining $\kappa$ with Planck 2018 and ACT data, the authors demonstrate compatibility for $\kappa$ in a broad range, with the inflation scale anchored by $A_s$ around $10^{16}$ GeV and negligible $f_{NL}$. A reheating analysis assuming a constant $\omega_{re}$ and entropy conservation yields $N_{re}$ and $T_{re}$ that span from MeV to $\sim 10^{15}$ GeV, depending on $\kappa$ and $\omega_{re}$, indicating a broader post-inflationary history than Starobinsky. Overall, the inverse-tangent potential provides a viable alternative to plateau-like models, aligning with current CMB constraints while offering flexible reheating scenarios that could accommodate non-standard thermal histories.

Abstract

In this work, we study the early universe inflation and the post-inflation reheating era employing an inverse tangent potential of the form $V=V_0 \cdot[tan^{-1}(\frac{κφ}{m_p})]^2$, where $κ$ 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 $κ$. 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 $2σ$ level by the recent sixth data release (DR6) of the Atacama Cosmology Telescope (ACT) collaboration.

Figures (10)

• Figure 1: Evolution of the co-moving horizon distance over time. The left plot is with assumption that $\omega_{re}=1$ and right one represents $\omega_{re}=-1/3$.
• Figure 2: Plot of Amplitude of scalar power spectrum $A_s$ vs $\kappa$
• Figure 3: Graph of spectral index $n_s$ vs $\kappa$ for various $N$. The dark and the light regions correspond to the 1$\sigma$ and 2$\sigma$ bounds on $n_s$ from Planck 2018 (left) and ACT (right) data respectively.
• Figure 4: Graph of tensor-to-scalar ratio $r$ vs $\kappa$ for various $N$
• Figure 5: Graph of running of spectral index $\frac{dn_s}{dlnk}$ vs $\kappa$ for various $N$