An Analytic Formalism of Inflation for Derivative Coupled Scalar Field and Validating its predictions for Some Inflationary Potentials

TL;DR

This paper develops an analytic formalism for inflation involving derivative-coupled scalar fields, predicting observable parameters consistent with recent ACT and Planck data across various inflationary potentials.

Contribution

It introduces a covariant derivative coupling model in inflationary cosmology and demonstrates its predictions align with observational constraints for multiple potentials.

Findings

The model produces $n_s$ and $r$ values consistent with observations.

Higher derivative terms are manageable without singularities in the slow-roll regime.

The formalism applies to diverse inflationary potentials.

Abstract

One of the fundamental objectives of contemporary cosmology is to understand the physics of the inflationary universe, owing to its observably verifiable predictions about the very early universe with an energy scale of $\sim 10^{16}$ GeV. Recent observations from the ACT and the Planck mission, constrain the values of the scalar spectral index, $n_s$, and the tensor-to-scalar ratio, with state-of-the-art accuracy and upper limits, respectively. In the current work, a type of non minimally coupled inflationary model in which the gravity and the background scalar field interact through a covariant product of the Ricci tensor and derivatives of the scalar field. With this interaction at the backdrop, we estimate $n_s$ and $r$ for a wide range of inflaton self-interaction potentials, including power law, exponential $\alpha$ attractor, Arctan, Hilltop, and polynomial model. We show that the higher derivative terms involving the scalar field resulting from the derivative coupling term can be handled without facing any singularity within the slow-roll regime. We show that it is possible to produce $n_s$ and $r$ values consistent with ACT and Planck observations for each of the chosen sets of potentials for the derivative coupled action.