The generalized $sl(2, R)$ and $su(1, 1)$ in non-minimal constant-roll inflation

TL;DR

This paper explores the hidden symmetries in non-minimal constant-roll inflation models, revealing generalized algebraic structures related to $sl(2, R)$ and $su(1, 1)$, using Lie symmetry methods and Heun functions.

Contribution

It introduces a novel approach to identify hidden symmetries in inflationary models via Lie symmetry and Heun functions, extending the understanding of algebraic structures in cosmology.

Findings

Hidden symmetries are characterized as generalized $sl(2, R)$ and $su(1, 1)$ algebras.

Power-law and exponential couplings correspond to these algebraic structures.

The method provides a new perspective on symmetry analysis in inflationary cosmology.

Abstract

In the present work, we consider the non-minimal coupling inflationary model in the context of the constant-roll idea which is investigated by the first-order formalism. We attempt to find the hidden symmetries behind the model by the Lie symmetry method. We supply this aim by using the symmetry features of the Heun function instead of Killing vector approach. We show that the hidden symmetries of the non-minimal constant-roll inflation in the cases of power-law and exponential couplings are characterized as a generalized form of $sl(2, R)$ and $su(1, 1)$ algebra, respectively.