Analytic solution and Noether symmetries for the hyperbolic inflationary model in the Jordan frame

TL;DR

This paper uses Noether symmetry analysis to find an analytic solution for a multifield hyperbolic inflation model in the Jordan frame, revealing conserved quantities and integrability of the system.

Contribution

It provides an analytic solution and identifies symmetries for a multifield inflation model with interacting scalar fields in the Jordan frame.

Findings

The model admits Noether symmetries constraining parameters.

The field equations form an integrable dynamical system.

An explicit analytic solution is derived.

Abstract

The Noether symmetry analysis is applied for the study of a multifield cosmological model in a spatially flat FLRW background geometry. The gravitational Action Integral consists of two scalar fields, the Brans-Dicke field and a second scalar field minimally coupled to gravity. However, the two scalar fields interact in the kinetic terms. This multifield has been found to describe the equivalent of hyperbolic inflation in the Jordan frame. The application of Noether's theorems constrain the free parameters of the model that conservation laws exist. We find that the field equations form an integrable dynamical system and the analytic solution is derived.