# Classes of non-minimally coupled scalar fields in spatially curved FRW spacetimes

## TL;DR

This paper analyzes the dynamics of non-minimally coupled scalar fields in curved FRW spacetimes, identifying key features and specific potential classes with cosmological implications.

## Contribution

It introduces a new dynamical framework for non-minimally coupled scalar fields in curved FRW spacetimes and explores specific potential classes with constant tracker parameters.

## Key findings

- Identification of symmetries and invariant subsets in the dynamical system
- Analysis of critical points and their cosmological significance
- Characterization of specific potential classes with constant tracker parameters

## Abstract

In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant, i.e. we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation.