Viable Cosmological Solutions from Hybrid Potentials

TL;DR

This paper analyzes cosmological models with a scalar field and hybrid potentials, revealing conditions for viable histories with matter, radiation, and late-time acceleration, using dynamical systems methods.

Contribution

It introduces a dynamical system approach to hybrid potential models, identifying invariant planes and equilibrium points relevant for cosmological evolution.

Findings

Viable cosmological histories require specific parameter regions.

Physically relevant trajectories are confined to an invariant plane.

The accelerated point is not a global attractor, depending on initial conditions.

Abstract

We study flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) models with a perfect fluid matter source and a scalar field minimally coupled to matter with power-law-exponential \textquotedblleft hybrid\textquotedblright potential. Using expansion-normalised variables, we formulate the field equations as a constrained three-dimensional dynamical system and determine its equilibrium structure. We show that viable cosmological histories, consisting of a transient matter or radiation era followed by late-time accelerated expansion, arise in restricted regions of parameter space. A central result is that the physically relevant trajectories are confined to an invariant plane, which contains both the transient matter point $\mathcal{B}$ and the accelerated point $\mathcal{C}$. We further show, by centre-manifold analysis, that the accelerated point $\mathcal{C}$ is not a global attractor: it attracts trajectories with $\phi>0$ and repels those with $\phi<0$. For dust, a standard matter era requires vanishing coupling of the scalar field to matter, while for radiation the interaction term vanishes identically. Finally, we discuss the issue that the qualitative cosmological dynamics may be independent of the precise functional form of the scalar-field potential.