Slow-Fast Evolution of Scalar Fields in Higher-Order Cosmological Gravity: Dynamics Inspired by the Pais--Uhlenbeck Oscillator

TL;DR

This paper explores the complex dynamics of scalar fields in higher-order gravity models inspired by the Pais-Uhlenbeck oscillator, revealing rich behaviors like cyclic evolution, stability of de Sitter states, and potential explanations for inflation and dark energy.

Contribution

It introduces a novel slow-fast dynamical system framework for analyzing higher-derivative scalar field cosmologies, combining numerical and geometric methods to uncover intricate phase space structures and stability properties.

Findings

Stable de Sitter solutions identified.

Crossing of the phantom divide demonstrated.

Realistic cosmological scenarios including matter and dark energy modeled.

Abstract

We investigate the cosmological dynamics of scalar fields governed by higher-order gravity, with particular emphasis on models inspired by the Pais-Uhlenbeck oscillator--a prototypical fourth-order system known for its connection to ghost-free formulations. By recasting the field equations into a slow-fast dynamical system, we analyze phase space evolution across exponential and power-law coupling regimes. Our approach integrates numerical simulations and geometric methods to visualize trajectories, stream flows, and asymptotic behavior under varying potential parameters. The underlying system admits singular surfaces and non-smooth transitions, revealing intricate dynamical structures. We examine the stability of de Sitter solutions, the crossing of the phantom divide, and the emergence of cyclic behavior through multiple-scale analysis. The inclusion of radiation and dust fluids enables the creation of realistic cosmological scenarios, including a transient matter-dominated era and a late-time accelerated expansion. Our results highlight the viability of Pais-Uhlenbeck scalar models in accounting for inflationary dynamics and dark energy, offering diagnostic tools for characterizing attractors and bifurcation phenomena in higher-derivative cosmology.