Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications

TL;DR

This paper explores higher derivative scalar field cosmologies inspired by the Pais-Uhlenbeck oscillator, analyzing stability, phantom divide crossing, and cyclic behavior, with implications for dark energy models.

Contribution

It introduces a novel coupling inspired by the Pais-Uhlenbeck oscillator into scalar cosmology and studies its stability and dynamical properties.

Findings

Stable de Sitter solutions for positive coupling with phantom divide crossing once

Cyclic behavior possible for negative coupling with benign or malicious ghost behavior

Conditions for stability and phantom crossing derived in the phase space analysis

Abstract

We study higher derivative terms associated with scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired by the Pais-Uhlenbeck oscillator, given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$, we provide conditions for the stability of de Sitter solutions. In this case the crossing of the phantom divide $w_{DE}=-1$ occurs once; thereafter, the equation of state parameter remains under this line, asymptotically reaching towards the de Sitter solution from below. For $\alpha<0,$ which is the portion of the parameter space where in addition to crossing the phantom divide, cyclic behavior is possible, we present regions in the parameter space where, according to Smilga's classification the ghost has benign or malicious behavior.