The cosmological constant and oscillating metrics

TL;DR

This paper explores how a cosmological constant in higher curvature gravity theories can lead to rapidly oscillating metrics, developing a perturbative method to find periodic solutions with implications for extra-dimensional models.

Contribution

It introduces a perturbative approach to generate periodic solutions in higher curvature gravity with a cosmological constant, revealing oscillations proportional to a0 and related to the Planck mass.

Findings

Oscillations have amplitude proportional to a0.

Oscillation frequency is of order the Planck mass.

Existence of periodic metrics in 4+1 dimensions parameterized by an effective cosmological constant.

Abstract

The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field equations for such actions based on a small amplitude expansion. We find that these oscillations have an amplitude proportional to \sqrt{\Lambda} and a frequency of order the Planck mass. In a 4+1 dimensional scenario, a family of metrics exists that are periodic in the extra dimension and are parameterized by an effective four-dimensional cosmological constant which drives a rapid oscillation.