Cosmological Gravitational Wave in a Gravity with Quadratic Order Curvature Couplings

TL;DR

This paper derives and analyzes the equations governing cosmological gravitational waves in gravity theories with quadratic curvature couplings, revealing differences in wave equations and similarities in background evolution.

Contribution

It introduces a set of equations for gravitational waves in quadratic curvature gravity theories, highlighting the distinct fourth-order differential equations and their impact on cosmological models.

Findings

Gravitational waves in quadratic curvature theories follow fourth-order differential equations.

Background evolution remains similar for different quadratic curvature terms.

Differences in wave equations do not significantly alter background cosmology.

Abstract

We present a set of equations describing the cosmological gravitational wave in a gravity theory with quadratic order gravitational coupling terms which naturally arise in quantum correction procedures. It is known that the gravitational wave equation in the gravity theories with a general $f(R)$ term in the action leads to a second order differential equation with the only correction factor appearing in the damping term. The case for a $R^{ab} R_{ab}$ term is completely different. The gravitational wave is described by a fourth order differential equation both in time and space. However, curiously, we find that the contributions to the background evolution are qualitatively the same for both terms.