Propagation of gravitational waves in a universe with slowly-changing equation of state

TL;DR

This paper derives an exact solution for gravitational wave propagation in a flat universe with evolving dark energy, revealing amplitude diminution due to a universe with both Big Bang and Big Rip singularities.

Contribution

It provides a novel analytical solution using confluent Heun functions for gravitational waves in a universe with changing dark energy and develops approximation methods for practical analysis.

Findings

Gravitational wave amplitude diminishes in such a universe.

Exact solutions involve confluent Heun functions.

Approximation methods are proposed for observational regimes.

Abstract

An exact solution for the expansion of a flat universe with dark energy evolving according to a simple model is explored. The equation for weak primordial gravitational waves propagating in this universe is solved and explored; gravitational waves in a flat cosmology possessing both a "big bang" singularity and a "big rip" singularity can be described with confluent Heun functions. We develop approximation methods for confluent Heun equations in regimes of interest to gravitational wave astronomers and predict the diminution in gravitational wave amplitude in a universe with both a Big Bang and a Big Rip.