# Dispersion relations for gravitational waves in different models of dark energy

## TL;DR

This paper derives dispersion relations for gravitational waves in various dark energy models using an approximate cosmological approach, enabling comparison with observations to test model viability.

## Contribution

It introduces a method to derive gravitational wave dispersion relations across different dark energy models using a power series expansion of the scale factor.

## Key findings

- Dispersion relations vary across dark energy models.
- Results can be used to compare models with observational data.
- Provides a framework for testing dark energy theories with gravitational waves.

## Abstract

The propagation of weak gravitational waves on the background of dark energy is studied. The consideration is carried out within the framework of an approximate approach where the cosmological scale factor is expanded as a power series for relatively small values of the redshift corresponding to the epoch of the present accelerated expansion of the Universe. For several different dark energy models, we obtain dispersion relations for gravitational waves which can be used to estimate the viability of every specific model by comparing with observational data.