# A nontrivial footprint of standard cosmology in the future observations of low-frequency gravitational waves

## TL;DR

This paper explores how the Hubble constant influences gravitational wave propagation in the universe, proposing a new method to test cosmological models using pulsar timing arrays and local gravitational wave observations.

## Contribution

It extends previous models by incorporating the Hubble constant into GW propagation analysis within the LCDM framework, providing a novel observational test.

## Key findings

- Timing residuals show a distinguishable peak depending on the local Hubble constant.
- Maximum timing residual correlates with the source's redshift.
- Framework can improve gravitational wave measurements with PTAs.

## Abstract

Recent research show that the cosmological components of the Universe should influence on the propagation of Gravitational Waves (GWs) and even it has been proposed a new way to measure the cosmological constant using Pulsar Timing Arrays (PTAs). However, these results have considered very particular cases (e.g. a de Sitter Universe or a mixing with non-relativistic matter). In this work we propose an extension of these results, using the Hubble constant as the natural parameter that includes all the cosmological information and studying its effect on the propagation of GWs. Using linearized gravity we considered a mixture of perfect fluids permeating the spacetime and studied the propagation of GWs within the context of the LCDM model. We found from numerical simulations that the timing residual of local pulsars should present a distinguishable peak depending on the local value of the Hubble constant. As a consequence, when assuming the standard LCDM model, our result predicts that the region of maximum timing residual is determined by the redshift of the source. This framework represents a new test for the standard cosmological model, and it can be used to facilitate the measurements of gravitational wave by ongoing PTAs projects.