  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.
