An alternative way to locally measure the Hubble constant using Gravitational Waves and Pulsar Timing Arrays
Recent research show that the cosmological components of the Universe should influence on the propagation of Gravitational Waves (GWs). Moreover, 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, studying its consequences on the propagation of GWs and exploring the possibilities of a local measurement. From linearized gravity we consider a mixture of perfect fluids permeating the spacetime and study the propagation of GWs within the context of the LCDM model. Using this framework we found a relationship, e.g. an analytical expression and an approximation that differs by 1.5% from numerical simulations, between the local value of the Hubble constant and some observables of Pulsar Timing Array experiments. The results show that the value of the Hubble constant is relevant within the measurement of pulsars timing residual and the simulations show that, under the accuracy expected by the IPTA collaboration in the next years, this effect could be eventually observed.