Impact of $H_0$ on gravitational wave propagation: prospects for the LISA mission

Abstract

It was previously shown that $H_0$ influences gravitational wave propagation beyond simple redshift, by modifying the effective wavenumber. While earlier studies focused on Pulsar Timing Arrays, we analyze the observability of this effect with LISA. Modeling the LISA arm geometry, we derive the timing residual and identify a clear angular enhancement at frequencies above 100 mHz. Using the stationary phase approximation and numerical methods, we show that the optimal incidence angle depends on $Z_A H_0$, providing a direct, redshift-independent measurement of the Hubble parameter. We estimate that LISA could determine $H_0$ to within a few percent using this method, independent of standard siren approaches.