Standard candles and sirens rescue $H_0$

We show that future observations of binary neutron star systems with electromagnetic counterparts together with the traditional probes of low- and high-redshift Type Ia supernovae (SNe Ia) can help resolve the Hubble tension. The luminosity distance inferred from these probes and its scatter depend on the underlying cosmology. By using the gravitational lensing of light or gravitational waves emitted by, and peculiar motion of, these systems we derive constraints on the sum of neutrino masses, the equation of state of dark energy parametrized in the form $w_0 + w_a (1-a)$, along with the Hubble constant and cold dark matter density in the universe. We show that even after marginalizing over poorly constrained physical quantities, such as the sum of neutrino masses and the nature of dark energy, low-redshift gravitational-wave observations, in combination with SNe Ia, have the potential to rule out new physics as the underlying cause of the Hubble tension at $\gtrsim 5.5\sigma$.