Measuring $H_0$ with pulsar timing arrays

TL;DR

This paper explores how gravitational wave signals in pulsar timing arrays are affected by the universe's expansion, revealing a potential method to measure the Hubble constant $H_0$ through signal enhancement at specific angles.

Contribution

It provides an alternative derivation of the signal enhancement effect, extends the formalism to include all cosmological components, and proposes an observational setup to detect this effect.

Findings

Signal enhancement depends on the angle between source and pulsar.

Proper solutions show a deviation from simple harmonic functions due to cosmological effects.

A feasible observational setup is proposed to measure $H_0$ using pulsar timing arrays.

Abstract

Pulsar Timing Arrays have yet to convincingly observe gravitational waves. Some time ago it was pointed out by one of the authors that a dramatic enhancement of the signal would take place for particular values of the angle subtended by the source and the observed pulsar. This enhancement is due to the fact that waves propagate in a Friedmann-Lemaitre-Robertson-Walker metric where, contrary to some wide-spread belief, a simple harmonic function with a red-shifted frequency is not a solution of the equation of motion. At the first non-trivial order, proper solutions have an effective wave number that differs from the frequency. This leads to some interesting effects in Pulsar Timing Arrays whose most visible manifestation is the enhancement of the signal that, all other parameters kept fixed, is related in a simple manner to the value of $H_0$. In this work, we rederive in an alternative way the main results, extend the formalism to a more realistic setting where all components in the cosmological budget are included, investigate in detail the dependence of the signal on the various parameters involved and propose an observational set-up to hopefully detect this very relevant effect.