Pulsar timing array

Pulsars, discovered in 1967, are highly magnetized rotating compact stars that emit beams of electromagnetic radiation from their magnetic poles, arriving at Earth as pulses when the poles point in our direction. The period of these pulses is extremely stable, and therefore, if, for example, a gravitational wave --- a distortion in space and time that is a necessary component of theories of gravity --- passes, the pulse signal is affected, and the period would change. We can measure this change in the period over time, and can infer details of the both whatever generated the gravitational waves, and of the theory of gravity in which they were produced. The default would be to expect these measurements to reflect that gravity is described by Einstein's theory of General Relativity, but any deviations form this would be one of the most important experimental results in decades. To obtain a larger signal-to-noise ratio from these measurements, astronomers have developed the idea of a {\it pulsar timing array} (PTA) which measures many pairs of pulsars in the system, and analyzes their correlated signatures. Given the typical distances between pulsar pairs, PTA measurements are sensitive to gravitational waves in the nano-Hertz frequency band. This makes them particularly useful probes, since this band cannot be probed by other gravitational wave detectors, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the proposed Laser Interferometer Space Antenna (LISA). For example, the gravitational wave background produced by the supermassive black holes that are generally thought to lie at the centers of galaxies should be in the nano-Hertz band. Furthermore, important early universe processes such as the formation of exotic objects such as cosmic strings from phase transitions in the quantum field theories that describe elementary particles, or {\it primordial} gravitational waves produced during the initial dynamics of the universe after the big bang, also predict waves within this low-frequency band.

In recent data released by North American NanoHertz Observatory for Gravitational Waves (NANOGrav \cite{NANOGrav:2020bcs}), the Parkes Pulsar Timing Array (PPTA \cite{Goncharov:2021oub}), the European Pulsar Timing Array (EPTA) \cite{Chen:2021rqp}, and the International Pulsar Timing Array (IPTA) \cite{Antoniadis:2022pcn}, strong evidence for a power-law power spectrum, the function that describes how the energy in gravitational waves depends of their frequencies, has been claimed. However, the shape of this signal as a function of the angle between the pulsar pairs has shown the first hints of something other than the predictions of general relativity. One possible provocative and exciting explanation is that the underlying theory of gravity theory may need to be modified.

In my recent work (with collaborators)\cite{Liang:2021bct}, we consider a generalization of Einstein gravity to allow the gravitational particle --- the graviton --- to have a mass. We have found that massive gravity theories can modify the shape of the signal, while leaving the frequency dependence of the power spectrum untouched. We also explored a related possibility --- that the signal might originate from the fluctuations of a dark matter halo, which is an important unknown component of our universe. We have shown explicitly how signals from upcoming PTA measurements may show evidence for either of these new sources of physics, and are anxiously awaiting the next round of PTA data. I will also include one ongoing project that is expected to be finished within the dissertation year. We are interested in what the PTA signal might look like if the gravitational wave background is not uniform in all directions. This is an important relaxation of one of the assumptions with which general relativity is tested against data, and including such anisotropic models may provide valuable information, allowing us to distinguish among different proposed sources of the stochastic gravitational-wave background.

The use of pulsar timing arrays as sensitive current and next-generation probes of fundamental physics is a wonderfully exciting opportunity. I have been delighted to make some important contributions already, and look forward to building on these, and including those results in my thesis, in the coming year before graduation.