Gravitational waves were first detected indirectly through observations of the orbital decay of the Hulse-Taylor binary. As the pulsars orbit, they radiate energy in the form of gravitational waves, which means the potential energy and hence distance between the two must decrease in order to compensate. As shown in Fig. 1, the observations of this decay (red data points) closely match the predictions from general relativity (blue line).

More recently, LIGO/Virgo detected gravitational waves more directly, by measuring the change in the relative arm lengths of an interferometer. The initial detection was of a merging black hole binary, and this was followed up by further observations of mergers, including of a neutron star binary and – if the latest rumours are to be believed – the current run has seen the merger of a neutron star and black hole.

Clearly this has opened up a new era of astrophysics. The sensitivity of the LIGO/Virgo detectors will continue to be improved which will increase the rate of binaries they detect. These detectors should soon be joined by KAGRA in Japan. Future planned observatories include the Einstein Telescope and the space based LISA interferometer.

The latter, planned to be launched in 2034, is sensitive to frequencies in the ~ mHz range, a completely different range compared to the ground based detectors which do best around ~100 Hz. Amongst many other observations, LISA will be sensitive to the initial low frequency inspiral of binary black holes, and for the right candidate binaries will be able to say exactly when the merger will be observed – years in the future – in the LIGO band.

For those interested in particle physics, LISA will also make a number of important observations. Many beyond the Standard Model theories lead to a strong first order phase transition, associated with the spontaneous symmetry breaking, when a scalar field obtains a vacuum expectation value. Bubbles of the new broken phase nucleate out of the symmetric phase plasma, these bubbles expand and eventually collide. Such collisions also produce a stochastic background of gravitational waves.

Of course, the phase transition must be strong enough in order to produce an observable signal. And much work has been undertaken in recent years in identifying such models and improving the prediction of the expected gravitational wave spectrum.

The peak frequency of the signal is set by the bubble size at collision, together with a factor taking into account the redshifting of the frequency from the phase transition to today, and a numerical factor which can be found through a more detailed calculation.

For the strongest of transitions, the bubbles are approximately the Hubble horizon size at collision. It turns out that strong phase transitions which occurred when the temperature of the Universe was at the ~TeV scale, lead to a peak frequency in the LISA sensitivity band. Thus LISA can act as a complementary probe of new physics associated with the TeV scale.

In particular LISA is will be able to test models with close-to -conformal scalar potentials. An example of such a gravitational wave signal, from a model of Dark Matter I worked on recently, is shown in Fig. 2. Also shown are sensitivity curves for the Einstein Telescope (ET) and the Big Bang Observer (BBO) a proposal for a second generation space based observatory, together with estimates of irreducible foregrounds from supermassive black hole and extragalactic white dwarf binaries.

Also of interest to particle physicists and cosmologists is the inflationary paradigm, which helps to solve the horizon and flatness problems of early Universe cosmology. A key prediction of inflation is the production of a stochastic background of gravitational waves.

The effects of the gravitational waves from inflation can be searched for in the B-mode polarization of the CMB encoded in the scalar-to-tensor ratio. Current observations limit this to about r < 0.1, which limits the Hubble scale at inflation to H < 10^{14} GeV.

The CMB signal would correspond to wavelengths of ~ 10^{8} light years today. In the simplest picture, these gravitational waves have a red-titled spectrum, and the CMB limit means no detectable signal at the LISA sensitive wavelength of ~ O(1) light minute. Nevertheless, in non-minimal models the spectrum may be blue tilted at higher frequencies, and LISA will set constraints on such scenarios.

Finally, there has been an increasing tension between the supernovae measurements which give a local Hubble parameter today, H_{o} ~ 72 km/s/Mpc, and the inferred value from the Planck CMB measurements which point to H_{o} ~ 68 km/s/Mpc. The tension has recently been quantified at ~ 4.4 standard deviations.

This signals either a systematic error in one of the determinations, or the breakdown of the standard ΛCDM cosmological paradigm. From a theorists perspective, the latter would be very exciting, as the two measurements can be reconciled if the vacuum energy density varies with time. This would give a new path and impetus in understanding why the vacuum energy density is decoupled from the energy scales of particle physics, i.e. the cosmological constant problem.

Gravitational wave observations can play a crucial observational role in resolving the H_{o }tension. This is because merging binaries can act as standard sirens, as the intrinsic (non-redshifted) amplitude of the signal can be recovered from the signal waveform itself, giving a new local measurement of H_{o }completely independent from the systematics of the local distance ladder used in supernovae observations. The observed neutron star merger gave a value H_{o} ~ (70 +- 10) km/s/Mpc showcasing the power of the technique with a single measurement. With greater statistics this technique will become competitive with the CMB and supernovae measurements.

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