The origin and evolution of the Universe as governed by the laws of gravity is currently best described by Einstein's highly successful theory of gravity, the theory of general relativity (GR). In GR (and in other relativistic theories of gravity), space and time are combined to form “spacetime” which is curved in the presence of mass. It is the curvature of space-time that itself determines how masses move. To date, GR has passed all observational tests with flying colours. The most recent experimental confirmation of GR came from the direct detection of gravitational waves (GWs) by laser interferometers. GWs are wave propagations of spacetime ripples that result when spacetime curvature is perturbed by accelerating masses (for non-spherically symmetric motions). GWs propagate through the Universe virtually unaffected by absorption and scattering, being therefore able to carry information to our detectors from processes happening far in the Universe's past. Their detection is technologically challenging due to their very small amplitudes.
The first detection, a GW signal (GW150914) created by the collision of two black holes of about 30 solar masses, was announced by the LIGO/Virgo collaboration on February 11th 2016, making the 100th-year anniversary of Einstein's 1916 paper predicting GWs a trully special one. This was the result from decades of work setting up this huge experiment and rightfully earned the 2017 Nobel Prize in Physics. This came 24 years after the 1993 Nobel prize was awarded for the first discovery of a binary pulsar which led to the first indirect confirmation of the existence of GWs, by demonstrating that the binary's orbital decay was in remarkable agreement with the predicted energy loss from GW emission. The European Pulsar Timing Array project and its partner collaborations have the ambitious aim to make the first direct detections of GWs in the nanohertz frequency regime, probing completely new physical processes of cosmological origin. This is to be achieved by observations of radio pulsars, this special class of astrophysical objects that led to the first (indirect) verification of the existence of GWs.
Pulsars are fast rotating, magnetized, compact and massive objects known as a neutron stars, which emits a narrow beam of radio emission along open magnetic field lines. As the pulsar rotates, it acts like a cosmic lighthouse and pulsar radiation directed to Earth can be observed once per rotation, producing a narrow pulse and hence a natural beacon for a terrestrial observer. Because pulsars are massive and compact (the mass of 1.4 Suns is concentrated in a sphere of only 20 km diameter), they represent massive flywheels in space, whose rotation and repetition rate can hardly be disturbed. This makes pulsars very precise cosmic clocks. It is therefore in principle possible to detect fluctuations in the pulse arrival times caused by propagating GWs. In practice, due to the very small expected amplitudes, only millisecond pulsars have so low levels of intrinsic noise that are capable of possibly detecting such small fluctuations (predicted to be below 200 nanoseconds). Because it is virtually impossible to say with certainty whether a candidate GW signal is or not intrinsic pulsar or instrumental noise, we simultaneously look for the same signals using Pulsar Timing Arrays (PTAs), ensemble of millisecond pulsars covering as many sky locations as possible.
The rewards for a successful detection of nanohertz GWs are immense and would have enormous consequences. Such GWs are expected from inspiralling supermassive black-hole binaries and cosmological gravitational-wave backgrounds and their detection will provide unique observational constraints on cosmological models and theories for formation of the observed large-scale structure Universe. It would also enable tests of GR and alternative gravity theories in the radiative regime in several, unprecedented ways. As most relativistic theories of gravity conjecture the existence of gravitational waves, the predictions of GR for GW properties, such as their polarization modes, propagation velocity and the mass of graviton, can be compared to those of alternative theories.
Direct detection of gravitational waves
The direct detection of GWs is extremely challenging. Their interaction with masses on Earth, for instance by changing the size or separation of masses, is almost unmeasurable as it will always be smaller than 1 part in 1020 (e.g. Schutz 2003, Cambridge University Press). Nevertheless, GW detectors have been constructed at several facilities around the world (e.g. GEO600 and VIRGO detectors in Europe, or the LIGO detectors in the US; see Danzmann 1995, in Edoardo Amaldi Conference on Gravitational Wave Experiments, eds. Coccia, Pizzella & Ronga, 100; Acernese et al., 2004, Astroparticle Physics, 21, 1; Abramovici et al., 1992, Science, 256, 325) conducting extraordinarily precise experiments which attempt to measure the changing distance between a number of test-masses. Unfortunately, due to their sensitivity limitations, the current generation of ground-based detectors has not been able to detect GWs yet. The detection of GWs on Earth is not only difficult because the displacement of the masses is so small, but it is also aggravated by seismic noise that causes the masses in a terrestrial laboratory to move. Fortunately, in addition to the high-frequency GWs in principle detectable on Earth (> few Hz), GWs could be produced and propagate at any frequency. Indeed, the amplitude of low-frequency GWs is expected to be much larger, and a wide variety of possible GW sources exists.
Another method exists that can detect GW at low frequencies, being sensitive to a variety of astrophysical and cosmological sources, ranging from the effects of “cosmic strings” (as predicted by theories of gravity known as “string theory”) and to the binary motion and merging of super-massive black holes at the heart of galaxies in the early Universe. The latter objects will produce signals in the range of a few nHz, i.e. well below the frequencies to which LISA might be sensitive. This complementary method is the high precision timing observations of an ensemble of radio millisecond pulsars in a so-called “Pulsar Timing Array” (PTA).
Pulsars as gravitational wave detectors
While pulsars already provide the indirect evidence for the existence of GWs, they can also be used to achieve the first direct detection. The idea is not new but was first proposed by Sazhin (1978, Soviet Astronomy, 22, 36) and Detweiler (1979, ApJ, 234, 1100). In this experiment, the observed pulsars would be timed to high precision, i.e. the arrival times of their pulses on Earth would be recorded accurately and compared with a rotational “timing“ model counting every single rotation of the neutron star. Slight deviations from the expected arrival times would be visible as significant “timing residuals”. Such timing residuals would be caused by a passing gravitational wave as each pulsar and the Earth can be considered as free masses whose positions respond to changes in the space-time metric. A perturbation by a GW would therefore displace both pulsars and the Earth slightly, leading to timing residuals that depend on the GW amplitude and the total observing time. The sensitivity of GW detection using pulsars scales directly with the achieved timing precision; the timing residuals are the figure of merit used to determine this precision.
A pulsar timing array and the nHz-GW sky
A variety of sources is expected to emit GWs in the frequency range detectable by pulsar timing. Each of these sources will typically have a different spectrum that allows us in principle to distinguish between the sources. In general, one can expect a random superposition of a GW emission from a large number of independent sources, leading to a stochastic GW background. The effect of such a GW background is such that the Earth is modified in a manner that is the same for all sources being timed. In other words, a displacement of the Earth causes the pulses from all pulsars in a particular sky direction to arrive early, while signals from sources in the opposite direction would come late. Pulse arrival times from pulsars in perpendicular directions would be unaffected. The consequence is the existence of a correlation between the timing residuals of an ensemble of timed pulsars in the PTA. A stochastic GW background manifests itself as a distinct trend in the correlation between these timing residuals as a function of pulsar angular separation on the sky – a quadrupole signature in this correlation, to be more precise (see Figure 2).
The most prominent contributor to a stochastic GW background is the population of supermassive binary black holes which are expected to have merged during the evolution of galaxies in the early Universe. In fact, a detection of such a signal would have direct consequences on cosmological models and their predictions for the expected merger rate (e.g. Jaffe & Backer 2003, ApJ, 584, 616; Jenet et al. 2006, ApJ, 653, 1571). However, more exotic GW sources also exist, and other contributions to a stochastic GW background include cosmological sources such as inflation and phase transitions (e.g. Maggiore, 2000, Phys. Rep. 331, 283), relic gravitational waves (Battye & Shellard, 1997, Classical Quantum Gravity, 13, A239; Grishuk 2005, Physics-Uspekhi, 38, 1235) or cosmic strings (e.g. Damour & Vilenkin, 2005, Phys. Rev. D, 71, 063510). It is also possible to detect single sources of GW emission, such as the periodic GW signal of a binary super-massive black hole in the centre of a nearby Galaxy (e.g. Jenet et al. 2004, ApJ, 606, 799) or a transient GW burst (e.g. Lommen 2002, in WE-Hereaus Seminar on “Neutron Stars, Pulsars, and Supernova Remnants”, ed. Becker, Lesch & Trümper, MPE-Garching, 114). In this case, however, a sufficiently good timing precision must be matched with a fortuitous relative geometrical alignment and an appropriately dense data span. It is possible but unlikely that such signals can be detected before the Square-Kilometre Array (SKA) may become operational at the end of the next decade (cf. Kramer et al. 2004, New Astronomy Reviews, 48, 993).
Hopefully it has been made sufficiently clear that the direct detection of GWs is crucial for a number of reasons. The most important and fundamental of these implications is the goal of eventually determining whether GR is the correct theory of gravity, or simply the best we have at the moment. If it is the latter, we can hope to answer the question that asks when, and under what circumstances, will GR break down. It can also allow us to explore the question of whether there are other current or heretofore unimagined theories that supercede it in describing everything from the evoution of our Milky Way and other galaxies to the formation and unfolding over time of our Universe. Pulsar timing array science is being performed by three major collaborations around the world: the EPTA in Europe, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), and the Parkes Pulsar Timing Array (PPTA) in Australia. This endeavour has begun to prove itself as an important – and possibly the first – method towards direct gravitational wave detection.