It is important to clarify the context in which the gravitational waves, and more globally the theory of General Relativity, have been postulated. Before the 20th century, gravity was essentially described by Newton’s theory. Capable of describing most of the planet orbital motions, it was nevertheless failing to explain the unusual eccentric orbit of Mercury, closest planet to the Sun.

 

It is not unusual to be faced to such situation in physics. Many historical examples show theoretical models working for long times and finally failing on a specific situation. In these cases, two options are possible: either the theory is simply wrong (and was previously working under specific assumptions), either the theory is correct and a new phenomenon is the cause of the specific failure. Let me give a concrete example here. In the 18th century, it has been realized that another planet had an anomaly in its orbit: Uranus. Naturally, scientific community got divided. On one side, those ready to give up on Newton’s theory of gravity. For them the theory had to be modified. On the other side, those thinking that the theory was correct but that a new phenomenon was the reason of the orbital anomaly. History gave reason to the second group, and few years later, Neptune was found and it was proved that its proximity to Uranus was the cause of the anomaly. The theory was therefore right. Let´s get back to the 20th Mercury’s anomaly. What could be its cause, a new planet again? Many people naturally went into that direction. However, in 1915 Albert Einstein proved that this time the theory has to be changed and proposed General Relativity as the new theory of gravity.

 

General relativity asserts that gravity is not a force but a result of massive objects warping the very fabric of spacetime. This theory introduced the notion that objects move along curved paths, or geodesics, determined by the curvature of spacetime created by mass and energy. The implications of General Relativity are numerous, from the bending of light by gravity, the precession of Mercury’s orbit, and the existence of black holes. But what remains one of the most important predictions is the appearance of gravitational waves. Intuitively, if the Universe is thought as a bendable fabric, oscillations could naturally propagate on it. Those are the gravitational waves. In this picture, gravitational waves could easily traverse the cosmos, unimpeded by matter or electromagnetic fields, offering a unique window into the hidden dynamics of the universe.

 

But what could produce such oscillations and what would be the consequences? Gravitational waves are usually produced via the acceleration of massive objects. The ripples on the spacetime structures

 

 

Figure 1. Representation of the experimental set up of LIGO.

 

of the Universe can therefore be compared with stones dropped into a calm pond creating ripples on the water’s surface. Nevertheless, the energy required to produce gravitational waves is enormous and can only be associated with the most violent events in the Universe. Hence, one of the most significant sources of gravitational waves is the interaction between binary systems, such as two massive black holes or neutron stars in orbit around each other. As these objects spiral inward due to the loss of energy in the form of gravitational waves, they accelerate and create intense gravitational waves that propagate through spacetime. But the most energetic gravitational waves are produced during the collisions and mergers of compact objects, such as black hole mergers or neutron star mergers. These cataclysmic events release a tremendous amount of energy in the form of gravitational waves. Gravitational waves can also be produced at the first seconds of the universe. These kind of sources are expected to fill in the whole Universe with a so-called gravitational wave background.

 

In the General Relativity picture, those waves are expected to stretch and compress the spacetime as they pass through it at the speed of light. For instance, we will see in the next section that gravitational waves going through a detector would change the typical lengths of its components. This is the primary mechanism through which gravitational waves are observed in these detectors.

 

 

The first theoretical proposal for the existence of gravitational waves by Albert Einstein was made in 1916. Only in 2015 was confirmed the first experimental detection, at the LIGO-VIRGO collaboration, of a signal coming from the merger of two black holes approximately 1.3 billion light-years away. How did they proceed?

 

At its core, LIGO (similar for VIRGO) uses a concept known as interferometry (see Fig.1), which involves splitting a laser beam into two perpendicular paths (several kilometers) and then recombining them to create an interference pattern. This allows extremely precise measurements of small changes in the relative lengths of these paths. Explicitly, the laser beams traveling down each arm are reflected by mirrors and then recombine at the beam splitter. When gravitational waves pass through the LIGO detector, they cause change in the length of one arm compared to the other, creating a phase shift in the returning laser beams. LIGO is highly sensitive and can detect incredibly small changes in length. To ensure accuracy, the detectors are calibrated and closely monitored to distinguish gravitational wave signals from other sources of noise, such as seismic vibrations or thermal fluctuations. Once a potential signal is detected, it is compared to theoretically modeled signals in order to confirm the identification of a gravitational wave. Since this first detection in 2015, many others have followed, providing an enormous amount of information of the fusion of black hole binaries.

 

LIGO and VIRGO are capable of covering a typical frequency range from ~1 Hz to ~10² Hz. This corresponds to waves with wavelengths around 10³ km. However, as emphasized in the previous section, many other sources can produce gravitational waves with multiple frequency ranges. Hence, different experiments exist in order to cover the most complete frequency range possible. The Pulsar Timing Arrays (PTAs) are for instance covering gravitational waves with nano Herzt frequencies. This corresponds to waves with astronomical wavelength ~10¹⁵ km. The functioning of the PTAs is essentially the following: Telescopes are used to record the light emitted by an array of pulsars (pulsars are objects that emit pulses of light with an extremely regular period). If a gravitational wave is coming between the pulsars and the Earth, the associated spacetime distortion would induce an unusual time delay between the pulses.

 

Interestingly, PTAs have recently observed a potential signal of gravitational waves. If the origin of those is not yet clear, two options are on the table. First, they may come from supermassive black hole binaries, located at the center of the galaxies. Let´s stress that those are infinitely more massive than the black holes observed in LIGO and VIRGO. The second option is that they would take their origin in the first seconds of the Universe. In the latter case, exotic phenomenon should have taken place, so that, if confirmed, this could constitute a strong hint that unknown physics has happened in the early Universe.

 

Therefore, it becomes obvious that gravitational wave observations are opening a new window on both astrophysics and cosmology. Unfortunately, the two previous experiments are the only ones that have observed any signal. They nevertheless confirmed the theory of General Relativity and offered the promise of new future discoveries.

 

 

After the success of LIGO and VIRGO, as well as the PTAs, many future experiments are on their way to be launched.

 

In order to reach larger wavelengths, one naturally needs to build larger detectors. This is for instance the case of LISA. Its functioning is essentially the same than LIGO-VIRGO but will be operating in space. The typical frequency at which LISA would be sensitive is around ~10^-3 Hz, which means wavelengths about one million times larger than those observed by LIGO. Interestingly, LISA is expected to observe massive binary systems in our galaxy as well as probe some of the early universe mechanisms of gravitational wave productions: phase transitions, cosmic strings and even inflation. Finally, the Einstein Telescope (ET) should appear as an underground detector similar to LIGO. However, its sensitivity should be much more important, making it possible to observe gravitational waves produced in the early Universe, as well as providing crucial information on dark matter.

 

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Virgile Dandoy

Karlsruhe Institute of Technology, Karlsruhe, Germany

virgile.dandoy@kit.edu