According to Einstein's General Relativity, planets, stars, and galaxies are in a lattice known as space-time, which is warped by mass and thus explains the existence of gravitational fields. This theory is based on the idea that matter tells space how to curve and space tells matter how to move. They do this using a very important formula known as the ‘Einstein field equation’. This equation, similar in importance to the famous ‘E=mc^2’, says that the curvature of an area of space is proportional to the amount of matter (and energy) it contains. Therefore, if the planets revolve around the Sun, it is because our star ‘collapses’ space-time so that the planets fall towards it, by the shortest path.

Shortly after proposing his field equation in 1915, Einstein discovered that he had defined a space-time that could stretch or contract, like a rubber band, but could not remain static. This indicated, no more and no less, that the Universe was not fixed, eternal, and unchanging, which, at the time, went against the scientific consensus. So in 1917 Einstein tweaked his field equation and introduced a parameter or variable, which ensured that the Universe was in equilibrium thanks to a kind of anti-gravitational force. This parameter was called the cosmological constant. According to Einstein, this constant must be expressing the action of an exotic form of energy, a kind of repulsive gravity, which would have the opposite effect to the force of gravity. Thanks to it, the Universe was in equilibrium and static, as astronomers believed at the time.

However, in 1929 Edwin Hubble claimed, based on his observations, that the Universe was expanding. From then on it also became increasingly clear that the Universe was much larger than our galaxy, and that there were an immense number of other galaxies. So Einstein declared that his cosmological constant, which kept the Universe static, had been the biggest mistake of his career. And his parameter fell into oblivion.

Expansion accelerates

However, as science progresses, it is overthrowing everything we think we know. The cosmological constant made a comeback in the 1990s. At that time, a surprising fact was discovered: that the expansion of the Universe is accelerating. So this time astronomers reintroduced the cosmological constant into the Einstein field equation. Their task was to give acceleration to the expansion, and so the idea of dark energy as the driving force of the ‘repulsion’ in the Universe gradually gained momentum.

This cosmological constant is nowadays represented by the letter lambda (Λ) and is also known as vacuum energy. It is closely related to the concept of dark energy and is one of the pillars of the cosmological model, which is the theoretical framework that explains the evolution of the Universe since the Big Bang and is called the Λ-CDM.

One of the keys to maintaining this model is to know exactly how the Universe is expanding. There is a number, the Hubble parameter or Hubble constant, which is fundamental to this task. This number expresses the expansion rate of the Universe and allows us to estimate its age. Together with other parameters, it also allows us to find its curvature and its fate.

Beacons of the Universe

So far, astronomers have been able to estimate the value of the Hubble parameter from observations of three different phenomena. On the one hand, it is inferred from the microwave background radiation, an echo of energy from the early Universe, and, on the other hand, from two astrospheric beacons: Type Ia supernovae and Cepheid variable stars.

Both the former and the latter are characterised by the fact that astronomers know exactly how much light they emit. Therefore, by observing the amount of their light reaching the Earth, it is easy to estimate how far away they are. In addition, the light they send us is redshifted, because these objects are moving away from us as the Universe expands. This effect also occurs with the sound emitted by an ambulance approaching or moving away from us: the waves change their wavelength because of the speed of the ambulance, and so we perceive a higher or lower-pitched sound as the car approaches or moves away, respectively. Well, with light this effect is similar, but it causes a red shift or a blue shift, depending on whether the object is moving away from or towards the Earth, respectively.

The problematic Hubble constant

The current problem is that the radiation background and measurements from supernovae and variable stars give astronomers different values for the Hubble constant. Not that changing the model is a big problem, because in cosmology models are changed when necessary, but doing so would have important implications the Hubble constant is the way they measure the age of the Universe and since scientists learned that the Universe is expanding, they know that there is a relationship between how far away objects are and how fast they are moving away from us.

The answer in neutron stars

In 2017 astronomers observed one of these mergers for the first time. The achievement was made possible thanks to a very new technology that can capture gravitational waves, distortions of space-time that spread through the Universe at the speed of light, for example when two black holes or two neutron stars merge. Well, after picking up these waves, it was possible to estimate where the source was and point ground-based telescopes to take a look for the light from the event.

In 2019, a group of scientists from University College London and the Flatiron Institute (USA), led by Stephen Feeney, proposed a way to finally refine the value of the Hubble constant. In a paper published in Physical Review Letters, they detail how, in just 10 years, astrophysicists will be able to calculate the expansion rate of the Universe accurately simply by observing a rare astronomical phenomenon: the merger of pairs of neutron stars. They have calculated that, with 50 of these, it will be possible to solve this enigma.

In addition, they have worked out a technique to calculate how gravitational waves can solve the Hubble constant problem to give a more accurate picture of how the Universe is expanding and help improve the cosmological model.

Albert Einstein would probably have been surprised to find out that gravitational waves, which his theory predicted but which he did not think could be measured, would help us understand how old the Universe is and what its fate will be.

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