Predicted in 1916 by Albert Einstein as a natural consequence of general relativity, gravitational waves were definitively detected on September 14, 2015 during the merger of two black holes (1). Not only do these provide further support for Einstein's theory but, as real vibrations of space-time, are also excellent tools for the study of our universe.
In their study published on September 12, 2017 (2) in the important journal Physical Review Letters , physicists Juri Smirnov (Max Planck Institute), Moritz Platscher (Max Planck Institute) and Kevin Max (School Normal Superior of Pisa), after having analyzed in depth the data of the LIGO collaboration (1), propose an oscillation model gravitational waves within the framework of a modified theory of gravity called "bimetric gravity" or "bigravity" (not to be confused with the theory of the bimetric universe developed by Andrei Sakharov, then by Jean-Pierre Petit).
The motivation for this hypothesis is based on the fact that only 5% of the density of the universe is known in the form of the classical matter that surrounds us. The remaining 95% is dominated by dark matter and dark energy. Most of the theories explaining these last two phenomena involve new types of particles or energies. However, as Juri Smirnov points out, “experiments such as the one carried out at the LHC have not, to date, detected any exotic particles. This therefore raises the question of whether it is not rather the theory of gravity that should be modified .
Smirnov goes on to say "in our study, we wonder what signal we should detect in the case of a change in gravity, and it turns out that the bigravity model predicts a characteristic signal that distinguishes it from other theories .
The main idea of the bigravity theory is to describe the structure and the dynamics of the universe via two metric tensors (mathematical tool allowing to describe the geometry of space-time). In the case of general relativity, i.e. the currently used theory of gravity, a single metric tensor is used to describe the local geometry of spacetime.
In bimetric gravity, an additional metric makes its appearance. However, these two metrics denoted "metric g" and "metric f" do not have the same dynamics. Indeed, only the metric g is coupled to the material, it alone interacts with the latter. While the metric f has no coupling with matter, it is said to be sterile.
The consequence of the existence of a double metric is the concomitant emergence of a second type of graviton. In the various quantum gravity theories unifying quantum field theory and general relativity, gravity is conveyed, in the same way as the other three interactions, by a gauge boson of zero mass traveling at the speed of light:the graviton.
However, with the addition of an additional metric, a new type of boson naturally appears, whose main characteristic is to be massive (non-zero mass).
The idea of a massive graviton moving at less than the speed of light in a vacuum is not new and dates back to the early 1930s, with physicist W. Pauli. However, it was not until 2010, thanks to the work of physicists C. de Rham, G. Gabadadze and A. Tolley, that a true and rigorous theory of massive graviton, called "theory of massive gravity", appeared. (3). The authors of bimetric gravity thus resumed the work of their predecessors to incorporate a second metric.
Bigravity therefore has two metrics implying the existence of two gravitons, a non-massive and a massive. Each graviton is a linear combination of the two metrics. In other words, each graviton comes from the "mixing" of the two metrics, this mixture being different for each of the gravitons, leading to a graviton of zero mass and another of positive mass.
It is possible to make here a direct analogy with neutrinos. There are three flavors of neutrinos:electron, muon and tau. Electronic neutrinos being the most stable, they are those produced during the various reactions. However, as Mr. Platscher points out, “electron neutrinos do not have a perfectly defined mass:their mass is a superposition of the different eigenstates of the masses of the three types of neutrinos ". The same goes for the two types of gravitons resulting from the combination of the two types of metrics.
But this is not the only common point with neutrinos. Indeed, just like the latter, gravitons, and therefore gravitational waves, can also oscillate.
Each type of graviton is a combination of the metrics g and f. This means that at some point in their journey, they have the possibility of oscillating, that is to say of passing from one type to another. Since the metric g is the only one able to couple with matter, it is g-type gravitational waves that are always produced during the various important cosmological phenomena (binary black holes, etc.).
However, once produced and along their journey through spacetime, these gravitational g-waves can oscillate and transform into gravitational f-waves. However, as Platscher explains, “We can only measure gravitational g-waves with our detectors (made of matter) while f-waves pass through completely invisibly. If bigravity is a correct description of gravity, such an oscillation should leave a large imprint in the gravitational wave signal .
So, does bigravity make verifiable predictions by observing and analyzing gravitational waves? As Smirnov rightly points out, “bigravity being a very recent theory, a long and important work still remains to be done to deepen it and explore its full potential. We have made some developments in this study, but many more will still be needed .
