Where do the matter and the light of the cosmic radiation come from? Physicists have had ideas about this since the early 1960s and these ideas are not unrelated to black hole radiation. Certain leads, stemming from quantum field theory in curved space-time, have just been tested for cosmology with a Bose-Einstein condensate in the laboratory on Earth.

The theory of big Bangbig Bang is a definitive achievement of the beginning of the 21st^{e} century. But it is so if by Big Bang theory we mean the theory which says that theUniverseUniverse observable, which does not mean all that exists, was in a much denser and hotter state, without atoms and stars, say between 10 and 20 billion years ago. It could therefore be that our observable Universe is only a region of a cosmoscosmos infinite in space and in time which one day collapsed gravitationally, like a star giving rise to a black hole, before bouncing back into an expansion phase after having reached a limit but finite density.

In any case, one can ask the question of the origin of the mattermatter and some lightlight of the fossil radiation that we observe all around us. The developments of quantum mechanics and in particular of quantum field theory from the years 1925 to 1935 make it possible to imagine processes not only for the creation of quanta of light but also of quanta of matter, the electronselectrons atoms and quarksquarks forming the protonsprotons and the neutronsneutrons being then cousins of photonsphotons.

Could these processes be used as part of the cosmologycosmology Einstein’s relativist to explain the origin of matter?

## A creation of matter produced by dynamic space-times

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The answer is yes and paradoxically, when in fact these are processes described by a quantum field theory in a space-timespace-time curve which is not quantified, we have known this since the 1960s before stephen hawkingstephen hawking did not use this theory at the beginning of the following decade to discover the production of particles by black holesblack holes now bearing his name under the title of Hawking Radiation.

We owe the discovery of the quantum creation of particles in cosmology to an American physicist who began to work on this question in 1962 in his thesis subject under the direction of the legendary Sydney Colman (see on this subject the article in Futura about Jean-Pierre Luminet’s latest book on black holes). The physicist in question is called Leonard Parker and you can find on *arXiv, *in the form of an interview, a fascinating history of the quantum theory of particles in curved space-time. We learn, for example, that in fact the first quantum calculations of these effects date back to 1939 and that we owe them to… Erwin Schrödinger !

Leonard Parker also explains there that some time after having passed his thesis he spoke to Fred Hoyle about his discovery of the production of particles by expanding space-times described by the famous family of solutions of equationsequations of Einstein said of Friedmann-Lemaitre-Robertson-Walker (FLRW) for cosmological models isotropicisotropic and homogeneous (therefore appearing identical to any observer everywhere and looking in different directions with regard in particular to the density of average particles and the speedspeed expansion at some point in the history of the observable cosmos).

Fred Hoyle, at that time arguably Britain’s finest cosmological theorist behind a Stephen Hawking whose star had just begun to shine, was known as the author in 1948, along with Hermann Bondi and Thomas Gold, of the now deceased stationary cosmological modelmodel denying the Big Bang theory of Lemaître and Gamow.

Hoyle, Bondi and Gold had proposed in this model, which then dominated cosmology before the discovery of quasarsquasars and above all from fossil radiation, that the cosmos was infinite in time and space, although paradoxically expanding. It was therefore absolutely homogeneous in space and time since no matter the place or the time at which an observer made measurements about it, he would always see the same things on average, without an evolution of the galaxies or the matter is really noticeable.

But for that, Hoyle must have assumed that a continual creation of matter must occur, leading to the equally continual birth of galaxies. Without this assumption, the cosmos would become more and more diluted with expansion.

Hoyle had developed some equations to account for certain aspects of this creation of matter, but they were more or less rudimentary. Parker’s work gave a much more accurate description and unfortunately, as he explained to Hoyle, it did not allow sufficient creation of matter with the measured expansion rate. But everything changed with a much faster primitive expansion phase.

The quantum field theory in curved space-time will develop rapidly during the 1970s under the impetus of multiple researchers both in England and in Russia, for cosmology of course but especially because of the discovery of Hawking radiation. . A second impulse will come at the beginning of the 1980s with the discovery of the theory of cosmological inflation which will make it possible to develop a scenario of creation of the matter which today constitutes the observable cosmos and also lead to the prediction of a production of gravitons, more generally ofgravitational wavesgravitational wavesby the prodigiously exponentially rapid expansion phase of the early history of the Universe in the theory of inflation.

These gravitational waves could leave traces observable today in the fossil radiation.

Can we test the mechanisms of particle production due to the expansion of the Universe proposed by Parker and later by his colleagues?

## Space-time simulators with Bose-Einstein condensates

Directly, it does not seem, but just as in the case of indirect tests of Hawking radiation, the Canadian physicist William Unruh, discoverer of a radiation cousin of that of black holes since called “Unruh effect” had shown as early as the 1980s that the equations of quantum field theory in curved space-time had analogues with phenomena in fluids and that one could therefore test the ideas and calculations involved in the laboratory, failing to be able to really reproduce the creation of particles in the space-time of relativity.

In fact, for more than a decade, we have indeed obtained in the laboratory, in particular with what are called sonic black holes, analogs not only of Hawking radiation but also of the Unruh effect. Famous examples have been obtained in Bose-Einstein condensates. We will therefore not be surprised by a recent publication in *Nature,* and which can be found freely on *arXiv,* precisely reporting a breakthrough in this field now allowing to explore the creation of particles in cosmology.

The article talks about work done by Markus Oberthaler of the University of Heidelberg, Germany, who together with his colleagues started by getting about 20,000 ultracold atoms from potassiumpotassium 39 using laserslasers to slow them down and lower their temperature to about 60 nanokelvins, or 60 billionths of a degree KelvinKelvin above absolute zeroabsolute zero.

These atoms then undergo a phase transitionphase transition which makes them behave like a single quantum wave and more precisely therefore a Bose-Einstein condensate. It is possible to manipulate this collection of atoms in such a way as to give rise to processes described by equations analogous to those governing the creation of quantum particles by a curved space-time of the expanding FLRW family, more precisely a space-time infinity of hyperbolic type to use the jargon of physicistsphysicists relativists.

Of course, the BE condensate is not infinite but part of it is described by equations related to what is called the Poincaré disk, i.e. a set of points in a disc in relation by a mathematical transformation with the points of a space with a hyperbolic geometry. So there is a sort of dictionary between the two spaces, so that we can study with each other what precisely allows us to translate quantum field theory in curved space-time in hyperbolic space into a quantum theory with sound wavessound waves quantized containing cousins of photons, the phonons.

In doing so, the researchers have just carried out the first experiment that used ultracold atoms to simulate a curved and expanding universe. The quantum sound waves in the BE condensate then exhibit the analog that the creation of particle pairs predicted by the work of Parker and his colleagues, which reinforces confidence in the theory of quantum fields in curved spacetime.

As a bonus, we now have a laboratory to explore unknown consequences of the equations of this theory that we have not yet been able to discover in the equations by calculation and reasoning.