Since the 1930s, researchers have found evidences that the mass of the Universe is made for about 85% of a puzzling and yet unknown form of matter manifesting itself at different scales (i.e., out to tens of kpc from galactic rotation curves measurements, out to 200 kpc from microlensing measurements and out to cosmological scales from cosmic microwave background measurements). Various are the hypotheses regarding this component’s origin, but so far physicists have not come to a definite conclusion on this matter.

The mysterious substance does not emit light, which is why it was called “dark” matter. Other properties that observations require dark matter particles to obey are vanishing electric charge and stability, or at least a very long lifetime. The fact that dark matter interacts with other particles only through gravity and possibly through weak interaction makes it very difficult to study it experimentally, because typically particles are detected through electromagnetic and strong interactions, which are usually much more intense.

Thus, no dark matter constituents have yet been observed, although many attempts have been made with ground-based detectors, as well as with the help of particle colliders and satellites. Nonetheless, astrophysicists have been studying this matter extensively and have proposed many possible candidates for the role of dark matter particles, some of which are beyond the scope of the Standard Model of elementary particles. These include hypothetical primordial black holes born in the early Universe, weakly interacting massive particles, ultralight axions, and many others.

Could gravitons be good candidates for dark matter?

A very interesting idea was put forward a few years ago in a study led by Klaus Werner, whose authors hypothesized that the elementary dark matter components could be compact configurations of gravitons — it is the particle that mediates the force of gravitation, — bound to each other by gravity. This candidate is very attractive for scientists, because it doesn’t require considering some unknown particles as it is done in many other theoretical models of dark matter, and simplicity is typically an important criterion in physics.

To analyze the interaction of gravitons, they used the general theory of relativity, a geometric theory treating gravity as a deformation of spacetime sourced by energies and masses of particles. These particles include gravitons, whose energy allows them to interact with other gravitons much like planets or stars interact with each other. It is thanks to this phenomenon that the particles mediating the gravitational interaction can be attracted to each other and form bounded systems, in a sense similar to the solar system.

However, their analysis had a flaw: general relativity is known to be an incomplete theory of gravity, because it does not include quantum effects. Currently, there is no generally accepted “quantum gravity” theory, but scientists have developed many possible candidates.

Changing the ball game

In a recent study published in The Journal of High Energy Physics, a team of physicists led by Leonardo Modesto of the Southern University of Science and Technology in China improved on the analysis carried out by Werner’s group by considering the interaction of gravitons in various theories of quantum gravity (string theory is the most well-known example) that generalize general relativity.

Through analytical calculations, the physicists have found that in almost all the theories they considered, gravitons indeed can attract each other and form compact objects that can constitute dark matter. They called these objects Planckballs because their size, according to the scientists’ computations, turned out to be of the order of the Planck length — a typical scale of any theory of quantum gravity and approximately equal to 10⁻³⁵ m.

For the formation of Planckballs, the energies of gravitons had to be very large — usually of the order of the Planck mass, a typical mass scale of quantum gravity, which is approximately 22 orders of magnitude heavier than an electron. It means that bound systems of gravitons could have formed only in the very early Universe, in which the temperature was extremely high (in some theories of quantum gravity it is of the order of 10³² degrees).

While the idea that the team came up with is very interesting from a theoretical point of view, only future more precise experimental studies can help determine which of the proposed dark matter theories is correct, or whether the reality is even more complex and dark matter is made up of objects that scientists haven’t even considered yet.

Reference: Zhongyou Mo, Tibério de Paula Netto, Nicolò Burzillà, and Leonardo Modesto, “Stringballs and Planckballs for dark matter,” Journal of High Energy Physics, 2022, 131

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