There is more unknown than known. It turns out that about 68% of the universe is dark energy. Dark matter makes up about 27%.

Albert Einstein was the first to realize that space is not nothing. It can own its energy, which could be the property of space itself. As more space arises, more of this energy-of-space will appear. As a result, this form of energy would cause the universe to expand faster and faster.

Moreover, it could reunite two powerful physical currents: quantum field theory and the general theory of relativity developed by Albert Einstein. But there’s a catch: calculations and observations are so different. Two researchers from Luxembourg have shown a new way to solve this 100-year-old riddle.

prof. Alexandre Tkachenko, professor of theoretical physics in the Department of Physics and Materials Science at the University of Luxembourg, said: *“Vacuum has energy. This is a fundamental result of quantum field theory. This theory was developed to combine quantum mechanics and special relativity, but quantum field theory seems incompatible with general relativity.”*

*“The essential feature: unlike quantum mechanics, the theory considers not only particles, but also matter-free fields as quantum objects. In this context, many researchers consider dark energy to be an expression of so-called vacuum energy: a physical quantity that, in a vivid picture, is caused by a constant emergence and interaction of pairs of particles and their antiparticles – such as electrons and positrons – in what is space. ”*

Physicists call this movement of virtual entities and their quantum fields vacuum or zero-point fluctuations. The pairs of particles leave behind a certain amount of energy, even though they quickly vanish into thin air.

Scientists noted, *“This vacuum energy also has a meaning in general relativity. It is reflected in Einstein’s cosmological constant included in his equations for physical reasons.”*

The cosmological constant can be calculated directly by astrophysical experiments, unlike vacuum energy, which can only be deduced from quantum field theory formulas. The Hubble Space Telescope and the Planck space mission measured the fundamental physical quantity and the results are close and reliable. Rather, dark energy calculations based on quantum field theory yield findings that correlate with a value of the cosmological constant that is up to 10120 times greater – a huge divergence, even though both quantities are assumed to be equal in the current state of physics.

Tkachenko said: *“The discrepancy found is known as the riddle of the cosmological constant. It is undoubtedly one of the greatest inconsistencies in modern science.”*

In this work, scientists proposed a new interpretation of dark energy. It assumes that the zero-point fluctuations lead to a polarizability of the vacuum, which can be measured and calculated.

Tkachenko explains, *“In pairs of virtual particles with an opposite electric charge, it arises from electrodynamic forces that these particles exert on each other during their extremely short existence.”*

*“This is called a vacuum self-interaction. It leads to an energy density that can be determined using a new model.”*

In 2018, scientists presented a basic model for atoms. The concept was initially used to explain the relationship between atomic polarizability and the equilibrium characteristics of some non-covalently bonded molecules and solids. Since it is easy to experimentally quantify the geometric properties, it is also possible to calculate the polarizability using their formula.

Luxembourg research colleague Dr. Dmitry Fedorov said: *“We have transferred this procedure to the processes in the vacuum. To this end, the two researchers looked at the behavior of quantum fields, in particular the ‘coming and going’ of electrons and positrons. The fluctuations of these fields can also be characterized by an equilibrium geometry already known from experiments. We put it into the formulas of our model and finally obtained the power of the intrinsic vacuum polarization.”*

The energy density of the self-interaction between fluctuations of electrons and positrons was then calculated using quantum mechanics. The finding of this method agrees with the observed values of the cosmological constant. This suggests that dark energy can be traced back to the energy density of quantum field interactions.

Scientists noted, *“So our work offers an elegant and unconventional approach to solving the conundrum of the cosmological constant. Moreover, it gives a verifiable prediction: namely that quantum fields such as those of electrons and positrons possess a small but ever-present intrinsic polarization.”*

Fedorov said, *“Our goal is to derive the cosmological constant from a rigorous quantum theoretical approach. And our work contains a recipe for making this a reality. The new results are the first step towards a better understanding of dark energy – and its connection to Albert Einstein’s cosmological constant. Ultimately, this could also shed light on how quantum field theory and general relativity are intertwined as two ways of looking at the universe and its components.”*

**Magazine reference:**

- Alexandre Tkatchenko and Dmitry V. Fedorov. Casimir self-interaction energy density of quantum electrodynamic fields. Physical Assessment Letters (2023). DOI: 10.1103/PhysRevLett.130.041601