Physicists discover a new approach to solving the bizarre dark energy mystery

**What’s behind dark energy – and what connects it to the cosmological constant introduced by Albert Einstein? Two physicists from the University of Luxembourg point the way to answering these open questions of physics.**

The universe has some bizarre properties that are difficult to understand with everyday experience. For example, the matter we know, consisting of elementary and compound particles that make up molecules and materials, apparently makes up only a small fraction of the universe’s energy. The largest contribution, about two-thirds, comes from “dark energy— a hypothetical form of energy that background physicists are still puzzling over. Moreover, the universe is not only expanding steadily, but also accelerating.

Both characteristics seem to be related, because dark energy is also considered a driver of accelerated expansion. Moreover, it could reunite two powerful physical currents: quantum field theory and the general theory of relativity developed by Albert Einstein. But there is a catch: calculations and observations have so far been far from matching. Now two researchers from Luxembourg have shown a new way to solve this 100-year-old riddle in a paper published by the journal *Physical assessment letters*.

#### The trail of virtual particles in a vacuum

“Vacuum has energy. This is a fundamental result of quantum field theory,” explains Prof. Alexandre Tkatchenko, Professor of Theoretical Physics at the Department of Physics and Materials Science at the University of Luxembourg. This theory was developed to bring together quantum mechanics and special relativity, but quantum field theory seems to be 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,” says Tkatchenko: a physical quantity that, in a vivid picture, is caused by a constant rise and interaction of particle pairs and their antiparticles. – such as electrons and positrons – in what is actually empty space.

Physicists speak of this coming and going of virtual particles and their quantum fields as vacuum or zero-point fluctuations. As the pairs of particles quickly fade back into nothingness, their existence leaves behind a certain amount of energy.

“This vacuum energy also has a meaning in general relativity,” notes the Luxembourg scientist: “It manifests itself in the cosmological constant that Einstein included in his equations for physical reasons.”

#### A colossal mismatch

Unlike vacuum energy, which can only be deduced from the formulas of quantum field theory, the cosmological constant can be determined directly by astrophysical experiments. Measurements with the Hubble Space Telescope and the Planck space mission have provided accurate and reliable values for the fundamental physical quantity. In contrast, dark energy calculations based on quantum field theory yield results that correspond to a value of the cosmological constant that is at most 10.^{120} times greater – a colossal discrepancy, although in today’s worldview of physicists, both values should be equal. The discrepancy found instead is known as the “cosmological constant conundrum.”

“It is undoubtedly one of the greatest inconsistencies in modern science,” says Alexandre Tkachenko.

#### Unconventional interpretation

Together with his Luxembourg research colleague Dr. Dmitry Fedorov, he has now brought the solution of this puzzle, which has been open for decades, a big step closer. In a theoretical work, the results of which they recently published in *Physical assessment letters*the two Luxembourg researchers propose a new interpretation of dark energy. It assumes that the zero-point fluctuations lead to a polarizability of the vacuum, which can be both measured and calculated.

“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,” explains Tkatchenko. The physicists call this a vacuum self-interaction. “It leads to an energy density that can be determined using a new model,” says the Luxembourg scientist.

Together with his research colleague Fedorov, they developed the basic model for atoms a few years ago and presented it for the first time in 2018. The model was originally used to describe atomic properties, specifically the relationship between the polarizability of atoms and the equilibrium properties. of certain non-covalently bonded molecules and solids. Since the geometric features are quite easy to measure experimentally, the polarizability can also be determined through their formula.

“We transferred this procedure to the processes in the vacuum,” explains Fedorov. 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 inserted it into the formulas of our model and in this way finally obtained the strength of the intrinsic vacuum polarization,” reports Fedorov.

The last step was then to calculate quantum mechanically the energy density of the self-interaction between fluctuations of electrons and positrons. The result thus obtained agrees well with the measured values for the cosmological constant. This means: “Dark energy can be traced back to the energy density of the self-interaction of quantum fields,” Alexandre Tkatchenko points out.

#### Consistent values and verifiable forecasts

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

This finding points the way for future experiments to detect this polarization in the laboratory as well, say the two Luxembourg researchers. “Our goal is to derive the cosmological constant from a rigorous quantum theoretical approach,” emphasizes Dmitry Fedorov. “And our work contains a recipe for making this a reality.”

He sees the new results obtained with Alexandre Tkatchenko as the first step towards a better understanding of dark energy – and its connection to Albert Einstein’s cosmological constant.

Finally, Tkachenko is convinced: “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.”

Reference: “Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields” by Alexandre Tkatchenko and Dmitry V. Fedorov, January 24, 2023, *Physical assessment letters*.

DOI: 10.1103/PhysRevLett.130.041601

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