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 atoms and molecules and other particles, apparently makes up only a small fraction of the energy density of the universe. The largest contribution, more than 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 features appear to be linked, as dark energy is also considered to be 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 way to solve this 100-year-old riddle in a paper published by *Physical assessment letters*.

## The trail of virtual particles in a vacuum

“Dark energy arises from the formulas of quantum field theory,” explains Prof. Alexandre Tkatchenko, professor of theoretical solid state physics at the Department of Physics and Materials Sciences at the University of Luxembourg. This theory was developed to bring together quantum mechanics and general relativity, which are incompatible in fundamental aspects.

The essential feature: Unlike quantum mechanics, the theory considers not only particles, but also materialless 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 of pairs of particles and their antiparticles – such as electrons and positrons – in which 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 particle pairs instantly vanish back into nothingness, they leave behind a certain amount of energy. “This vacuum energy also has a meaning in general relativity,” notes the Luxembourg scientist. “It is reflected in the cosmological constant that Einstein inserted into his equations for mathematical reasons.”

## A colossal mismatch

Unlike dark 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 larger – 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. Dimitry Fedorov, he has now brought the solution of this puzzle, which has been open for decades, a big step closer. In a theoretical article, the results of which they recently published, 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.

“Virtual particle pairs with an electric charge are caused by electrodynamic forces that these particles exert on each other during their extremely short existence,” explains Tkatchenko. The physicists call this a self-interaction, the polarizability in such particles is a characteristic of the reaction to it. “It leads to an energy density that can be determined using a new model,” says the Luxembourg scientist.

Together with his research colleague Fedorov, he developed this model and presented it for the first time in 2018, originally used to describe atomic properties, for example in solids. Because the geometrical characteristics are fairly easy to measure experimentally, the polarizability can also be determined via these diversions.

“We transferred this procedure to the processes in the vacuum,” explains Fedorov. To do this, the two researchers looked at the behavior of electrons and positrons, which they treated as fields according to the principles of quantum field theory. The fluctuations of these fields can also be characterized by an equilibrium geometry whose value is already known from experiments.

“We inserted it into the formulas of our model and in this way finally obtained the strength of the polarization of the vacuum,” reports Fedorov. The last step was then to calculate quantum mechanically the energy density of the self-interaction between the electrons and positrons. The result obtained in this way agrees well with the measured values for the cosmological constant: this means: “Dark energy can be reduced 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 polarization.”

This finding points the way for future experiments to detect this polarization in the lab as well, say the two Luxembourg researchers, who now want to apply their model to other particle-antiparticle pairs. “Our conceptual idea should be applicable in any field,” emphasizes Alexandre Tkachenko. He sees the new results obtained with Dimitry Fedorov as the first step towards a better understanding of dark energy – and its connection to Albert Einstein’s cosmological constant.

Tkatchenko is convinced: “Ultimately, this will also shed light on how quantum field theory and general reactivity theory are intertwined as two ways of looking at the universe and its components.”

**More information:**

Alexandre Tkatchenko et al, Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields, *Physical assessment letters* (2023). DOI: 10.1103/PhysRevLett.130.041601

Offered by the University of Luxembourg

**Quote**: A New Approach to Solving the Mystery of Dark Energy (2023, January 24) Retrieved January 25, 2023 from https://phys.org/news/2023-01-approach-mystery-dark-energy.html

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