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

The universe possesses a number of bizarre characteristics that are tough to fully grasp with day experience. The matter that we understand, for instance, comprising of atoms and molecules and other particles, only compensates a tiny portion of the complete energy density of the universe. The largest contribution, more than two thirds, comes from “dark energy,” a hypothetical kind of energy whose background physicists continue to be puzzled over.

Furthermore, the universe is growing continuously, and at a faster rate than before. Since dark energy is additionally regarded as a driver of accelerated expansion, these two traits seem to be linked. Furthermore, it might unite two powerful physical schools of thought: Albert Einstein developed the quantum field theory and the general theory of relativity. There is a trap, though: Till now, the computations and observations have been far from overlapping. In a paper these days published in the journal Physical Review Letters, two scientists from Luxembourg have demonstrated a way to solve this 100-year-old problem.

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

“Dark energy comes out of the formulations of quantum field theory,” says Prof. Alexandre Tkatchenko, Professor of Theoretical Solid State Physics in the Department of Physics and Material Sciences in the University of Luxembourg. This concept was created to bring together general relativity and quantum mechanics, which in fundamental elements are incompatible.

It’s an important characteristic: In contrast to quantum mechanics, the theory deals with not just particles, but also materialless areas as quantum items. “In this framework, a lot of researchers regard dark power as an expression of vacuum energy,” Tkatchenko stated. a physical amount that’s brought on in a vivid picture by a continuous emergence of pairs of particles as well as their antiparticles (like positrons and electrons) in what’s in fact empty space.

Physicists talk about this passing as well as coming of real particles and their quantum fields as vacuum or zero-point variations. Although the particle pairs vanish into nothingness for one minute, they leave behind a particular amount of power. “This vacuum energy has a significance in general relativity,” says the Luxembourger. “It shows itself in the cosmological constant Einstein placed for mathematical explanations into his equations,” he stated.

**A colossal mismatch**

In contrast to dark energy, which can only be deduced from the formulae of quantum field theory, the cosmological constant can be directly determined by astrophysical experiments. Measurements created with the Hubble space telescope and the Planck space mission have created close and reliable values for the fundamental physical quantity.

However, calculations of dark energy on the basis of quantum field theory produce results which correspond to a value of the cosmological constant that’s up to 10120 times larger, although both values must be equivalent in the world view of physicists common nowadays. Rather, the discrepancy is known as the “cosmological constant enigma.” Alexandre Tkatchenko states, “It is undoubtedly one of the greatest inconsistencies in contemporary science.”

**Unconventional way of interpretation**

Together with his Luxembourg research colleague Dr. Dimitry Fedorov, he’s now brought the answer to this puzzle, that has been open for decades, a considerable step closer. The two Luxembourg researchers propose a new interpretation of dark power in a theoretical paper released recently. It assumes that zero-point variations cause a polarization of vacuum, which may both be measured as well as calculated.

“In virtual pairs of particles possessing an electric charge, it originates out of the electrodynamic forces that these particles exert on one another during their extremely short existence,” Tkatchenko said. Physical scientists describe this as a self-interaction, the polarizability being a feature of response to it in this sort of particles. “It results in an energy density which could be established with the help of a brand new model,” the scientist from Luxembourg said.

He developed this model with his research associate Fedorov and presented it first in 2018 initially used to describe atomic properties, for instance in solids. Because geometric characteristics are experimentally quite simple to measure, polarizability can also be determined through these deviations.

Fedorov says, “We transferred this procedure to the processes in the vacuum. To accomplish this, the 2 researchers looked at the behavior of positrons and electrons, which they dealt with based on the rules of quantum field theory as fields. Fluctuations of these areas can in addition be characterized by an equilibrium geometry whose value has already been recognized from experiments.

“We inserted it into the formulas of our model, and in this way, ultimately, we got the strength of the polarization of vacuum,” Fedorov said. The last action was to calculate the vitality density of self-interaction between electrons and positrons quantum mechanically. The obtained result in this particular manner is in agreement along with the measured values for the cosmological constant: This means: “Dark energy can be traced to the electricity density of the self-interaction of quantum fields,” Alexandre Tkatchenko, a researcher at MIT, noted.

**Consistent values and verifiable forecasts**

Hence, “our work provides an unconventional and elegant way of solving the riddle of the cosmological constant,” he said. “Furthermore, it gives a verifiable prediction:” More specifically, quantum fields like electrons and positrons do indeed have a little but ever-present polarization. “

The results opened the way for future tests to identify this polarization in the lab, the two Luxembourg scientists said. They wish to apply their model to other particle-antiparticle pairs. Alexandre Tkatchenko, however, pointed out that “our conceptual idea must be relevant to almost any field.” He views the new results obtained along with Dimitry Fedorov as the very first step towards a clear understanding of dark energy – as well as its connection with Albert Einstein’s cosmological constant.

Tkatchenko is convinced. “this will likewise illuminate the manner in which in which quantum field theory as well as general reactivity theory are linked as two methods of looking at the universe as well as its components,” he said.

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