What is behind dark energy – and what links it to the cosmological constant introduced by Albert Einstein? Two physicists from the University of Luxembourg point to a way to answer these open questions in physics.
The universe has a number of strange properties that are difficult to understand through everyday experience. For example, the matter we know, which is made up of elementary and composite particles made up of molecules and matter, apparently makes up only a small part of the energy of the universe. The largest contribution, about two-thirds, comes fromdark energy— a hypothetical form of energy whose background physicists are still baffled by. Moreover, not only is the universe expanding steadily, but it is also doing so at an ever faster pace.
It seems that both properties are related, because dark energy It is also considered a driver of accelerated expansion. Moreover, it can unite two powerful physics schools of thought: quantum field theory and the general theory of relativity developed by Albert Einstein. But there is a catch: the accounts and notes are far from identical. Two Luxembourg researchers show a new way to solve this 100-year-old mystery in a research paper published by the journal Physical review letters.
The effect of virtual particles in a vacuum
“Vacuum has energy. This is a fundamental result of quantum field theory,” explains Professor Alexander Tkachenko, Professor of Theoretical Physics in the Department of Physics and Materials Sciences at University of Luxembourg. This theory was developed to combine quantum mechanics and special relativity, but quantum field theory appears to be incompatible with general relativity. Its main advantage: unlike quantum mechanics, the theory considers not only particles but also spheres devoid of matter as quantum objects.
“Within this framework, many researchers consider dark energy to be an expression of what is called vacuum energy,” says Tkatchenko, a physical quantity that results, in living form, from the appearance and continuous interaction of pairs of particles and their antiparticles — such as electrons and positrons — in what is in reality Empty space.
Physicists speak of the comings and goings of virtual particles and their quantum fields as fluctuations in a vacuum, or zero point. As pairs of particles rapidly fade back into nothingness, their presence leaves behind a certain amount of energy.
The Luxembourg scientist notes that “this vacuum energy also has a meaning in general relativity”: “It manifests itself in the cosmological constant that Einstein included in his equations for physical reasons.”
Unlike the energy of a vacuum, which can only be deduced from the equations 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 yielded close and reliable values for the fundamental physical quantity. On the other hand, dark energy calculations based on quantum field theory lead to results consistent with the value of the cosmological constant being 10120 times greater – a colossal discrepancy, although according to the prevailing view of physicists today, both values should be equal. The contradiction that exists is instead known as the “enigma of the cosmological constant”.
“It is without a doubt one of the greatest contradictions in modern science,” says Alexander Tkachenko.
Unconventional way of interpretation
Together with fellow Luxembourg researcher Dr Dmitry Fedorov, he has now brought the solution to this mystery, which has been open-ended for decades, an important step closer. In a theoretical work, they recently published their results in Physical review lettersThe two researchers in Luxembourg proposed a new explanation for dark energy. Zero point fluctuations are assumed to result in vacuum polarization, which can be measured and calculated.
“In pairs of virtual particles of opposite electric charge, they arise from the electrodynamic forces that these particles exert on each other during their very short time of existence,” explains Tkachenko. Physicists refer to this as a self-interacting vacuum. “It leads to an energy density that can be determined with the help of a new model,” says scientist Luxembourg.
Together with research colleague Fedorov, they developed the fundamental model of atoms a few years ago and presented it for the first time in 2018. The model was originally used to describe atomic properties, in particular the relationship between the polarizations of atoms and the equilibrium properties of some non-covalently bonded molecules and solids. Since it is very easy to measure geometrical properties experimentally, polarization can also be determined by their formula.
“We transferred this procedure to operations in a vacuum,” Fedorov explains. To this end, the two researchers looked at the behavior of quantum domains, in particular the representation of the “coming and going” of electrons and positrons. 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 we finally obtained the polarization force of the inner void,” says Fedorov.
The final step then was to mechanically calculate the energy density of the self-interaction between fluctuations of electrons and positrons. The result obtained in this way is in good agreement with the measured values of the cosmological constant. This means: “Dark energy can be traced back to the energy density of the self-interaction of quantum fields,” asserts Alexander Tkachenko.
Consistent values and verifiable expectations
“Our work thus offers an elegant and unconventional approach to solving the mystery of the cosmological constant,” the physicist concludes. “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-based researchers. “Our goal is to derive the cosmological constant from a rigorous quantum theory approach,” asserts Dmitry Fedorov. “And our work includes a recipe for how to realize that.”
He sees the new results obtained with Alexander Tkachenko as the first step towards a better understanding of dark energy – and its relationship to Albert Einstein’s cosmological constant.
Finally, Tkatchenko is convinced: “Ultimately, this can also shed light on the way quantum field theory and general relativity theory intertwine as two ways of looking at the universe and its components.”
Reference: “Casimir self-interaction energy density in quantum electrodynamic fields” by Aleksandr Tkachenko and Dmitry Fedorov, Jan. 24, 2023, Available here. Physical review letters.