Science & Nature

The Uneven Universe: Cosmic Expansion and Einstein’s Theory of General Relativity

The Uneven Universe: Cosmic Expansion and Einstein’s Theory of General Relativity thumbnail

Universe Expansion Funnel Animation

A representation of the evolution of the universe over 13.77 billion years. The far left depicts the earliest moment we can now probe, when a period of “inflation” produced a burst of exponential growth in the universe. (Size is depicted by the vertical extent of the grid in this graphic.) For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity. More recently, the expansion has begun to speed up again as the repulsive effects of dark energy have come to dominate the expansion of the universe. Credit: NASA’s Goddard Space Flight Center

Researchers study cosmic expansion using methods from many-body physics.

It is almost always assumed in cosmological calculations that there is an even distribution of matter in the universe. This is because the calculations would be much too complicated if the position of every single star were to be included. In reality, the universe is not uniform: in some places there are stars and planets, in others there is just a void.

Physicists Michael te Vrugt and Prof. Raphael Wittkowski from the Institute of Theoretical Physics and the Center for Soft Nanoscience (SoN) at the

gravitational waves
Gravitational waves are distortions or ripples in the fabric of space and time. They were first detected in 2015 by the Advanced LIGO detectors and are produced by catastrophic events such as colliding black holes, supernovae, or merging neutron stars.

“>gravitational waves, and in 2020 for the discovery of a

“Strictly speaking, it is mathematically wrong to include the mean value of the universe’s energy density in the equations of general relativity,” says Sabine Hossenfelder. The question is now how “bad” this mistake is. Some experts consider it to be irrelevant, others see in it the solution to the enigma of dark energy, whose physical nature is still unknown. An uneven distribution of the mass in the universe may have an effect on the speed of cosmic expansion.

“The Mori-Zwanzig formalism is already being successfully used in many fields of research, from biophysics to particle physics,” says Raphael Wittkowski, “so it also offered a promising approach to this astrophysical problem.” The team generalized this formalism so that it could be applied to general relativity and, in doing so, derived a model for cosmic expansion while taking into consideration the uneven distribution of matter in the universe.

The model makes a concrete prediction for the effect of these so-called inhomogeneities on the speed of the expansion of the universe. This prediction deviates slightly from that given by the Lambda-CDM model and thus provides an opportunity to test the new model experimentally. “At present, the astronomical data are not precise enough to measure this deviation,” says Michael te Vrugt, “but the great progress made – for example, in the measurement of gravitational waves – gives us reason to hope that this will change. Also, the new variant of the Mori-Zwanzig formalism can also be applied to other astrophysical problems – so the work is relevant not only to cosmology.”

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Reference: “Mori-Zwanzig Formalism for General Relativity: A New Approach to the Averaging Problem” by Michael te Vrugt, Sabine Hossenfelder and Raphael Wittkowski, 1 December 2021, Physical Review Letters.

DOI: 10.1103/PhysRevLett.127.231101

Funding: Michael te Vrugt receives funding in the form of a doctoral scholarship from the Studienstiftung des deutschen Volkes (German Academic Scholarship Foundation). Sabine Hossenfelder receives financial support from the German Research Foundation (DFG, HO 2601/8-1). The Wittkowski working group is also financed by the German Research Foundation (DFG, WI 4170/3-1).

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