The theory of general relativity developed by Albert Einstein has actual application in describing the universe’s expansion since the Big Bang. The speed of this expansion is determined by the amount of energy in the universe.

According to the Lambda-CDM model, along with visible matter, dark matter, and dark energy also play a role in this cosmic expansion. Scientists believe 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.

The truth is: Universe is not uniform. In some places, there are stars, planets whereas, in some places, there is nothing.

Physicists Michael te Vrugt and Prof. Raphael Wittkowski from the Institute of Theoretical Physics and the Center for Soft Nanoscience (SoN) at the University of Münster have physicist Dr. Sabine Hossenfelder from the Frankfurt Institute for Advanced Studies (FIAS), developed a new model for this problem.

At first, they considered the Mori-Zwanzig formalism. It is a method to describe systems comprising many particles with a small number of measurands.

Dr. Hossenfelder said, “Strictly speaking, it is mathematically wrong to include the mean value of the universe’s energy density in the equations of general relativity. 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. Uneven distribution of the mass in the universe may affect the speed of cosmic expansion.”

The team generalized this formalism so that it could be applied to general relativity. While doing so, the team derived a model for the cosmic expansion of the universe.

Their model predicted the effect of these inhomogeneities on the speed of the universe’s expansion. This prediction differs somewhat from that given by the Lambda-CDM model and subsequently offers an opportunity to test the new model experimentally.

Raphael Wittkowski said, “The Mori-Zwanzig formalism is already being successfully used in many fields of research. It also offered a promising approach to this astrophysical problem.”

Michael te Vrugt said, “At present, the astronomical data are not precise enough to measure this deviation, 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 be applied to other astrophysical problems – so the work is relevant not only to cosmology.”

Journal Reference:

M. te Vrugt, S. Hossenfelder, R. Wittkowski (2021). Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem. Physical Review Letters 127, 231101. DOI: 10.1103/PhysRevLett.127.231101