What is space-time isotropy and homogeneity

Gravitation brings about the homogeneity of the universe

Gravitation can explain the process of homogenization of space-time in the course of the evolution of the universe. This finding is based on theoretical studies by the physicist David Fajman at the University of Vienna. The mathematical methods developed within the framework of the research project enable the investigation of fundamental, open questions in cosmology such as why today's universe appears so homogeneous. The results have been published in the journal "Physical Review Letters".

The development of the universe over time, from the Big Bang to the present, is described by Einstein's field equations of general relativity. However, there are still a number of unanswered questions about cosmological dynamics, the origin of which lies in supposed discrepancies between theory and observation. One of these open questions is: Why is the universe in its current state so homogeneous on large scales?

From the big bang to today
It is assumed that shortly after the Big Bang, the universe was in an extreme state, which was characterized in particular by strong fluctuations in the curvature of space-time. During the long process of expansion, the universe then developed to its present state, which is homogeneous and isotropic on large scales - simplified: the cosmos looks the same everywhere. This is concluded, among other things, from the measurement of the so-called background radiation, which appears to us to be extremely uniform in every direction of observation. This homogeneity is surprising insofar as even two areas of the universe that were causally decoupled from one another - that is, could not exchange information, nevertheless have identical values ​​of the background radiation.

Alternative theories
In order to resolve this supposed contradiction, the so-called inflation theory was invented, which postulates a phase of extremely rapid expansion immediately after the Big Bang, which in turn can explain the homogeneity in the background radiation.
How this phase can be explained in the context of Einstein's theory, however, requires a number of modifications of the theory that appear artificial and cannot be directly verified.

New findings: homogenization through gravity
It was not yet clear whether the homogenization of the universe could not be fully explained by Einstein's equations. The reason for this is the complexity of the equations and the associated difficulty of analyzing your solutions - models for the universe - and predicting their behavior.

In the concrete problem, the time development of the originally strong deviations from the homogeneous state is to be mathematically analyzed as cosmological gravitational waves and to show that these decay in the course of the expansion and thus the universe receives its homogeneous structure.

Such analyzes are based on modern mathematical methods in the field of geometric analysis. So far, these methods have only been able to achieve such results for small deviations from the homogeneous space-time geometry. David Fajman from the University of Vienna has now succeeded for the first time in transferring these methods to the case of any large deviations.

The results published in the journal PRL show that homogenization in the examined class of models is already fully explained by Einstein's theory and that no additional modifications are required. If this knowledge can be transferred to more general models, this means that it does not necessarily need a mechanism like that of inflation to explain the state of our universe today, but that Einstein's theory could ultimately triumph again.

Publication in "Physical Review Letters":
"Future Attractors in 2 + 1 Dimensional Gravity", David Fajman, Physical Review Letters, vol. 125, 2020
DOI: 10.1103 / PhysRevLett.125.121102

Scientific contact

Ass.-Prof. Dr. David Miro Fajman

Gravitational Physics Faculty of Physics
University of Vienna
1090 - Vienna, Boltzmanngasse 5
[email protected]

Consultation notice

Pia Gardener, MA

Press office of the University of Vienna
University of Vienna
1010 - Vienna, Universitätsring 1
[email protected]


Universe (© NASA / WMAP Science Team)