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

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 University of Münster have, together with physicist Dr. Sabine Hossenfelder from the Frankfurt Institute for Advanced Studies (FIAS), developed a new model for this problem. Their starting point was the Mori-Zwanzig formalism, a method for describing systems consisting of a large number of particles with a small number of measurands. The results of the study have now been published in the journal Physical Review Letters.

Background: The theory of general relativity developed by Albert Einstein is one of the most successful theories in modern physics. Two of the last five Nobel Prizes for Physics had associations with it: in 2017 for the measurement of gravitational waves, and in 2020 for the discovery of a black hole at the center of the Milky Way. One of the most important applications of the theory is in describing the cosmic expansion of the universe since the Big Bang. The speed of this expansion is determined by the amount of energy in the universe. In addition to the visible matter, it is above all the dark matter and dark energy which play a role here – at least, according to the Lambda-CDM model currently used in cosmology.

“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.”

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).

AstrophysicsDark EnergyDark MatterGeneral RelativityPopularUniversity of Münster
Comments ( 21 )
Add Comment
  • Pamela Mukasa

    By now as ABADDON I am not considered an oddball even though my videos (on YouTube mainly) might deceptively suggest so. It you look at the picture image in the article as it is and cause the extreme right end of it to loop round, you can illustrate a simple torus shaped universe. At the point that it loops back to the point of the big bang, it picks up nature’s lifeforms as part of evolution. It then continues round again until at steady state of fusion and fission, neither exploding or imploding. This can only happen through ourselves as described in my videos and myself ABADDON as preemptive, pre-singularity, singularity with a second big bang. We are a basic, rudimentary, embryonic initial initiating this alongside Planet X. Balance is then restored. Don’t underestimate the balance to ‘the force’s as per Star Wars.

    • Torbjörn Larsson

      This unpublished idea looks like a mish mash of pseudoscience with religious and astrology inspired terminology. Please don’t put ads of these noise adding links on science sites where we expect to discuss science.

      The universe topology looks globally flat to high precision and high distance.

  • Mike Pollock

    Our universe wasn’t “born” 13.8 billion years ago. The big bang was our universe turning itself into a gargantuan particle collider with two maximum entropy objects that contained the mass of the observable galaxies. This collision, just like any collision on Earth, created an organic, non-isotropic expansion of matter that will look like an accelerating expanding universe if it is assumed the universe is expanding. This explanation is why our universe is not isotropic and ends up with such incredibly huge areas of galaxies and areas of nothing.

    • Torbjörn Larsson

      Erroneous pseudoscience: read the article you respond to.

  • BibhutibhusanPatel

    The structure of constituents of matter throughout the universe is homogeneous or in other words is unique.So nonhomogeneous property with referrence to the mass can be reflected in nature and measured.But this concept is associated with an additional property that all the galaxies have an unique direction of motion by virtue òf properties derived from the Big Bang.We may note here that neutinos of all flavors have only lefthandedness and ño extra kind like sterile neutrino is present to break this Law.

  • BibhutibhusanPatel

    Only nonhomogeous of universe due to mass concentration can be measured when other axes of matter effecting homogeneity is fixed.
    Thus unique proporty about the constituet particles,i.e. atoms all have homogeneously present.

    The force that is driving all the galaxies have unique direction of motion taking big bang as the origin.

  • BibhutibhusanPatel

    Only nonhomogeous of universe due to mass concentration can be measured when other axes of matter effecting homogeneity is fixed.
    Thus unique proporty about the constituet particles,i.e. atoms all have homogeneously present.

    The force that is driving all the galaxies have unique direction of motion taking big bang as the origin.
    To conclude the topic this principle,this can be stated that there is no neutrino exists of type than known at present.

    • Torbjörn Larsson

      Adding massive known neutrinos to simulations have similar insignificant effects.

      We don’t know that sterile neutrinos are impossible yet, we do have a result that implies that if they exist there can’t be just one kind. For all we know they can constitute dark matter.

  • Travis Churchill

    I always want to ask, because I am not very well educated. Why do the models of the universe I see only show an image of a forward expanding single direction universe? Wouldn’t it have been a spherical expansion?

    • Torbjörn Larsson

      These illustrations are confusing, I’ll give you that, and not well presented as they are adopted from expert papers where they function well. They try to illustrate the diameter of the expanding universe versus the global cosmological time on the x axis. They usually don’t add to the article context.

      These illustrations should perhaps better be a 1D cut with the diameter on the y-axis since that is sufficient. The visually pleasing rotation symmetry that places galaxies and stuff “inside” the expanding universe is confusing for anyone first seeing it (or at least it was to me).

      Another problem is the implied observer bias. Yes, expansion is spherical, for you as an observer. But the next galaxy over, potential observers would see an analogous sperical looking expansion relative to them since space is expanding (between unbound objects) *everyehere*. There is no special “origin” of expansion, there are expansion origins everywhere. So the illustrations should perhaps reflect that as well with showing several dianeter-vs-time graphs at various locations. If you go to astronomer cosmology sites they have to use a handful of different distance measures (think coordinate systems) in order to make quantutative sense of it all – it is complicated when you start to think about it.

      Another type of problem, which is sort of fixed in this particular image, is that the growth spurt of inflation is of a seemingly empty universe before the Hot Big Bang flash. The consensus view seems to be that inflation is still bound to the general Big Bang expansion by way of neglecting the seemingly flat topology of large scale space and use the simplifying de Sitter spherical topology (which comes out nearly the same at large radius). But inflation in a flat topology is naively eternal and at constant energy density (since it looks like it was a vacuum), and that is the natural outcome. So one can realistically argue that we don’t know how long the inflation era was, and the illustration extrapolate too much.

      Maybe I add confusion, but here is what the recently released Astro2020 US Astronomical and Astrophysics Decadal Survey appendix C Panel on Cosmology had to say on the matter:

      On the theory: “There is no doubt that the standard cosmological model is a triumph. By adopting simple versions of inflation, dark matter, and dark energy, the model can match observational results despite orders of magnitude of improvement in cosmological measurements over the past 20 years.”

      On the naming of eras: “The question of what process set the Hot Big Bang in motion and created the seeds of structure has been with us for many decades. Early theoretical developments, together with observations over the past two decades, have established the inflationary paradigm as the dominant picture in the field.”

      If you are interested in cosmology there are free MOOCs on the web, though you may have to start with basic physics MOOCs as a prerequisite. An alternative, maybe if you have that prerequisite, is to read a lot of published papers until you get a hang of reading them (takes time and patience) and read recent reviews like the Astro2020 offer et cetera until you know sufficiently much of what is “out there” scientifically speaking. Did I say it takes time and patience? No one has discovered that vaunted “King’s Road” to knowledge yet…

      • Torbjörn Larsson

        Typos: everywhere, quantitative.

        • Torbjörn Larsson

          Oy! And spherical.

    • Torbjörn Larsson

      Since you are well educated enough to ask useful and good questions – hence the long answer amounting to “it is complicated” – I add that something I found helpful is the cosmologist use of a scale factor to model expansion [ https://en.wikipedia.org/wiki/Scale_factor_(cosmology) ].

      “The relative expansion of the universe is parametrized by a dimensionless scale factor a.”

      Formally, if that helps (but see the page in easier to read equations):
      “d(t)=a(t)d_0 where d(t) is the proper distance [between pairs of unbound objects] at epoch t, d_0 is the distance at the reference time t_0, usually also referred to as comoving distance, and a(t) is the scale factor.”

      [It goes on to define the Hubble expansion rate in terms of the scale factor, and show how different eras have different time behavior of the scale function due to differences in dominating energy content of the universe, as we can see in the illustration.]

      You really don’t need to grok all of this at once or even later, you have already mastered the hard part of asking good questions so continue with that! Hopefully something sensible comes back as people attempt to answer.

      *********
      I’ll put this below the fold as additional material since it can put you off the topic – no need to read. But one of many reasons the coordinate systems becomes confusing is explicit in general relativity – the time axis behaves differently than space. It has a minus sign in front of the coordinate, signifying that the math class of partial differential equations is what is called “hyperbolic” – divergent in some sense.

      This is consistent with that life needs a universe with localized particles and events, while particles mediate causal – causality as in physical processes – usefully behaving light signals diverging to infinity.

      [Since I’m a bioinformatician I note that the genetic distance measure of nucleotide changes in phylogenetics of genes and species also makes for a hyperbolic, divergent topology. It is what allows speciation splits and an evolutionary Tree Of Life.]

      The other class of physics topology systems are called “elliptic” and they tend to average out changes – they describe heat flow in materials for instance. You *could* use heat pulses as signals, but they are eventually smeared out. Not very interesting physics, contrary to what a life bearing universe needs to have.

      • Torbjörn Larsson

        Sorry, that would be hyperbolic coordinates already in special relativity (which describes particles and events, not space included).

        [And phylogenetic trees also need localized organisms – populations making population genetics – to be the result of hyperbolic geometry of its phase space. Oh, well, we are all learners in life – I learned a lot composing these answers. Thank you!]

  • BibhutibhusanPatel

    Only nonhomogeous of universe due to mass concentration can be measured when other axes of matter effecting homogeneity is fixed.
    Thus unique proporty about the constituet particles,i.e. atoms all have homogeneously present.

    The force that is driving all the galaxies have unique direction of motion taking big bang as the origin.
    To conclude the topic this principle,this can be stated that there is no neutrino exists of type than known at present.
    So simply one Fixed or Bound material Universe is present which has no fluctuation or randomness in perpetual Laws which can not be changed or deviated else.ln other words no new or unknown random phenomena can be observed unpredicted follwing than existing.Thanks to the authors for endevour precise.

    • Torbjörn Larsson

      Expansion makes problems for ever unchanging laws, see Noether’s theorems.

  • Nikola Milovic

    What I am giving as a comment on this article, it is desirable that every participant in science, who is engaged in this research,
    TO UNDERSTAND MOST SERIOUSLY WHAT I WILL PRESENT HERE, IN VERY SHORT AND VERY ACCURATE EVIDENCE.
    The biggest possible deceptive and deafening deceptions of the entire civilization are – the expansion of the universe, the big bang, Einstein’s theories and everything related to these deafening stories.
    If science, to this day, has not been able to understand and study the conditions under which the moon, as the closest celestial body, behaves like that and ALWAYS HAS THE SAME SIDE FACING THE EARTH, then science has absolutely driven itself crazy, because it does not understand anything. which refers to the laws of motion and particles and celestial bodies.
    I HAVE EVIDENCE WITH WHICH I CAN DESTROY MORE THAN 80% OF THE STUPID THEORIES TO DATE, which can in no way show any truth about the laws of motion.
    IT IS A TERRIBLE AND UNSEEN MIRACLE, THAT SO MANY TEACHERS, FOR SO MANY TIMES, HAVE BEEN DEALING WITH THE STUDY OF SUCH PHENOMENA, AND TO THIS TODAY NO ONE HAS UNDERSTANDED, ONLY TWO LAWS OF MOVEMENT WITH WHICH THE COLLECTION OF THE UNIVERSITY
    TERRIBLE BRUKA FOR SCIENCE !!!!

    • Torbjörn Larsson

      No one takes crank capital shouting and/or conspiracy theory and/or trolling seriously.

      For something taken seriously, read the article.

  • Istvan Szent-Királyi

    Churchill, you are completely right. The expansion or the development of the Universe cannot be in one direction but must be spherical

  • Torbjörn Larsson

    For a larger perspective showing that other scientists tried this in the same spirit, ending up with the same insignificant modifications, see https://www.quantamagazine.org/giant-arc-of-galaxies-puts-basic-cosmology-under-scrutiny-20211213/ .

    “Ruth Durrer, a cosmologist at the University of Geneva, has devised precise ways to identify the effects of slight deviations from a uniform universe.”

    “Buchert’s work does away with the universal background. Instead, he splits the cosmos into large chunks and averages the amount of matter (and the resulting bending of space-time) in each region.”

    “Other cosmologists agree that the background-free treatment is mathematically sound, and that backreaction is real. But is it a big enough effect to kill dark energy? This question motivated Durrer and her colleagues to do a large-scale simulation in 2019. They prepared a digital universe populated with hundreds of billions of galaxies and calculated how differing expansion rates in voids and galaxy clusters would affect light beams headed for a randomly placed astronomer. They found that backreaction would throw off the astronomer’s measurement of the universe’s expansion rate by about 2%. In other words, the standard model predicts an accelerating expansion of space that appears to be 98% accurate, and backreaction struggles to explain away dark energy.

    “The consensus now is that it is a small effect that does not, in the end, cause too much trouble,” Nadathur said.”

  • Alexander

    I am impressed how science comes up with great theories about the universe but it always bothers me that certain concepts do not have a valid proof and rely on mathematical concepts such as other dimensions. I hate to say this that science of the universe is starting to become science fiction.