Beyond Einstein: A Solution to One of the Great Mysteries of Cosmology

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A recent study proposes that the “Hubble tension,” a discrepancy in measurements of the universe’s expansion rate, can be resolved using the alternative MOND theory of gravity. This theory suggests local matter density variations account for the observed discrepancies.

Study by the Universities of Bonn and St. Andrews proposes a new possible explanation for the Hubble tension.

The universe is expanding. How fast it does so is described by the so-called Hubble-Lemaitre constant. But there is a dispute about how big this constant actually is: Different measurement methods provide contradictory values. This so-called “Hubble tension” poses a puzzle for cosmologists. Researchers from the Universities of Bonn and St. Andrews are now proposing a new solution: Using an alternative theory of gravity, the discrepancy in the measured values can be easily explained — the Hubble tension disappears. The study has now been published in the Monthly Notices of the Royal Astronomical Society (MNRAS).

Understanding the Universe’s Expansion

The expansion of the universe causes the galaxies to move away from each other. The speed at which they do this is proportional to the distance between them. For instance, if galaxy A is twice as far away from Earth as galaxy B, its distance from us also grows twice as fast. The US astronomer Edwin Hubble was one of the first to recognize this connection.

In order to calculate how fast two galaxies are moving away from each other, it is therefore necessary to know how far apart they are. However, this also requires a constant by which this distance must be multiplied. This is the so-called Hubble-Lemaitre constant, a fundamental parameter in cosmology. Its value can be determined, for example, by looking at the very distant regions of the universe. This gives a speed of almost 244,000 kilometers per hour per megaparsec distance (one megaparsec is just over three million light-years).

Distribution of Matter in Space

(blue; the yellow dots represent individual galaxies). The Milky Way (green) lies in an area with little matter. The galaxies in the bubble move in the direction of the higher matter densities (red arrows). The universe therefore appears to be expanding faster inside the bubble. Credit: AG Kroupa/University of Bonn

Discrepancy in Measurements

“But you can also look at celestial bodies that are much closer to us — so-called category 1a supernovae, which are a certain type of exploding star,” explains Prof. Dr. Pavel Kroupa from the Helmholtz Institute of Radiation and Nuclear Physics at the University of Bonn. It is possible to determine the distance of a 1a supernova to Earth very precisely. We also know that shining objects change color when they move away from us — and the faster they move, the stronger the change. This is similar to an ambulance, whose siren sounds deeper as it moves away from us.

If we now calculate the speed of the 1a supernovae from their color shift and correlate this with their distance, we arrive at a different value for the Hubble-Lemaitre constant — namely just under 264,000 kilometers per hour per megaparsec distance. “The universe therefore appears to be expanding faster in our vicinity — that is, up to a distance of around three billion light years — than in its entirety,” says Kroupa. “And that shouldn’t really be the case.”

However, there has recently been an observation that could explain this. According to this, the Earth is located in a region of space where there is relatively little matter — comparable to an air bubble in a cake. The density of matter is higher around the bubble. Gravitational forces emanate from this surrounding matter, which pull the galaxies in the bubble towards the edges of the cavity. “That’s why they are moving away from us faster than would actually be expected,” explains Dr. Indranil Banik from St. Andrews University. The deviations could therefore simply be explained by a local “under-density.”

In fact, another research group recently measured the average speed of a large number of galaxies that are 600 million light years away from us. “It was found that these galaxies are moving away from us four times faster than the standard model of cosmology allows,” explains Sergij Mazurenko from Kroupa’s research group, who was involved in the current study.

Bubble in the Dough of the Universe

This is because the standard model does not provide for such under-densities or “bubbles” — they should not actually exist. Instead, matter should be evenly distributed in space. If this were the case, however, it would be difficult to explain which forces propel the galaxies to their high speed.

“The standard model is based on a theory of the nature of gravity put forward by Albert Einstein,” says Kroupa. “However, the gravitational forces may behave differently than Einstein expected.” The working groups from the Universities of Bonn and St. Andrews have used a modified theory of gravity in a computer simulation. This “modified Newtonian dynamics” (abbreviation: MOND) was proposed four decades ago by the Israeli physicist Prof. Dr. Mordehai Milgrom. It is still considered an outsider theory today. “In our calculations, however, MOND does accurately predict the existence of such bubbles,” says Kroupa.

If one were to assume that gravity actually behaves according to Milgrom’s assumptions, the Hubble tension would disappear: There would actually only be one constant for the expansion of the universe, and the observed deviations would be due to irregularities in the distribution of matter.

Reference: “A simultaneous solution to the Hubble tension and observed bulk flow within 250 h−1 Mpc” by Sergij Mazurenko, Indranil Banik, Pavel Kroupa and Moritz Haslbauer, 2 November 2023, Monthly Notices of the Royal Astronomical Society.
DOI: 10.1093/mnras/stad3357

In addition to the University of Bonn, the University of Saint Andrews (Scotland) and Charles University in Prague (Czech Republic) were also involved in the study. The work was funded by the British Science and Technology Facilities Council.

15 Comments on "Beyond Einstein: A Solution to One of the Great Mysteries of Cosmology"

  1. MOND, iirc, has been recently falsified with wide binary stars. I’m not a specialist, in any case.

    • Torbjörn Larsson | December 9, 2023 at 11:52 am | Reply

      Indeed. That falsification is damning since MOND is really in a dire situation where that was one of its last retreat points. But with more data and better statistical analysis it too went away, a typical sign of a dying alternative. While the winning general relativity – which goes into the standard cosmology – had another victory, a typical sign of a robust theory.

      But all this is when setting aside the original wholesale falsification which happened in 2017 with the first multimessenger observation of a neutron star binary merger. The signals arrived simultaneously showing that gravity travel at light speed precisely as general relativity predicts and MOND models fail to predict. (Unless you tweak them *just so*, an unlikely state of affairs.) C.f. “Troubled Times for Alternatives to Einstein’s Theory of Gravity New observations of extreme astrophysical systems have “brutally and pitilessly murdered” attempts to replace Einstein’s general theory of relativity.” Quanta Magazine 2018.

  2. Basudeba Mishra | December 8, 2023 at 3:47 am | Reply

    The whole paper is based on assumptions.

    Firstly, if the universe is expanding, how do we see blueshift and galactic merger?

    Locally, we see some planets appear to move away at times to come close at other times. Why a similar phenomenon can’t happen in the case of distant galaxies? The universe is not expanding, but revolving around a common galactic center?

    From the description, it appears as if the Earth is the center of the universe, as the expansion rate of the universe is the same in all directions. This is obviously wrong.

    As per Newtonian Dynamics, gravity is NOT an attractive force. All parameters of the right hand side of his equation are constants. Hence, the force of gravity on the left hand side should also be a constant. Gravity is a stabilizing force that stabilizes bodies against a common barycenter.

    The so-called gravitational constant G is not a constant at all, but at Earth, it is known to be a variable with a periodicity of 5.93 Earth Years. At Jupiter or Mercury, it would be different. At galactic level, it would be totally different.

    The basic Friedmann equation needs a review. Some parameters in it have questionable values. How do you measure the diameter or total mass of the universe?

    • Torbjörn Larsson | December 9, 2023 at 12:09 pm | Reply

      Space expansion is not in question, it is solidly based on originally cosmological redshift and today on standard cosmology.

      Local peculiar blueshifts and a global propensity for galactic mergers is natural for both cases, but a detailed outcome of cosmological simulations in the latter case. It isn’t until the far future that local cohesive aggregates as our Local Group of galaxies will have finished merging and the remaining super massive elliptical galaxies will disperse without interaction until they are isolated by the future cosmological horizon. C.f. “Scale factor (cosmology)”, “Hubble’s law” and “Cosmological horizon” in Wikipedia.

      Why would the diameter or total mass of the universe figure in the Friedmann equations that govern cosmological models of a homogeneous and isotropic universe within general relativity? Those parameters are not studied – note the Scale factor article above – and the equations explicitly use the average mass density! C.f. “Friedmann equations” in Wikipedia.


    When the 1980 Robert Altman movie POPEYE came out, I was intrigued by the line in the song What Am I? delivered by the lead character Popeye The Sailorman: “I ain’t no physickist, but I knows what matters.”
    Today I would say: “I’m no particle physicist, but I know what matter is.”
    1. There is no matter. Everything is coalesced energy systems. (a)
    2. There is no mass-energy equivalence. E=Mc^2 restated is E=E. (b)
    3. Energy is not generated, only converted from one form to another. (c)
    4. There is no Dark Energy. There are instead, Gravitons. (d)
    5. Gravitons give “mass” to other energy systems. (e)
    6. Gravity does not attract, it repels. (f)
    7. Gravitons do not flow. (g)
    8. SpaceTime does not bend. (h)
    (a) Particle physicists are burning up vast resources seeking the “smallest particle” but keep finding smaller and smaller energy systems with life spans so short that new, smaller units of time have to be invented to describe them. All atoms are comprised entirely of bonded energy systems and include gravitons. While it is certainly convenient to think of photons, gluons, bosons and gravitons as force carrier particles, it is more accurate to think of them as coalesced energy waves vibrating at various frequencies just as are quarks and leptons. Particles are merely the shadows on the walls of Plato’s cave. “Particles” are made up of aggregates of energy wave packets bound with gravitons. New particles are not discovered by use of colliders, the collider creates new or previously unobserved energy systems. Energy does not convert to matter (particles) without starting with matter in collision with other matter. Coalesced energy that exhibits mass will include gravitons and spin. It is a process of converting one form of energy into another form of energy. So many of the theories of particles come with the disclaimer “hasn’t been observed”. That everything is made up of energy vibrations at various frequencies and spin waves opens the mind to a Universe of energy, not matter, and makes converting that energy to use for the betterment of humanity less distracting.
    (b) Albert Einstein was blessed with a 3rd eye to see what others could not see, and with a 6th sense to experience what others could not.
    Let us restate the mass-energy equivalence, E=M^2 :
    The speed of light raised to the power of 2 is 89,875,517,873,681,764 meters per second. That is equal to the number of resultant Joules for 1 kilogram of mass. The only input variable to this equation is the number of kilograms of mass. Are we to assume then that 1 kilogram of enriched uranium would yield the same output of Joules as a 1-kilogram water balloon? Then we have the question of what is a kilogram. A kilogram near the Earth’s surface is very different than a kilogram near the surface of the moon or at the barycenter. If everything is Energy, then E=E. All the rest is some conversion factor. It is a matter of energy in vs. energy out.
    (c) Faraday would today easily understand the principles behind even the most sophisticated propulsion systems in our most modern submarines: converting fuel to heat energy, converted to kinetic energy, converted to electrical energy, and converted finally back to kinetic energy to drive the propeller. Becquerel on the other hand would be appalled by how little progress we had made converting the sun’s rays into electricity. He would no doubt shake his head that Tesla’s idea for a resonant cavity that would convert the Earth’s spin into electricity was never funded for even given a trial. But he would quickly understand that a graviton-electric cell would also realize his dreams of limitless free electricity, but from the Earth’s gravity. It is highly possible to create a non-kinetic graviton-electric cell that would convert the force of graviton energy into electricity much as solar-electric cells convert photon energy or as Tesla’s Resonant Cavity.
    The 1830s were a critical time for energy physics as were the 1930s and as will be in the 2030s. We were presented with two divergent paths in the 1830s on the road to harvesting abundant energy: Faraday’s disk and Becquerel’s photo voltaic cell. New and improved kinetic “generators” and methods to turn the crank led us to a deep dependence upon the purveyors of fossil fuels to power them. Investors could not see far enough into the future to forgo immediate profits for unproven methods to convert free energy from the sun, let alone from gravity. Lenz’s Law (1834) of induced current in a changing magnetic field applies equally to a gravitational field. Rabi’s work on nuclear magnetic resonance suggests nuclear graviton resonance. Thinking of muons as energy systems instead of particles suggest gravitons as the carrier of mass.
    The graviton-electric cell has at least two possible solutions, both non-kinetic. Firstly, an electromagnetic stress-energy tensor field generating an electric flux via a magnonic crystal or similar substances that would work like piezoelectricity but without Poynting vector acceleration. Secondly, there would be the gyromagnetic factor-like polarizability of a dielectric and Mott insulators with a strong permanent magnet creating a magnon-rich environment causing a magnetic/electrostatic/electrostatic induction inside a transformer. The resulting electric energy could be stored in carbon-cement flux supercapacitors. The Born-Oppenheimer Approximation regarding photons applies equally to gravitons when absorbed energy starts to vibrate, the vibrations enable spin to flip, changing electronic states. This inter-system crossing results in a spin-vibronic effect. MOND acceleration at zero allows for a different gravitational behavior to take over.
    (d) There was always the fabric of homogenous graviton energy systems that made up the infinite Universe much like the water in the seas. Gravitons not bound to other energy aggregates are free gravitons and make up the bulk of the energy in the Universe. Then about 13.8 billion years ago some of that graviton energy converted into different energy systems, combined with gravitons and rapidly reproduced and formed other graviton bonded energy systems and expanded out into the Universe, it continues to do so now by graviton forces pushing out in all direction. A useful corollary would the beginnings of life through some mutation and recombination of energy systems 3.5 billion years ago. When I was young, my Norwegian mother told me a folktale about a mystical stone when put in a pot of hot water, the skeptical villagers observed the water magically transform into soup. Perhaps the “Big-Bang” was like that stone. Or, perhaps analogous to how rock candy is formed; to the observer, there is nothing to see in a jar of super-saturated sugar-water until a after a single sugar seed-crystal is introduced. Much like the primordial soup from which life emerged, there was the primordial energy soup of gravitons that was the Universe before the various other energy systems emerged.
    (e) Gravitons are wave packets, not bosons, and give other wave packets “mass”. Gravitons with positive monopole massless systems of fundamental force energy that can be free in the expanding known Universe as quintessence or aggregate with and give “mass” to other, different energy wave packets. Graviton energy systems are closely associated with subatomic hadron energy in the proton energy system. Gravitons are part of all atomic nuclei and most associated with the proton. Gravitons only act upon other gravitons only influence associated bound aggrigated energy systems such a hadron energy systems. Baryonic “matter” is graviton energy systems aggregated to other energy systems, “dark matter” is comprised of free gravitons. While we think of measuring gravity in units of newtons, the force of gravity does not necessarily entail the acceleration of mass. It is the transfer of energy from one graviton to another in a line that gives mass to objects. Gravitons are the quintessential manifestation of electroweak unification. The higher the frequency of a graviton, the higher the energy. When the vibrations of gravitons and the vibrations of associated energy systems are in resonance the forces cancel each other out causing “weightlessness”. The greater the frequency difference between a “mass” and a graviton, the greater the acceleration of that mass. When a mass absorbs a graviton, it gains a unique energy. This energy is then converted into momentum, which causes the mass to accelerate. The amount of acceleration that the mass experience depends on the frequency of the graviton and the associated mass. The higher the frequency of the graviton, the more energy it has and the more acceleration the mass will experience. This is because the mass is absorbing more energy in a shorter amount of time.
    (f) Gravitons exert energy flux as a Poynting vector to the “gravitational center” of the nearest, largest object. In our case, Earth is the nearest, largest object. All energy systems, being also comprised of gravitons, are drawn along toward that center. Being the largest concentration of aggregated gravitons, the gravitational force is greatest near the surface of the earth and almost completely absent at the geocenter, being balanced out in all directions by the graviton force of the surrounding Earth and increasing closer to the surface. Likewise, the force of free gravitons surrounding the Earth lessens with the distance away from the surface of the Earth. The barycenter between the Earth and the Moon also serves to balance the forces of gravitons between and around them. The internal forces within the Earth are inversely proportional to the graviton energy at every depth. The pressure in pascals at the center of a very large object such as the Earth is a result of the combined pressures from the surface to the center while the actual graviton force decreases. By way of illustration only, (your results will vary) let us describe four levels of the Earth from the surface of the crust to the surface of the inner core. At the surface of the Earth we have one atmosphere of pressure and four units of graviton energy. At the first depth level we have 1+0.9 = 1.9 atmospheres of pressure and 4-0.9=3.1 units of graviton force. At the next depth level we have 1+0.9+0.8=2.17 atmospheres of pressure and 4-0.9-0.8=2.3 units of graviton force. At the final level we would have 1+0.9+0.8+0.7=3.4 atmospheres of pressure and 4-0.9-0.8-0.7=1.6 units of graviton force. Although the atmospheres of pressure decrease linearly for each level, the total atmospheres of pressure grow exponentially. Finally, at the center of the core we would have the maximum atmospheres of pressure and minimal or no graviton pressure force. Electrostatic repulsion keep molecules from being compressed/collapsed.
    (g) Gravitons transfer energy as a wave or as the quantum entanglement of the suspended balls of Newton’s cradle. Enter Bell states and The Hadamard gate. Tesla’s Wardenclyffe Tower would have pushed electric energy packets against one another to have the energy transferred and received at great distances without wires.
    (h) SpaceTime does not bend like a bowling ball pushing upon the flexible surface of a trampoline, but rather flows like the water pressure from all directions upon a displacing bathysphere in the ocean. When a sufficient amount of gravitons aggregated with other energy systems come together in close proximity, the repellant force of free gravitons becomes so great that a black hole is created.
    It is the observable Universe that is expanding rather than an eternal, infinite unobservable Universe. As Kierkegaard once wrote, “There are two ways to be fooled: Believe what is not true. Refuse to believe what is true.” If our only reality is what we can apprehend via our senses, we may as well be just another prisoner in Plato’s cave.
    Fred Jacobsen
    Escondido, California
    [email protected]

    • Torbjörn Larsson | December 9, 2023 at 12:12 pm | Reply

      So you have nothing to say on the science, such as the article above, by referencing what is based in peer published papers? That was a very long comment to say nothing of relevance by.

  4. Howard Jeffrey Bender, Ph.D. | December 8, 2023 at 2:00 pm | Reply

    Another way to explain Dark Energy is suggested by String Theory. All matter and energy, including photons (light), have vibrating strings as their basis.

    String and anti-string pairs are speculated to be created in the quantum foam, a roiling energy field suggested by quantum mechanics, and they immediately annihilate each other. If light passes near these string/anti-string annihilations, perhaps some of that annihilation energy is absorbed by the string in the light. Then the Fraunhofer lines in that light will move a bit towards the blue and away from the red shift. As this continues in an expanding universe we get the same curve displayed by Perlmutter and colleagues at their Nobel Prize lecture, without the need for Dark Energy.

    This speculation has the universe behaving in a much more direct way. Specifics on this can be found by searching YouTube for “Dark Energy – a String Theory Way”

  5. Torbjörn Larsson | December 9, 2023 at 11:43 am | Reply

    Kroupa is a long standing critic of standard cosmology, so the press releases of his work should be scrutinized for overstatements.

    The standard cosmology predicts galaxy clusters and voids as a natural consequence of the cosmic web development, and the KBC void that the paper analyse is a proposed void associated with our own Laniakea Supercluster. It is not known yet if it is inconsistent with standard cosmology:

    “It is debated whether the existence of the KBC void is consistent with the ΛCDM model. While Haslbauer et al. say that voids as large as the KBC void are inconsistent with ΛCDM,[6] Sahlén et al. argue that the existence of supervoids such as the KBC void is consistent with ΛCDM.[7]”

  6. Would you be able to calculate if the whole multiverse Is spinning and depending on the distance. You are from the center you would be going faster than in another position?

  7. Fixed gravity for you. | December 10, 2023 at 1:20 am | Reply

    Kroupa is allowed out there with high profile exposure because he’s flacking for an idea by a new hero of famously top-dog self-victimizing self-absorbed insect opportunists, as Einstein’s gravity theory is becoming known as a closet failure over-celebrated by the generation that bred said famously top-dog self-victimizing self-absorbed insect opportunists.

  8. Fixed gravity for you. | December 10, 2023 at 1:48 am | Reply

    The overexposed cat icon seems to be a free-range reddit group run by AI frat boys.

  9. Fixed gravity for you. | December 10, 2023 at 8:35 am | Reply

    Replacing “expansion of the universe” with “dilation of the photon” would not be respecting “an establishment of religion” (establishment of a religion-based theory) but science has no bill of rights and gravity experts are prone to shunning reason anyway.

  10. Great

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