Modified Theories of Gravity may Soon Replace Dark Matter

For more than a decade the astrophysical community has been gathering observational evidence that seem to contradict the concept of dark matter in favor of new theories of gravity. In this article we summarize the most important ones, from to 2016 to present.

^{By Dr. Inés Urdaneta, Physicist at the International Space Federation}

From Newton’s law and the distribution of visible matter, astrophysicists would expect the rotational velocity of stars and gas inside a galaxy to decrease with distance, but in the 70’s astronomers found a flattened anomaly, spiral galaxies were found to rotate at a nearly constant rate, independently of its radius. As we have explained in former articles, dark matter was inferred as an additional gravitational source that could explain the flattened rotation curves of spiral galaxies.

Nevertheless, many teams have found astronomical evidence pointing towards modified gravity models instead. For instance, in 2016, a significant new relationship in spiral and irregular galaxies, in which the acceleration observed in rotation curves is strongly correlated with the gravitational acceleration expected from the visible mass only, was found. This study utilized a recent developed technique called near-infrared photometry, that connects directly the starlight and the stellar mass, with no adjustable parameters. The mass-to-light ratio is the conversion factor needed for the study [1].

Galaxies have a wide range of shapes, masses, sizes and densities, and generally they are ellipticals (supported by pressure) of spiral and irregular (supported by rotation). The authors of the study considered only the rotationally supported systems because their rotation curve provides a direct tracer of the centripetal acceleration.

The data base used came from the new Spitzer Photometry and Accurate Rotation Curves (SPARC), the largest galaxy sample to date with spatially resolved data on the distribution of both stars and gas as well as rotation curves for every galaxy, containing a sample of 175 disk galaxies representing all rotationally supported morphological types, including near-infrared (3.6μm) observations that trace the distribution of stellar mass and 21cm observations that trace the atomic gas. As the authors explain in the paper [1], the 21cm data also provide velocity fields from which the rotation curves are derived.

The image below reports their findings, where we see the correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of standard mass (baryonic mass), in almost 2700 points from 153 galaxies with very different morphologies, masses, sizes and gas fractions.  

^{Figure 1 (taken from preprint): The centripetal acceleration observed in rotation curves, gobs = V^2/R, is plotted against that predicted for the observed distribution of baryons, gbar = |∂Φbar/∂R| in the upper panel. Nearly 2700 individual data points for 153 SPARC galaxies are shown in grayscale. The mean uncertainty on individual points is illustrated in the lower left corner. Large squares show the mean of binned data. Dashed lines show the width of the ridge as measured by the rms in each bin. The dotted line is the line of unity. The solid line is the fit of eq. 4 to the unbinned data using an orthogonal-distance-regression algorithm that considers errors on both variables. The inset shows the histogram of all residuals and a Gaussian of width σ = 0.11 dex. The residuals are shown as a function of gobs in the lower panel. The error bars on the binned data are smaller than the size of the points. The solid lines show the scatter expected from observational uncertainties and galaxy to galaxy variation in the stellar mass-to-light ratio. This extrinsic scatter closely follows the observed rms scatter (dashed lines): the data are consistent with negligible intrinsic scatter.}

This radial acceleration relation is completely empirical and it persists even when dark matter dominates, therefore its contribution is totally specified by that of the baryons. In this study no particular halo model for the dark matter was utilized, they are unnecessary. The image above also shows that the observed scatter is small and largely governed by the observed uncertainties.

At the time these results were published (2016) the authors concluded that these galaxies required no dark matter, and this was not understood at the time, an explanation was needed.

Among the alternative models to dark matter, MoND (for Modified Newtonian dynamics) is a controversial alternative to general relativity and its hypothesis that the dynamics of galaxies are determined by massive, invisible dark matter halos.

MoND is an example of a class of theories known as modified gravity, where Newton’s laws are modified. It was published in 1983 by Israeli physicist Mordehai Milgrom, who noted that the discrepancies that have been tried to be explained by dark matter, could be resolved if the gravitational force experienced by a star in the outer regions of a galaxy was proportional to the square of its centripetal acceleration (as opposed to the centripetal acceleration itself, as in Newton's second law) or alternatively, if gravitational force came to vary inversely linearly with radius (as opposed to the inverse square of the radius, as in Newton's law of gravity). In MoND, violation of Newton's laws occurs at extremely small accelerations, characteristic of galaxies far below anything typically encountered in the Solar System or on Earth [2]. This means that gravity at low accelerations would be stronger than predicted by a pure Newtonian description.

MoND has been very successful for predicting the observed features of galaxies and to explain a vast wealth of data on galactic rotation speeds using only their visible stars and gas, though it was thought to be debunked by a case published in the journal Nature which claimed that MoND couldn't be true because the internal motions within dwarf galaxy NGC1052-DF2, a small galaxy comprising about 200 million stars, were too slow.

Apparently, those claims were premature, because in 2018 new research argued that the previous work did not consider the influence of the gravitational environment around the dwarf, which could affect motions within it. If the dwarf galaxy were close to a massive galaxy – which is the case here – then the motions within the dwarf would be slower [3].

“Our modeling of the MoND environmental effect was later confirmed by another group.” Dr. Hongsheng Zhao, School of Physics and Astronomy at the University of St Andrews.

This sort of external field effect or EFE due to masses surrounding the gravitational system, is not predicted by neither Newtonian, nor Einstein’s relativity theory (and therefore, dark matter cannot explain it). MoND predicts that the internal motions of an object in the cosmos should not only depend on the mass of the object itself, but also the gravitational pull from all other masses in the universe, and this is in good agreement with astronomical observations, in particular for the 153 galaxies tested for EFE later in 2020.  

The non-linearity of MoND gives rise to the so-called EFE, which causes the self-gravity of a system to be weakened if the system as a whole is accelerated uniformly by an external field even in the complete absence of tidal effects.

In that year, a team of astrophysicists and astronomers led by Kyu-Hyun Chae, from Sejong University in South Korea, detected this EFE in 153 galaxies selected from the SPARC database, and their findings were published in The Astrophysical Journal [4].

“Initially, I was reluctant to interpret our own results in favor of MoND. But now I cannot deny the fact that the results as they stand clearly support MoND rather than the dark matter hypothesis.” Dr. Chae

The group analyzed 153 rotation curves of disk galaxies as part of their study, and they deduced the EFE by observing that galaxies in strong external fields slowed or exhibited declining rotation curves more frequently than galaxies in weaker external fields—as predicted by MoND alone.

“I came from the same place as those in dark matter community. It hurts to think that we could be so wrong. But Milgrom predicted this over 30 years ago with MoND. No other theory anticipated the observed behavior.” Dr. McGaugh, part of the research team.

One year later, in 2021, a paper published in EPJ C, by Gerson Otto Ludwig, National Institute for Space Research, Brazil [5], suggests that if the framework of Newtonian accounts of gravity is substituted with a general relativity-based model, to include the effects of gravitomagnetism, there is no need to recourse to dark matter.

When a massive rotating object like a star or black hole ‘drags’ the very fabric of spacetime along with it – an effect in general relativity not present in Newton’s theory of gravity, called frame-dragging or the Lense Thirring effect-, this gives rise to a gravitomagnetic field.  In his paper, Ludwig presents a new model for the rotational curves of galaxies and demonstrates that even though the effects of gravitomagnetic fields are weak, factoring them into models wipes out the difference between theories of gravity and observed rotational curves, eliminating the need for dark matter.

As the abstract of his paper states [5]:

“the measured rotation curve of galaxies provided much experimental support to the dark matter concept. However, most theories used to explain the rotation curve have been restricted to the Newtonian potential framework, disregarding the general relativistic corrections associated with mass currents. In this paper it is shown that the gravitomagnetic field produced by the currents modifies the galactic rotation curve, notably at large distances. The coupling between the Newtonian potential and the gravitomagnetic flux function results in a nonlinear differential equation that relates the rotation velocity to the mass density. The solution of this equation reproduces the galactic rotation curve without recourse to obscure dark matter components, as exemplified by three characteristic cases. A bi-dimensional model is developed that allows to estimate the total mass, the central mass density, and the overall shape of the galaxies, while fitting the measured luminosity and rotation curves. The effects attributed to dark matter can be simply explained by the gravitomagnetic field produced by the mass currents.”

As Ludwig notes, the gravitomagnetic forces replace the dark matter effects. As listed in his paper, the gravitomagnetic field produced by the currents plays four important roles in the self-consistent solution [5]:

(1) the Lorentz force associated to the gravitomagnetic field balances the Newtonian attractive force in the direction perpendicular to the equatorial plane in a pressureless equilibrium;

(2) the gravitomagnetic field effects flow vorticity in an otherwise irrotational motion in an inviscid fluid;

(3) the nonlinear coupling between the gravitomagnetic and Newtonian fields provides the mechanism for the transition between the rigid rotation flow near the origin and the constant speed flow near the edge;

(4) at large distances the nearly constant gravitomagnetic Lorentz force added to the decaying centrifugal force balances the equally decaying gravitational attraction.

Then, in 2022 a study of the rotation speed of gas in the dwarf galaxy AGC 114905 [6] set a push back again against the MoND theory, because the study found that the gas rotated very slowly with respect to what MoND predicted. Nevertheless, such a slow speed contradicted the expected one in a universe governed by General Relativity with large amounts of dark matter, reason why doubts were casted at the astronomical observations as well.

By conducting hydrodynamical MoND simulations of a gas-rich disc galaxy with a similar mass distribution to AGC 114905, first in isolation and then including the EFE, the mystery has apparently been solved.

“Our simulations show that the inclination of AGC 114905 might be significantly less than reported, which would mean the galaxy is actually rotating much faster than people think, in line with MoND expectations.” -Dr. Banik, lead author.

This means that the galaxy could be much closer to face-on than the observers thought, and therefore, the galaxy is rotating much faster than reported, removing the tension with MoND. Dr. Banik’s group predicted that the high rotation speed in the MoND gravity theory is consistent with observations if the inclination of the galaxy is overestimated, and this seems to be the case here [7].

A second paper by Banik from 2022 [8], in which the author shows the many failures of the standard cosmological model when compared to MOND, reviews the MOND theory that is often able to naturally explain the observations. His review can be considered critical to show why Mond leads over the standard cosmological model, getting to the conclusion that galaxies really do lack dark matter.

As the abstract of his review[8] states:

“This missing gravity problem may indicate a breakdown of GR at low accelerations, as postulated by Milgromian dynamics (MoND). We review the MoND theory and its consequences, including in a cosmological context where we advocate a hybrid approach involving light sterile neutrinos to address MoND’s cluster-scale issues. We then test the novel predictions of MoND using evidence from galaxies, galaxy groups, galaxy clusters, and the large-scale structure of the universe. We also consider whether the standard cosmological paradigm (ΛCDM) can explain the observations and review several previously published highly significant falsifications of it. Our overall assessment considers both the extent to which the data agree with each theory and how much flexibility each has when accommodating the data, with the gold standard being a clear a priori prediction not informed by the data in question. Our conclusion is that MoND is favoured by a wealth of data across a huge range of astrophysical scales, ranging from the kpc scales of galactic bars to the Gpc scale of the local supervoid and the Hubble tension, which is alleviated in MoND through enhanced cosmic variance. We also consider several future tests, mostly at scales much smaller than galaxies.”

Finally, we would like to address this last study of galactic rotation that supports a generalization of the MoND model, called AQUAL, that aims to do more realistic modeling of Chae’s previous works that used an analytic spherical MOND model where the external fields inferred from internal dynamics based on such a simple model agreed with those expected from cosmic environments.

In order to do so, in this second work by Chae [9], the inner and outer parts of the rotational curves were separated and numerical solutions of modified gravity were used, including the EFE effect. One main difference between AQUAL and the standard cold matter model, abbreviated ΛCDM (or LCMD), is that the rotation speeds of inner orbit stars vs. outer orbit stars should be both governed by the distribution of matter, therefore, the curve should be smooth. Meanwhile, the nonlinear, self-gravitational dynamics of the AQUAL theory predicts a tiny kink in the curve. Even though it is too small to be measured in a single galaxy, there should be a small shift between the inner and outer velocity distributions when measured in a large sample of galaxies.

When analyzing the high-resolution velocity curves of 152 galaxies as observed in the Spitzer Photometry and Accurate Rotation Curves (SPARC) database, the author of this study found a shift in agreement with AQUAL over standard dark matter cosmology, when the EFE effects are included[9].

^{Figure 2 (taken from [9]): Comparison of results for two Dark Matter (DM) halo models with SPARC data. (A) The leftmost panel shows the SPARC data of 3097 points from 152 galaxies with mass-to-light ratios Υdisk = 0.5Υ for the disk and Υbulge = 0.7Υ for the bulge. Typical uncertainties of the logarithm of accelerations are indicated by errorbars at the bottom of the panel. The inset defines the orthogonal residual ∆⊥from the algebraic MOND relation, i.e., the interpolating function, for a0 = 1.199×10−10ms−2 fitted to the outer rotation curves.  (B) This panel shows the trend of the medians of orthogonal residuals in the orthogonal bins. DM halo models systematically deviate from the SPARC data, in contrast to the AQUAL model[9]. Dashed lines are results for a subsample of 111 galaxies without a bulge.}

^{Figure 3 (taken from [9]): The inner and outer parts of rotation curves in the acceleration plane. (A) Each SPARC rotation curve shown in Figure 2(a) is separated into the inner rising and outer quasi-flat parts. Data for the two parts are displayed separately and compared with the AQUAL simulated results for the same galaxies. Each panel is in the same format as Figure 2(a). The dashed curve and band indicate the Bayesian fit of Equation (6) to the SPARC data points of the inner or outer part. (B) Histograms show orthogonal residuals from the algebraic MOND relation (red line) for the outer (upper panel) and inner (lower panel) data points. Histograms are fitted with a Gaussian model, and the fitted mean μ (with a bootstrap error) and standard deviation σ are indicated. (C) Solid and dashed lines show the trend of orthogonal residuals in orthogonal bins for the outer and inner parts, respectively. Thick black lines represent the SPARC data while magenta lines represent the AQUAL simulated results. Green lines represent the MCMC fitted results for a subsample of 65 galaxies [9] of a good dynamic range that are relatively more massive and larger. Orange lines represent the DC14 results for 111 bulgeless galaxies with L < 1011L , which is the most favorable CDM case shown in Figure 2.}

As concluded from his study of the ΛCDM and MoND Bayesian analyses and AQUAL numerical simulations of the inner and outer parts of the 152 SPARC RCs, the AQUAL modified gravity model predicts correctly both the inner and outer parts of RCs, while the current ΛCDM halo models tend to deviate outside the range allowed by the systematic uncertainty of stellar mass-to-light ratios (see figures 2 and 3).

Additionally, the current SPARC database rules out at 7σ significance the hypothesis that the inner and outer parts follow a universal curve on the acceleration plane. This would contradict current proposals of modified inertia. Therefore, the EFE interpretation of galactic rotation curves is upheld and its origin is likely to be modified gravity rather than modified inertia.

Unified Science in perspective-

The existence of dark energy and dark matter was inferred so that Einstein’s Field Equations could correctly predict the expansion of the universe and the rotation velocity of galaxies. In this view, dark energy is the source of an expanding force in the universe (it is what accounts for the Hubble constant in the leading theories), while dark matter provides an additional gravity source necessary to stabilize galaxies and clusters of galaxies, since there is not enough ordinary mass to keep them together given thecelerated expansion of the Universe. This additional gravity would also explain the rotation velocity of galaxies.

Dark matter particles have never been discovered, despite many decades of sensitive research, often using large detectors. Meanwhile, as this article addresses, modified theories of gravity are having very promising results, and they all lack dark matter.

Such is the case of the generalized holographic model developed by Nassim Haramein to solve the vacuum catastrophe problem -the 122 order of magnitude difference between energy density at quantum scale and that at astronomical scale-, where dark matter and dark energy are explained by the quantum vacuum and its dynamics, in terms of the organization of the vacuum fluctuations depicted as Planck spherical units (PSU), and a surface to volume information transfer rate that scales from the Planck scale to the universal scale [10], creating an information flow and screening (boundary conditions) that concerns all structures in the universe.

His work [11,12] will be completed with the study to be published soon, entitled “Invariant unification of forces, fields and particles, in the quantum vacuum plasma [13]” showing the mass-to-radius relationship distribution of stellar masses, galaxies, clusters and all astronomical objects. The scaling law will clearly demonstrate that there is no need for dark mass and dark energy … they aren’t real.

References

[1] Stacy S. McGaugh and Federico Lelli,  The radial acceleration relation in rotationally supported galaxies Phys. Rev. Lett. 117, 201101 (2016) https://doi.org/10.1103/PhysRevLett.117.201101

[2] https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

[3] Kroupa, P., Haghi, H., Javanmardi, B. et al. Does the galaxy NGC1052–DF2 falsify Milgromian dynamics?. Nature 561, E4–E5 (2018). https://doi.org/10.1038/s41586-018-0429-z

[4] Kyu-Hyun Chae et al, Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies, The Astrophysical Journal (2020). DOI: 10.3847/1538-4357/abbb96

[5] G. O. Ludwig, Galactic rotation curve and dark matter according to gravitomagnetism, The European Physical Journal C (2021). DOI: 10.1140/epjc/s10052-021-08967-3

[6] Pavel E Mancera Piña et al, No need for dark matter: resolved kinematics of the ultra-diffuse galaxy AGC 114905, Monthly Notices of the Royal Astronomical Society (2021). DOI: 10.1093/mnras/stab3491

[7] Indranil Banik et al, Overestimated inclinations of Milgromian disc galaxies: the case of the ultradiffuse galaxy AGC 114905, Monthly Notices of the Royal Astronomical Society (2022). DOI: 10.1093/mnras/stac1073.  

[8] Indranil Banik et al, From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity, Symmetry (2022). DOI: 10.3390/sym14071331

[9] Kyu-Hyun Chae, Distinguishing Dark Matter, Modified Gravity, and Modified Inertia with the Inner and Outer Parts of Galactic Rotation Curves, arXiv (2022). DOI: 10.48550/arxiv.2207.11069

[10] Haramein, N. and Val Baker, A. (2019) Resolving the Vacuum Catastrophe: A Generalized Holographic Approach. Journal of High Energy Physics, Gravitation and Cosmology, 5, 412-424. https://doi.org/10.4236/jhepgc.2019.52023

[11] Haramein, N. (2012). Quantum Gravity and the Holographic Mass, Physical Review & Research International, ISSN: 2231-1815, Page 270-292 

[12] Val baker, A.K.F, Haramein, N. and Alirol, O. (2019). The Electron and the Holographic Mass Solution, Physics Essays, Vol 32, Pages 255-262.

[13] Scale invariant unification of forces, fields and particles in a Planck vacuum plasma,