# From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, slightly more than the galactocentric orbital acceleration of the solar system due to the combined gravitational pull of the entire galaxy [1]. The gravitational fields of individual particles are thus immeasurably small.

^{2}∝ its orbital semi-major axis

^{3}. A field theoretical basis was then put forth in terms of the Poisson equation, which clarified that the inverse square decline of both gravity and the electrostatic force can be understood in terms of field lines spreading in 3D. Newtonian gravity is an excellent description of non-relativistic motions in the solar system, so much so that discrepancies it faced with the motion of Uranus were attributed to a previously unknown planet that was subsequently discovered.

^{2}causes the dark energy density to dominate the late universe and increases its age for a given Hubble expansion rate ${H}_{{}_{0}}$. The higher age arises from an accelerated cosmic expansion at late times, which was confirmed by observations of distant Type Ia supernovae [37,38]. Though these do not all have the same intrinsic luminosity, they are standardizable candles using the Phillips relation between peak luminosity and light curve shape [39,40]. Combined with other lines of evidence, this led to the currently standard $\Lambda $CDM paradigm [41,42].

## 2. Theoretical Background to MOND

^{2}, with ${M}_{\odot}$ being the solar mass. ${g}_{\odot}$ on Voyager 2 is much larger than the $\left(\right)open="("\; close=")">2.32\pm 0.16$ m/s

^{2}acceleration of the solar system as a whole relative to distant quasars [1], with the dominant contribution no doubt arising from its galactocentric orbit given that the acceleration is almost exactly towards the galactic centre (see their Figure 10). Consequently, it is possible that Newtonian dynamics breaks down when the gravitational field g drops three orders of magnitude below the solar gravity on Voyager 2. This might explain the observed flat RCs of disc galaxies and the similar problem in pressure-supported galaxies, which typically have a much higher internal velocity dispersion ${\sigma}_{{}_{i}}$ than the Newtonian expectation without CDM.

^{2}, which was shown to fit all 15 RCs quite well (see its Figure 1). A better estimate of ${a}_{{}_{0}}$ can be obtained by jointly fitting the RCs of several galaxies with a single adjustable parameter ${a}_{{}_{0}}$ that is consistent between galaxies. Only a handful of RCs are required to empirically determine that the common acceleration scale ${a}_{{}_{0}}=1.2\times {10}^{-10}$ m/s

^{2}[69]. More recent studies confirm this value [70,71], which has therefore not changed for many decades.

#### 2.1. Spacetime Scale Invariance

#### 2.2. Possible Fundamental Basis

^{2}. This very low value is similar to various acceleration scales of cosmological significance, including that defined by the inverse timescale that is the Hubble constant ${H}_{{}_{0}}$. A particle accelerating at ${a}_{{}_{0}}$ for a Hubble time would reach a speed

#### 2.3. Non-Relativistic Theories

#### Numerical Solvers

#### 2.4. The External Field Effect (EFE)

#### The Two-Body Force Law

#### 2.5. Modified Inertia

#### 2.6. Relativistic Theories

#### 2.7. Theoretical Uncertainties in the Missing Gravity Problem

## 3. Equilibrium Galaxy Dynamics

#### 3.1. Disc Galaxies

#### 3.1.1. Rotation Curves

^{2}[172]. More generally, the RCs of gas-rich dwarf galaxies with low internal accelerations offer a powerful test of MOND because of reduced sensitivity to both the interpolating function and the ${M}_{\u2605}/L$ ratio. MOND fares well when confronted with the data for 12 such galaxies [173]. Another possible systematic is that galaxies might contain an additional undetected gas component. The authors of [174] approximately considered this by scaling up the conventionally estimated gas mass by some factor f, which was then inferred observationally from MOND fits to the SPARC sample of galaxy RCs. Those authors inferred that $f=2.4\pm 1.3$, indicating no strong preference for an additional component of “cold dark baryons”. However, including such a component would reduce the best-fitting ${a}_{{}_{0}}$ as there would be more baryonic mass for the same RC.

#### 3.1.2. Vertical Dynamics

#### 3.2. Elliptical Galaxies and Dwarf Spheroidals

#### 3.2.1. Velocity Dispersion

^{3D}[287] and SDSS-IV MaNGA [288], an extension of the original Sloan Digital Sky Survey (SDSS [289]). The so-obtained stellar ${\sigma}_{{}_{\mathrm{LOS}}}$ profiles of 19 galaxies reveal a characteristic acceleration scale consistent with ${a}_{{}_{0}}$ as determined using spirals [290]. While the uncertainties are larger and their study consists of 387 data points rather than the 2693 in SPARC [167], it is still important to note that MOND works fairly well in elliptical galaxies.

#### 3.2.2. Rotation of a Sub-Dominant Component

^{3D}survey [306]. Using 21 cm HI observations extending beyond 5 effective radii, those authors showed that the analysed galaxies very closely follow the BTFR defined by spiral galaxies. The BTFR was again the most fundamental relation (smallest scatter), not, e.g., the relation between ${M}_{\u2605}$ and ${v}_{{}_{f}}$. The results for these 16 galaxies are shown on an RAR diagram in Figure 8 of [211], revealing good agreement with the RAR defined by disc galaxies.

#### 3.3. Observational Signatures of the EFE

#### 3.4. Strong Gravitational Lensing

#### 3.5. Weak Gravitational Lensing

#### 3.6. Implications for Alternatives to ΛCDM and MOND

## 4. Disc Galaxy Stability and Secular Evolution

#### 4.1. Survival of Thin Disc Galaxies

#### 4.2. Number of Spiral Arms

- The radial velocity dispersion ${\sigma}_{r}$,
- Disc self-gravity, and
- Shear caused by differential rotation of the disc.

#### 4.3. Bar Strength

^{4}G [427]). Their estimated bar fraction of $\approx 60\%$ is in agreement with earlier estimates using near-infrared data [428,429]. Moreover, the authors of [428] found that “strong bars are nearly twice as prevalent in the near-infrared as in the optical.” Similar conclusions were reached by [427], who argued that the superior resolution of the Spitzer Space Telescope allowed the detection of shorter bars that might be missed in SDSS images. This may well explain the higher bar fraction in higher-resolution images, though the reduced dust extinction at longer wavelengths might help as well. It is therefore clear that the majority of disc galaxies have a bar, but ≈40% are unbarred or have only a very weak bar.

#### 4.4. Bar Fraction

^{4}G that uses data from the Spitzer Space Telescope [427]. As argued in Section 4.3, S

^{4}G should provide a much more accurate estimate, especially at the low-mass end, where shorter bars can be difficult to resolve in SDSS. The bar fractions in different numerical and observational studies are shown in Figure 18, which reproduces Figure 1 of [449]. It is clear that there is a very significant disagreement between the latest observations and the bar fraction expected in $\Lambda $CDM, which is similar between TNG100 and the much higher-resolution TNG50 (albeit slightly higher than in EAGLE100). The numbers refer to the approximate side length of the cubic simulation volume, expressed in co-moving Mpc. A similar analysis for TNG100 had previously been conducted by [450] and gave similar results (the grey curve). The zoom-in NewHorizon simulation [451] also produces too few barred galaxies at the low-mass end [452] despite having a multi-phase interstellar medium.

#### 4.5. Bar Pattern Speed

## 5. Interacting Galaxies and Satellite Planes

#### 5.1. Tidal Stability

#### 5.2. Tidal Streams and EFE-Induced Asymmetry

#### 5.3. Polar Ring Galaxies

#### 5.4. Shell Galaxies

#### 5.5. Tidal Dwarf Galaxies (TDGs)

#### 5.6. The Local Group Satellite Planes

#### 5.7. Satellite Planes beyond the Local Group

## 6. Galaxy Groups

#### 6.1. The Local Group and the NGC 3109 Association

#### 6.2. M81 and Hickson Compact Groups

#### 6.3. Binary Galaxies

#### 6.4. Virial Analysis of Galaxy Groups

## 7. Galaxy Clusters

#### 7.1. Internal Dynamics

#### 7.2. Probing Structure Formation

## 8. Large-Scale Structure

#### 8.1. The KBC Void and Hubble Tension

#### 8.2. Other Anomalies in Large-Scale Structure

#### 8.3. Cosmic Shear and the Matter Power Spectrum

## 9. Cosmological Context

#### 9.1. Time Variation of ${a}_{{}_{0}}$

#### 9.2. The $\nu $HDM Model

#### 9.2.1. At High Redshift

#### 9.2.2. At Low Redshift

#### 9.3. Towards a Relativistic Model

## 10. Comparing $\Lambda $CDM and MOND with Observations

#### 10.1. ΛCDM

#### 10.2. MOND

#### 10.3. Comparing the Models

#### 10.4. Parallels with the Heliocentric Revolution

- All currently proposed models are surely wrong at some level, but it is still worthwhile to find a model which is more nearly correct as this would form a more reliable stepping stone to a more complete theory.
- At an early stage of development, the more realistic model will not be able to explain everything it seeks to explain.
- Even if both models are fully developed, the less realistic model will provide a better explanation of some observables, similarly to how a broken clock tells the correct time twice each day.

## 11. Future Tests of MOND

#### 11.1. Galaxy Cluster Collision Velocities

#### 11.2. Dynamically Old TDGs

#### 11.3. Wide Binaries

#### 11.3.1. Using the Velocity Distribution

#### 11.3.2. Using the Acceleration of Proxima Centauri

#### 11.4. Solar System Ephemerides

#### 11.5. Spacecraft Tests

#### 11.5.1. Within the Solar System

#### 11.5.2. Beyond the Solar System

## 12. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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