The KBC void is a local underdensity with the observed relative density contrast δ ≡ 1 − ρ/ρ0 = 0.46 ± 0.06 between 40 and 300 Mpc around the Local Group. If mass is conserved in the Universe, such a void could explain the 5.3σ Hubble tension. However, the MXXL simulation shows that the KBC void causes 6.04σ tension with standard cosmology (ΛCDM). Combined with the Hubble tension, ΛCDM is ruled out at 7.09σ confidence. Consequently, the density and velocity distribution on Gpc scales suggest a long-range modification to gravity. In this context, we consider a cosmological MOND model supplemented with $11 \, \rm {eV}/c^{2}$ sterile neutrinos. We explain why this νHDM model has a nearly standard expansion history, primordial abundances of light elements, and cosmic microwave background (CMB) anisotropies. In MOND, structure growth is self-regulated by external fields from surrounding structures. We constrain our model parameters with the KBC void density profile, the local Hubble and deceleration parameters derived jointly from supernovae at redshifts 0.023−0.15, time delays in strong lensing systems, and the Local Group velocity relative to the CMB. Our best-fitting model simultaneously explains these observables at the $1.14{{\ \rm per\ cent}}$ confidence level (2.53σ tension) if the void is embedded in a time-independent external field of ${0.055 \, a_{_0}}$. Thus, we show for the first time that the KBC void can naturally resolve the Hubble tension in Milgromian dynamics. Given the many successful a priori MOND predictions on galaxy scales that are difficult to reconcile with ΛCDM, Milgromian dynamics supplemented by $11 \, \rm {eV}/c^{2}$ sterile neutrinos may provide a more holistic explanation for astronomical observations across all scales.

The dynamical stability of disk galaxies is sensitive to whether their anomalous rotation curves are caused by dark matter halos or Milgromian dynamics (MOND). We investigate this by setting up a MOND model of M33. We first simulate it in isolation for 6 Gyr, starting from an initial good match to the rotation curve (RC). Too large a bar and bulge form when the gas is too hot, but this is avoided by reducing the gas temperature. A strong bar still forms in 1 Gyr, but rapidly weakens and becomes consistent with the observed weak bar. Previous work showed this to be challenging in Newtonian models with a live dark matter halo, which developed strong bars. The bar pattern speed implies a realistic corotation radius of 3 kpc. However, the RC still rises too steeply, and the central line-of-sight velocity dispersion (LOSVD) is too high. We then add a constant external acceleration field of 8.4 × 10−12 m s−2 at 30° to the disk as a first-order estimate for the gravity exerted by M31. This suppresses buildup of material at the center, causing the RC to rise more slowly and reducing the central LOSVD. Overall, this simulation bears good resemblance to several global properties of M33, and highlights the importance of including even a weak external field on the stability and evolution of disk galaxies. Further simulations with a time-varying external field, modeling the full orbit of M33, will be needed to confirm its resemblance to observations.

We consider the feasibility of testing Newtonian gravity at low accelerations using wide binary (WB) stars separated by 3 kAU. These systems probe the accelerations at which galaxy rotation curves unexpectedly flatline, possibly due to Modified Newtonian Dynamics (MOND). We conduct Newtonian and MOND simulations of WBs covering a grid of model parameters in the system mass, semi-major axis, eccentricity and orbital plane. We self-consistently include the external field (EF) from the rest of the Galaxy on the Solar neighbourhood using an axisymmetric algorithm. For a given projected separation, WB relative velocities reach larger values in MOND. The excess is ≈ 20% adopting its simple interpolating function, as works best with a range of Galactic and extragalactic observations. This causes noticeable MOND effects in accurate observations of ≈ 500 WBs, even without radial velocity measurements.We show that the proposed Theia mission may be able to directly measure the orbital acceleration of Proxima Centauri towards the 13 kAU-distant α Centauri. This requires an astrometric accuracy of ≈ 1 µas over 5 years. We also consider the long-term orbital stability of WBs with different orbital planes. As each system rotates around the Galaxy, it experiences a time-varying EF because this is directed towards the Galactic Centre. We demonstrate approximate conservation of the angular momentum component along this direction, a consequence of the WB orbit adiabatically adjusting to the much slower Galactic orbit. WBs with very little angular momentum in this direction are less stable over Gyr periods. This novel direction-dependent effect might allow for further tests of MOND.

The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured globular clusters (GCs) with a line-of-sight velocity dispersion of σ = 7.8 +5.2 −2.2 km/s (σ = 10.6 +3.9 −2.3 km/s). Our conventional statistical analysis of the original ten GCs gives σ = 8.0 +4.3 −3.0 km/s. The overall distribution of velocities agrees well with a Gaussian of this width. Due to the non-linear Poisson equation in MOND, a dwarf galaxy has weaker self-gravity when in close proximity to a massive host. This external field effect is investigated using a new analytic formulation and fully self-consistent live N-body models in MOND. Our formulation agrees well with that of Famaey and McGaugh (2012). These new simulations confirm our analytic results and suggest that DF2 may be in a deep-freeze state unique to MOND. The correctly calculated MOND velocity dispersion agrees with our inferred dispersion and that of van Dokkum et al. (2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs of DF2 are however significantly brighter and larger than normal GCs, a problem which disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc makes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc distance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4, finding good agreement with MOND. We also discuss possible massive galaxies near DF2 and DF4 along with their distances and peculiar velocities, noting that NGC 1052 may lie at a distance near 10 Mpc.

When bars form within galaxy formation simulations in the standard cosmological context, dynamical friction with dark matter (DM) causes them to rotate rather slowly. However, almost all observed galactic bars are fast in terms of the ratio between corotation radius and bar length. Here, we explicitly display an 8σ tension between the observed distribution of this ratio and that in the EAGLE simulation at redshift 0. We also compare the evolution of Newtonian galactic discs embedded in DM haloes to their evolution in three extended gravity theories: Milgromian Dynamics (MOND), a model of non-local gravity, and a scalar-tensor-vector gravity theory (MOG). Although our models start with the same initial baryonic distribution and rotation curve, the long-term evolution is different. The bar instability happens more violently in MOND compared to the other models. There are some common features between the extended gravity models, in particular the negligible role played by dynamical friction − which plays a key role in the DM model. Partly for this reason, all extended gravity models predict weaker bars and faster bar pattern speeds compared to the DM case. Although the absence of strong bars in our idealized, isolated extended gravity simulations is in tension with observations, they reproduce the strong observational preference for ‘fast’ bar pattern speeds, which we could not do with DM. We confirm previous findings that apparently ‘ultrafast’ bars can be due to bar-spiral arm alignment leading to an overestimated bar length, especially in extended gravity scenarios where the bar is already fast.

The positions and velocities of galaxies in the Local Group (LG) measure the gravitational field within it. This is mostly due to the Milky Way (MW) and Andromeda (M31). We constrain their masses using distance and radial velocity (RV) measurements of 32 LG galaxies. To do this, we follow the trajectories of many simulated particles starting on a pure Hubble flow at redshift 9. For each observed galaxy, we obtain a trajectory which today is at the same position. Its final velocity is the model prediction for the velocity of that galaxy.Unlike previous simulations based on spherical symmetry, ours are axisymmetric and include gravity from Centaurus A. We find the total LG mass is 4.33 +0.37 −0.32 × 10 12 M , with 0.14 ± 0.07 of this being in the MW. We approximately account for IC 342, M81, the Great Attractor and the Large Magellanic Cloud.No plausible set of initial conditions yields a good match to the RVs of our sample of LG galaxies. Observed RVs systematically exceed those predicted by the bestfitting ΛCDM model, with a typical disagreement of 45.1 +7.0 −5.7 km/s and a maximum of 110 ± 13 km/s for DDO 99. Interactions between LG dwarf galaxies can't easily explain this.One possibility is a past close flyby of the MW and M31. This arises in some modified gravity theories but not in ΛCDM. Gravitational slingshot encounters of material in the LG with either of these massive fast-moving galaxies could plausibly explain why some non-satellite LG galaxies are moving away from us even faster than a pure Hubble flow.

El Gordo (ACT-CL J0102-4915) is an extremely massive galaxy cluster (M200 ≈ 3 × 1015  M⊙) at redshift z = 0.87 composed of two subclusters with mass ratio 3.6 merging at speed Vinfall ≈ 2500 km/s. Such a fast collision between individually rare massive clusters is unexpected in ΛCDM cosmology at such high z. However, this is required for non-cosmological hydrodynamical simulations of the merger to match its observed properties (Zhang et al. 2015). Here, we determine the probability of finding a similar object in a ΛCDM context using the Jubilee simulation box with side length 6 h−1 Gpc. We search for galaxy cluster pairs that have turned around from the cosmic expansion with properties similar to El Gordo in terms of total mass, mass ratio, redshift, and collision velocity relative to virial velocity. We fit the distribution of pair total mass quite accurately, with the fits used in two methods to infer the probability of observing El Gordo in the surveyed region. The more conservative (and detailed) method involves considering the expected distribution of pairwise mass and redshift for analogue pairs with similar dimensionless parameters to El Gordo in the past lightcone of a z = 0 observer. Detecting one pair with its mass and redshift rules out ΛCDM cosmology at 6.16σ. We also use the results of Kraljic & Sarkar (2015) to show that the Bullet Cluster is in 2.78σ tension once the sky coverage of its discovery survey is accounted for. Using a χ2 approach, the combined tension can be estimated as 6.43σ. Both collisions arise naturally in a MOND cosmology with light sterile neutrinos.

A great challenge in present-day physics is to understand whether the observed internal dynamics of galaxies is due to dark matter matter or due to a modification of the law of gravity. Recently, van Dokkum et al. 1 reported that the ultra-diffuse dwarf galaxy NGC1052-DF2 lacks dark matter, and they claimed that this would -paradoxically -be problematic for modified gravity theories like Milgromian dynamics (MOND 2,3 ). However, NGC1052-DF2 is not isolated, so that a valid prediction of its internal dynamics in MOND cannot be made without properly accounting for the external gravitational fields from neighbouring galaxies. Including this external field effect following Haghi et al. 4 shows that NGC1052-DF2 is consistent with MOND.In any viable cosmological model, both primordial and tidal dwarf galaxies, which form in gas-rich tidal debris when galaxies interact, should exist. Within the standard darkmatter based cosmological model, primordial dwarfs are dark-matter dominated, whereas tidal dwarf galaxies contain very little (if any) dark matter 5 . In MOND -a classical potential theory of gravity derivable from a Lagrangian with conserved energy, total momentum and angular momentum 2, 6 -the two types of dwarf galaxies cannot be distinguished. Until now, all known dwarf galaxies have shown similar dynamical behaviour, possibly implying falsification of the dark-matter models 7 . The discovery by van Dokkum et al. 1 of a galaxy lacking dark matter would thus constitute an important verification of the standard darkmatter cosmological model. Given the density distribution of baryonic matter, ρ, the gravitational potential of iii Milgromian gravitation, φ, is determined by the generalised nonlinear Poisson equation 6 ∇ · µ | ∇φ|/a o ∇φ = 4 π G ρ, where the function µ | ∇φ|/a o describes the transition from the Newtonian (| ∇φ|/a o 1) to the Milgromian (| ∇φ|/a o 1) regime 3, 9 , a 0 = 3600 km 2 s −2 kpc −1 is Milgrom's constant 2, 3 and G is Newton's universal constant of gravitation. An equation of this form has been used in investigations of classical models of quark dynamics and is therefore not without precedent in physics 6 . One implication of this equation is that the coupling strength of an object described by ρ depends on the position of another object, whereas its inertial mass is given only by its baryonic component. This breaking of the equivalence of the active gravitating and inertial mass of an object constitutes a prediction of a new physical phenomenon, which does not exist in standard gravitation models and may be visualised as the phantom dark-matter halo (incorporated in φ) being reduced in the presence of a sufficiently strong constant external field 8 . This may be related to the quantum vacuum 9 . A dwarf galaxy in the vicinity of a major galaxy may thus lose its phantom dark-matter halo appearing as a purely Newtonian system 3, 10, 11 . Following van Dokkum et al. 1 we assume NGC1052-DF2 is located at a distance of D = 20 Mpc from the Earth in the NGC1052 group, has a globular cluster po...