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.