The ultra-diffuse dwarf galaxies NGC 1052-DF2 and 1052-DF4 are in conflict with standard cosmology

Recently van Dokkum et al. reported that the galaxy NGC 1052-DF2 (DF2) lacks dark matter if located at 20 Mpc from Earth. In contrast, DF2 is a dark-matter-dominated dwarf galaxy with a normal globular cluster population if it has a much shorter distance near 10 Mpc. However, DF2 then has a high peculiar velocity wrt. the cosmic microwave background of 886 {km s^{-1}}, which differs from that of the Local Group (LG) velocity vector by 1298 {km s^{-1}} with an angle of 117 ^{circ }. Taking into account the dynamical M/L ratio, the stellar mass, half-light radius, peculiar velocity, motion relative to the LG, and the luminosities of the globular clusters, we show that the probability of finding DF2-like galaxies in the lambda cold dark matter (ΛCDM) TNG100-1 simulation is at most 1.0 × 10^-4 at 11.5 Mpc and is 4.8 × 10^-7 at 20.0 Mpc. At 11.5 Mpc, the peculiar velocity is in significant tension in the TNG100-1, TNG300-1, and Millennium simulations, but naturally in a Milgromian cosmology. At 20.0 Mpc, the unusual globular cluster population would challenge any cosmological model. Estimating that precise measurements of the internal velocity dispersion, stellar mass, and distance exist for 100 galaxies, DF2 is in 2.6σ (11.5 Mpc) and 4.1σ (20.0 Mpc) tension with standard cosmology. Adopting the former distance for DF2 and assuming that NGC 1052-DF4 is at 20.0 Mpc, the existence of both is in tension at ≥4.8σ with the ΛCDM model. If both galaxies are at 20.0 Mpc the ΛCDM cosmology has to be rejected by ≥5.8σ.