The ultra-diffuse dwarf galaxies NGC 1052-DF2 and 1052-DF4 are in
  conflict with standard cosmology
  Recently van Dokkum et al. (2018b) 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 $886$
$\rm{km\,s^{-1}}$, which differs from that of the Local Group (LG) velocity
vector by $1298$ $\rm{km\,s^{-1}}$ 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 ($\Lambda$CDM) TNG100-1 simulation is at most
$1.0\times10^{-4}$ at $11.5$ Mpc and is $4.8\times10^{-7}$ at $20.0$ Mpc. At
$11.5$ Mpc, the peculiar velocity is in significant tension with the TNG100-1,
TNG300-1, and Millennium simulations, but occurs 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 $2.6\sigma$ ($11.5$ Mpc) and $4.1\sigma$ ($20.0$ 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 $\geq4.8\sigma$ with the $\Lambda$CDM model. If both galaxies are at
$20.0$ Mpc the $\Lambda$CDM cosmology has to be rejected by $\geq5.8\sigma$.
