How does a MOND cosmology fare on Gpc scales? − collisionless <i>N</i> -body simulations of νHDM

ABSTRACT We present the largest collisionless N-body cosmological simulations in a MOdified Newtonian Dynamics (MOND) cosmology to date. Our four simulations cover Lambda cold dark matter ($\Lambda$CDM) as a baseline, a MOND with hot dark matter model known as $\nu$HDM, and two unphysical models we call $\Lambda$HDM and $\nu$CDM to test the individual contributions of hot dark matter and MOND gravity, respectively. $\nu$HDM reproduces the cosmic microwave background power spectrum while also theoretically matching cluster dynamics and preserving MOND predictions for galactic rotation curves. We test its viability on cosmological scales using simulations with $256^{3}$ particles in a box of size $800\,h^{-1}$ comoving Mpc. We find generically that the MOND models massively overproduce large-scale structures by $z=0$, with a most massive cluster in $\nu$HDM of $\approx 5 \times 10^{17} \, {\rm M}_{\odot }\,h^{-1}$ and typical peculiar velocities of several thousand $\;\mathrm{ km}\,\mathrm{ s}^{-1}$. We also explore a local void solution to the Hubble tension in these models. Analogues to the observed ‘Local Hole’ do form in the MOND models, but values for the deceleration parameter $\lt -1.5$ in these regions prevent a satisfactory resolution to the Hubble tension. While $\Lambda$CDM significantly underpredicts the observed bulk flow in Cosmicflows-4, the high peculiar velocities that arise in the MOND models create the opposite problem, ruling out $\nu$HDM at $\gt 5\sigma$ confidence. Observations clearly require a much milder enhancement to the rate of structure growth in $\Lambda$CDM than is provided by the $\nu$HDM paradigm. Our results also suggest that replacing cold dark matter with hot dark matter is unlikely to provide a viable cosmological model, regardless of the gravity law.