How does a MOND cosmology fare on Gpc scales? - Collisionless $N$-body simulations of $\nu$HDM

Abstract

We present the largest collisionless $N$-body cosmological simulations in a MOdified Newtonian Dynamics (MOND) cosmology to date. Our 4 simulations cover $\Lambda$CDM as a baseline, a MOND with hot dark matter model known as $\nu$HDM, and 2 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 CMB power spectrum whilst 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 $800/h$ 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 $\approx 5 \times 10^{17} M_{\odot}/h$ and typical peculiar velocities of several thousand km/s. 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 $<-1.5$ in these regions prevent a satisfactory resolution to the Hubble tension. Whilst $\Lambda$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 $>5\sigma$ 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.