How does a MOND cosmology fare on Gpc scales? − Collisionless N -body simulations of νHDM

Abstract We present the largest collisionless N-body cosmological simulations in a MOdified Newtonian Dynamics (MOND) cosmology to date. Our 4 simulations cover ΛCDM as a baseline, a MOND with hot dark matter model known as νHDM, and 2 unphysical models we call ΛHDM and νCDM to test the individual contributions of hot dark matter and MOND gravity, respectively. νHDM 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 2563 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 νHDM of ≈5 × 1017 M⊙/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 ΛCDM 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 νHDM at 5σ confidence. Observations clearly require a much milder enhancement to the rate of structure growth in ΛCDM than is provided by the νHDM 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.