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

Abstract

We present the largest collisionless $N$-body cosmological simulations in a MOdified Newtonian Dynamics (MOND) cosmology to date. Our 4 simulations cover $Λ$CDM as a baseline, a MOND with hot dark matter model known as $ν$HDM, and 2 unphysical models we call $Λ$HDM and $ν$CDM to test the individual contributions of hot dark matter and MOND gravity, respectively. $ν$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 $ν$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 $Λ$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 $ν$HDM at $>5σ$ confidence. Observations clearly require a much milder enhancement to the rate of structure growth in $Λ$CDM than is provided by the $ν$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.

Figures (9)

• Figure 1: The density projected along the $z$ direction through the whole simulation box at $z = 0$ for $\Lambda$CDM (top left), $\Lambda$HDM (top right), $\nu$CDM (bottom left), and $\nu$HDM (bottom right). The colour of each pixel shows the average 3D density in the pixel in units of the cosmic mean, as indicated using the logarithmic colour bar. The colour scale is identical for each plot.
• Figure 2: Evolution of the median particle peculiar velocity $v$ with the cosmic scale factor $a$ for $\Lambda$CDM (top left), $\Lambda$HDM (top right), $\nu$CDM (bottom left), and $\nu$HDM (bottom right). Results are shown on logarithmic axes. The grey dashed-dotted line shows the predicted $v \propto \sqrt{a}$ evolution from linear Newtonian theory in the absence of dark energy, the maroon dashed line shows the $z = 50$ epoch at which overdensities are predicted to enter the MOND regime Haslbauer_2020, and the black dashed line shows the epoch of matter-dark energy equality.
• Figure 3: Histograms showing the distribution of particle peculiar velocities in each simulation at $z = 0$. From the leftmost peak to the rightmost peak, these are $\Lambda$CDM, $\Lambda$HDM, $\nu$CDM, and $\nu$HDM. The Local Group peculiar velocity of 627 km/s is shown for reference using a solid vertical line Kogut_1993. The typical peculiar velocities in the MOND simulations are thousands of km/s.
• Figure 4: The solid lines with markers show the cumulative halo mass function (CHMF) of each simulation at $z=0$, as indicated in the legend. The first and last markers represent the lightest and heaviest halo mass in each simulation, whilst the other markers denote intervals of 0.2 dex in mass. The black solid line shows the CHMF observed by Driver_2022 extrapolated to $z=0$, with the shaded region representing the $1\sigma$ confidence interval. The dashed vertical lines represent the minimum halo mass in each simulation, with the MOND simulations having a higher minimum mass due to the use of Newtonian dynamical masses (\ref{['eq:Dynamical mass']}). Poisson uncertainties on simulation results are too small to be visible here. $\Lambda$CDM fits the high mass end of the observations, whilst the $\Lambda$HDM and MOND simulations appear to overproduce large structures.
• Figure 5: Histograms showing the local density contrast at $z = 0$ within $225/h$ Mpc of each VP for our simulation of $\Lambda$CDM (top left), $\Lambda$HDM (top right), $\nu$CDM (bottom left), and $\nu$HDM (bottom right). Each panel contains two histograms, with the lighter histogram representing the true density contrast and the darker histogram with a black edge representing the apparent (RSD corrected) density contrast an observer would measure (Equation \ref{['eq:redshift_distortion']}). The apparent density contrast measured by Keenan_2013 is shown as a solid black vertical line, with uncertainty indicated using the grey shaded band. The same bins are used in all panels to make comparison easier.