🔭 astrophysics

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

The largest collisionless N-body simulations to date demonstrate that the MOND-based $\nu$ HDM cosmology fails on Gpc scales by massively overproducing large-scale structures and generating unrealistic peculiar velocities, thereby ruling it out as a viable alternative to $\Lambda$ CDM.

Original authors: Alfie Russell, Indranil Banik, Oscar Cray, Hongsheng Zhao

Published 2026-03-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alfie Russell, Indranil Banik, Oscar Cray, Hongsheng Zhao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Cosmic Tug-of-War

Imagine the universe is a giant, expanding balloon. For decades, scientists have been trying to figure out exactly how the "paint" on that balloon (galaxies and stars) got there.

The standard theory, called $\Lambda$ CDM, says the universe is mostly made of invisible "dark matter" (like a heavy, invisible glue) that holds everything together. This theory works great for small things, but it's having trouble explaining why the universe is expanding faster than expected (the "Hubble Tension") and why some galaxy clusters are moving too fast.

Enter MOND (Modified Newtonian Dynamics). This is a rival theory that says: "Maybe we don't need invisible glue. Maybe the laws of gravity just change when things get very weak or far apart." To make MOND work on the scale of galaxy clusters, scientists proposed a hybrid model called $\nu$ HDM. This model says: "Let's use MOND's new gravity rules, but add a tiny bit of 'hot' dark matter (like fast-moving sterile neutrinos) to help out."

The Question: Does this hybrid model ( $\nu$ HDM) actually work when we look at the entire universe, or does it break down?

The Experiment: A Cosmic Video Game

The authors of this paper built the largest "cosmic video game" simulation ever run for a MOND universe.

The Box: They created a virtual universe 800 million light-years across.
The Players: They filled it with 16 million particles (representing chunks of matter).
The Race: They ran four different versions of the game to see which one looked like our real universe:
1. $\Lambda$ CDM: The standard model (Invisible Glue + Normal Gravity).
2. $\nu$ HDM: The hybrid model (Hot Neutrinos + MOND Gravity).
3. $\Lambda$ HDM: A weird mix (Hot Neutrinos + Normal Gravity).
4. $\nu$ CDM: Another weird mix (Cold Glue + MOND Gravity).

They let these universes evolve from the Big Bang to today ( $z=0$ ) and then checked the results.

The Results: The Hybrid Model Goes Off the Rails

Here is what happened when they ran the simulation, explained with analogies:

1. The "Over-Enthusiastic" Builder

In the standard model ( $\Lambda$ CDM), gravity builds structures slowly and steadily. In the MOND model ( $\nu$ HDM), the new gravity rules act like a hyper-active construction crew.

What happened: Instead of building a few skyscrapers (galaxy clusters), the MOND universe built monsters. By the time the simulation reached "today," it had created galaxy clusters so massive they were practically impossible ( $5 \times 10^{17}$ times the mass of our Sun).
The Analogy: Imagine you are baking cookies. The standard recipe makes perfect cookies. The MOND recipe, however, makes cookies that keep growing until they are the size of houses. It's too much of a good thing.

2. The "Speeding Ticket" Problem

In our real universe, our Local Group of galaxies is moving at about 600 km/s relative to the cosmic background.

What happened: In the MOND simulation, the galaxies were moving at thousands of km/s.
The Analogy: If the standard universe is a highway with a speed limit of 60 mph, the MOND universe is a highway where everyone is driving at 300 mph. Our actual universe is a "speeding ticket" outlier in the MOND world. The model predicts we should be moving much faster than we actually are.

3. The "Local Hole" Paradox

One of the main reasons scientists like MOND is that it might explain a giant "void" (empty space) near us called the KBC Void. Some think this empty space is pushing us away, making the universe look like it's expanding faster than it really is (solving the Hubble Tension).

What happened: The MOND simulation did create these giant empty holes. However, the hole was too empty and the push was too strong.
The Analogy: Imagine you are trying to explain why a car is speeding up. You say, "It's going downhill!" The MOND model says, "It's going down a vertical cliff!" It solves the problem of speeding up, but it creates a new problem: the car would be moving so fast it would fly off the road. The "push" from the void was so violent it broke the model.

4. The "Late Bloomer" Problem

The simulation also looked at when galaxies formed.

What happened: In the MOND universe, galaxies formed much later than we see them in the real universe. The James Webb Space Telescope (JWST) sees massive galaxies existing when the universe was very young (14 billion years ago). The MOND simulation said, "Those galaxies wouldn't exist yet; they are still forming."
The Analogy: If the universe is a 100-year-old person, the standard model says they have been an adult for 80 years. The MOND model says they are still a teenager. But we have photos of them as adults from when they were only 10 years old. The model is too slow to explain the early universe.

The Verdict: "Worst of Both Worlds"

The authors conclude that the $\nu$ HDM model is a "worst of both worlds" scenario.

It takes the problems of the standard model (needing dark matter) and the problems of MOND (too much gravity).
It creates too much structure (massive clusters), too much speed (peculiar velocities), and too much delay (late galaxy formation).

The Final Takeaway:
While the standard model ( $\Lambda$ CDM) has its own headaches (like the Hubble Tension), the MOND hybrid model tries to fix them by turning the volume up to 11, only to blow out the speakers. The universe we live in seems to require a much more subtle adjustment than the "sledgehammer" approach of MOND.

In short: The MOND universe is a chaotic, high-speed, monster-filled place that doesn't look anything like the calm, structured, and slightly mysterious universe we actually observe.

1. Problem Statement

The paper addresses the viability of Modified Newtonian Dynamics (MOND) as a cosmological framework, specifically testing the $\nu$ HDM (neutrino-Hot Dark Matter) model.

Context: While MOND successfully explains galactic rotation curves without Cold Dark Matter (CDM), it struggles with galaxy cluster dynamics and the Cosmic Microwave Background (CMB). The $\nu$ HDM model attempts to resolve this by combining MOND gravity with a component of Hot Dark Matter (HDM) in the form of 11 eV sterile neutrinos.
The Tension: Previous semi-analytic work suggested $\nu$ HDM could explain the KBC supervoid (a local underdensity) and the Hubble tension (the discrepancy between local $H_0$ and CMB-inferred $H_0$ ). However, hydrodynamical simulations indicated that $\nu$ HDM delays galaxy formation too much ( $z \approx 4$ ), conflicting with JWST observations of galaxies at $z \approx 14$ .
The Gap: There was a lack of large-scale, collisionless $N$ -body simulations to test whether $\nu$ HDM can reproduce the observed Large Scale Structure (LSS), specifically the Cumulative Halo Mass Function (CHMF), bulk flows, and local density contrasts on Gpc scales.

2. Methodology

The authors performed the largest collisionless $N$ -body simulations of a MOND cosmology to date.

Simulation Setup:
- Code: Used phantom of RAMSES (PoR), a modified version of the AMR code RAMSES, implementing QUMOND (Quasi-Linear MOND).
- Box Size: $800/h$ comoving Mpc (cMpc).
- Resolution: $256^3$ particles ( $N_{part} = 16,777,216$ ), with a mass per particle of $2.67 \times 10^{12} h^{-1} M_\odot$ .
- Initial Conditions: Generated using CAMB and MUSIC based on Planck 2018 parameters ( $\Omega_m \approx 0.315$ , $H_0 = 67.4$ km/s/Mpc). The initial power spectrum was evolved from $z=199$ to $z=0$ .
Models Compared:
To isolate the effects of gravity vs. dark matter type, four models were simulated:
1. $\Lambda$ CDM: Standard General Relativity (GR) + Cold Dark Matter (Baseline).
2. $\nu$ HDM: MOND gravity + Hot Dark Matter (11 eV sterile neutrinos).
3. $\Lambda$ HDM: GR + Hot Dark Matter (Unphysical control).
4. $\nu$ CDM: MOND gravity + Cold Dark Matter (Unphysical control).
Analysis Techniques:
- Halo Finding: Used the HOP algorithm to identify halos. For MOND models, masses were converted to "Newtonian dynamical masses" ( $M_N = \nu(g_N/a_0)M_{200}$ ) to allow fair comparison with observational data.
- Vantage Points (VPs): Analyzed 253 random locations within the simulation box to measure local observables (density contrast, bulk flow, apparent $H_0$ , deceleration parameter $q_0$ ).
- Observables: Calculated the Cumulative Halo Mass Function (CHMF), peculiar velocity distributions, bulk flow curves (comparing to Watkins et al. 2023), and local Hubble dipole (comparing to Migkas et al. 2021).

3. Key Contributions

Scale: This represents the first Gpc-scale collisionless simulation of a MOND cosmology, moving beyond previous smaller-box or hydrodynamical studies.
Decoupling Variables: By running the four distinct models ( $\Lambda$ CDM, $\nu$ HDM, $\Lambda$ HDM, $\nu$ CDM), the authors successfully disentangled the effects of the gravity law (MOND vs. GR) from the dark matter nature (HDM vs. CDM).
Systematic Testing: The study rigorously tests $\nu$ HDM against multiple cosmological tensions simultaneously: the Hubble tension, bulk flow tension, KBC void, and high-redshift galaxy formation.

4. Key Results

A. Structure Formation and Halo Mass Function

Overproduction of Structure: The MOND models ( $\nu$ HDM and $\nu$ CDM) massively overproduce large-scale structures by $z=0$ .
Massive Clusters: The most massive cluster in the $\nu$ HDM simulation reached $\approx 5 \times 10^{17} M_\odot/h$ , far exceeding observational limits.
CHMF Mismatch: The $\nu$ HDM model fails to reproduce the observed steep decline of the CHMF at the high-mass end (Driver et al. 2022). While $\Lambda$ CDM fits the high-mass end, $\nu$ HDM predicts too many massive halos.
Gravity vs. DM: The overproduction is driven primarily by the MOND gravity law, which enhances structure growth significantly once accelerations drop below $a_0$ (at $z \lesssim 50$ ).

B. Peculiar Velocities and Bulk Flows

Extreme Velocities: Typical peculiar velocities in $\nu$ HDM are several thousand km/s (median $\approx 5000$ km/s), whereas the Local Group's observed velocity is only $627$ km/s.
Statistical Outlier: The Local Group's velocity is a $3.2\sigma$ outlier in the $\nu$ HDM simulation.
Bulk Flow Tension:
- $\Lambda$ CDM underpredicts the observed bulk flow (Watkins et al. 2023) by $>5\sigma$ .
- $\nu$ HDM overpredicts the bulk flow by a factor of $\approx 10$ , ruling it out at $>5\sigma$ confidence.
- Interestingly, the unphysical $\Lambda$ HDM model (GR + HDM) produced bulk flows closest to observations, suggesting that HDM alone (without MOND) might offer a milder enhancement to structure growth.

C. Local Void and Hubble Tension

Void Formation: Analogues to the observed "Local Hole" (KBC void) do form in $\nu$ HDM models.
Hubble Tension Resolution: While these voids can locally inflate the apparent Hubble constant ( $H_0$ ), the associated deceleration parameter ( $q_0$ ) becomes extremely negative ( $< -1.5$ ) in these regions.
Conclusion: The voids in $\nu$ HDM are too extreme; they overcorrect the Hubble tension, creating a deceleration parameter inconsistent with observations. A viable solution requires a milder enhancement of structure growth than $\nu$ HDM provides.

D. Hubble Dipole

Directional Mismatch: The observed Hubble dipole (Migkas et al. 2021) is anti-aligned with the local bulk flow.
Simulation Outcome: In all simulations, the Hubble dipole and bulk flow are generally aligned ( $\cos \theta \approx +1$ ). The observed anti-alignment ( $\cos \theta \approx -0.91$ ) is extremely rare ( $<0.3\%$ probability) in these models, suggesting the observed dipole is unlikely to be sourced by a large-scale bulk flow.

E. Galaxy Formation Epoch

Late Formation: Analytic estimates and previous hydrodynamical simulations confirm that in $\nu$ HDM, galaxies form around $z \approx 4-5$ .
JWST Conflict: This is incompatible with JWST observations of massive galaxies at $z \gtrsim 14$ . The lack of CDM prevents early structure formation, and the delayed onset of MOND effects (until $z \lesssim 50$ ) cannot compensate fast enough to form galaxies by $z=14$ .

5. Significance and Conclusion

Ruling out $\nu$ HDM: The study concludes that the $\nu$ $ν$ HDM paradigm is not a viable cosmological model. It suffers from a "worst of both worlds" scenario:
1. Too little structure early on: Fails to form high-redshift galaxies ( $z > 10$ ).
2. Too much structure late on: Overproduces massive clusters and peculiar velocities by $z=0$ .
Implications for MOND: The results suggest that simply replacing CDM with HDM in a MOND framework does not work. The enhanced gravity of MOND leads to runaway structure growth on large scales that contradicts observations.
Future Directions: The authors argue that any successful resolution to cosmological tensions (Hubble tension, bulk flows) must involve a much more subtle modification to $\Lambda$ CDM than the drastic changes proposed by $\nu$ HDM. The data implies that while structure growth may need slight enhancement over $\Lambda$ CDM, the $\nu$ HDM enhancement is orders of magnitude too strong.
Sterile Neutrinos: The paper also notes that the physical motivation for 11 eV sterile neutrinos is weakening due to null results in particle physics experiments (KATRIN, MicroBooNE) and constraints from Big Bang Nucleosynthesis.

In summary, while MOND excels on galactic scales, this large-scale simulation demonstrates that the $\nu$ HDM cosmology fails catastrophically on Gpc scales, producing a universe that is structurally and kinematically inconsistent with current observations.