The Autobahn Stress Test: When a Galaxy-Winning Gravity Law Crashes on the Cosmic Highway

MOND fixes galaxy rotation curves perfectly. But the largest-ever gigaparsec-scale simulations reveal why this dark matter alternative spins wildly out of control across the wider universe.

> You love MOND because it predicts galaxy rotation curves with one neat tweak.
> You worry it might blow up when stretched to cosmic scales.
> Small-box sims and linear tricks dodge the nasty global couplings.
> So the real question: does a galaxy‑winning gravity law survive the Gpc autobahn?


> Step 1: Why this matters
> Galaxy fits force you to take MOND seriously.
> But the CMB needs extra gravitating mass at recombination.
> MOND is nonlinear and couples long and short modes.
> Only full Gpc simulations can show if galaxy success breaks cosmology.

> Step 2: Why prior attempts were insufficient
> Analytic or linearized work misses mode coupling.
> Small boxes omit long wavelengths that drive bulk flows.
> Hybrid patches hide dynamical instabilities.
> So prior wins were necessary but not sufficient.

> Step 3: The core idea
> Run gigaparsec, collisionless N‑body sims with MOND gravity.
> Add hot sterile neutrinos (νHDM) to supply early‑time mass.
> Let MOND respond self‑consistently to that mass field.
> Compare to matched ΛCDM and control runs.

> Step 4: How they implemented it
> Use QUMOND: two Poisson solves per timestep.
> Apply the Famaey & Binney ν interpolating function.
> Collisionless particles for baryons and ~11 eV sterile neutrinos.
> ICs from CAMB + MUSIC at zi = 199 so MOND is initially tiny.
> Codebase: AMR "phantom of ramses" patched for QUMOND.

> Step 5: Simulation suite (controls)
> ΛCDM — GR with CDM ICs.
> νHDM — QUMOND with sterile‑neutrino ICs.
> ΛHDM — Newtonian with HDM ICs.
> νCDM — QUMOND with CDM ICs.
> This isolates gravity vs initial power effects.

> Step 6: Observables they measure
> Halo counts converted to Newtonian dynamical masses.
> Local density contrast at virtual observer locations.
> Mass‑weighted bulk flows in concentric shells.
> Apparent H0 and q0 biases from radial velocity fits.
> Hubble dipole amplitude and direction within ~350/h Mpc.

> Step 7: The headline results
> MOND+νHDM produces far too much large‑scale power.
> Cluster and massive halo counts are overproduced.
> Peculiar velocities and bulk flows are much larger than observed.
> Our Local Group speed becomes a rare outlier in these runs.
> The excess is broad, not a small scale tuning issue.

> Step 8: Why this fails observationally
> MOND nonlinearity amplifies growth from the νHDM seed.
> Hot neutrinos give early mass but also free‑streaming; interplay is bad.
> Excess power appears on hundreds of Mpc — baryons won't erase it.
> Velocity statistics disagree with surveys and bulk‑flow measures.

> Step 9: Caveats and escape routes
> They used one ν interpolating function; others matter.
> Sterile‑neutrino properties could differ (mass, interactions).
> Simulations were collisionless — no hydrodynamic feedback included.
> A different relativistic embedding of MOND might alter growth.
> But none of these is a guaranteed fix for Gpc‑scale excesses.

> Step 10: The takeaway
> Collisionless QUMOND + ≈11 eV νHDM fails the Gpc stress test.
> MOND still kills it on galaxy scales.
> But this particular cosmological patch is observationally untenable.
> The result narrows viable alternatives and points where to look next.

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