Modes of space with two seats and a gravitational exclusion principle: rotation curves, lensing, clusters and simulations

We develop a hypothetical microscopic picture behind a cosmological exchange law between dark matter and a vacuum-like component, Q=bHρs(ρm-kρs)/(ρm+ρs) with k=2 and b=1, which fits current CMB, BAO and supernova data better than ΛCDM with the same number of parameters. In the picture, space consists of fixed spatial slices made of modes; each mode has a resting energy, observed as dark energy, can vibrate, which is light, can be deformed, which is gravity, and has two seats for matter. The form of the exchange law and k=2 follow heuristically, the vacuum-like energy behaves as a cosmological constant because free modes have a fixed size, and only dark matter converts, silently, because it shapes the modes without making them vibrate. Reading a seat as a unit of energy, a quantum ε by which the energy of matter is counted, removes the need for a coincidence between particle and mode energies, and keeps exclusion where it belongs, on particles rather than on quanta. Reading gravitation as a variation of the rate of passage between slices, and fixing the length of a jump by the mean of the rates of passage at its two ends, reproduces the Schwarzschild solution exactly. A minimum jump, set by the period of the slice, gives the acceleration scale a0=cH0/2π, which matches 147 SPARC rotation curves without fitting; the form of the transition follows, under stated readings of the picture, from surface waves released by jumps and absorbed by matter, which repeat its steps with Bose–Einstein statistics. A gravitational exclusion principle, by which only the stronger of the ordinary and minimum-jump accelerations acts, written in a momentum-conserving field form, is consistent with rotation curves, with weak lensing around blue galaxies and with X-COP clusters, and predicts the amount of hot gas around red galaxies. In three-dimensional simulations from z=50 it removes dark matter from halos up to 10¹³ M☉ and keeps about 90 per cent of it from 3×10¹³ to 10¹⁵ M☉, so that small galaxy groups should behave like galaxies and massive groups and clusters should contain dark matter, as observed. The cosmological model does not depend on this interpretation. Version 4 adds a first test of the predicted transition between galaxy groups without and with dark matter: 55 small groups follow the minimum-jump law on ordinary matter alone (median mass ratio 0.83), while all 23 Chandra groups with M500 = 1.5–15 × 10^13 solar masses show an excess (1.4–1.6), as the simulations predict.