TITLE:
A Combinatorial-Geometric Conjecture on the Origin of Dark Matter and Dark Energy in Higher-Dimensional Spacetime
AUTHORS:
Zhuoxiao Yao
KEYWORDS:
Dark Matter, Extra Dimensions, String Theory, Brane World, Combinatorial Statistics
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.4,
October
8,
2026
ABSTRACT: The cosmic dark matter density parameter Ωc ≈ 0.268 and dark energy density parameter ΩΛ ≈ 0.684 still lack a unified theoretical understanding. String/M-theory requires the number of spatial dimensions to be N = 9 or N = 10. We explore a phenomenological hypothesis: if all orientations of 3-dimensional subspaces (3-branes) were produced with equal a priori probability in the early universe, and each brane carries ordinary matter, then branes that share no spatial dimensions with the visible brane interact only via higher-dimensional gravity, behaving as cold dark matter. Its abundance is given by the purely combinatorial factor fDM = C(N − 3, 3)/C(N, 3): for N = 9 it is ≈23.8%, and for N = 10 ≈ 29.2%, which bracket the Planck value of 26.8%. The remaining branes naturally split into a unity-sum classification: the visible brane (≈1%), fully invisible branes (dark matter), and partially overlapping branes (sharing 1 or 2 dimensions). The statistical weight of the partially overlapping class is 75.0% (N = 9) and 70.0% (N = 10), of the same order as ΩΛ ≈ 68.4%. We propose a geometric interpretation in which gravitational contraction of matter on partially overlapping branes projects as an effective accelerating expansion on the visible brane, and illustrate it with a 5-dimensional toy model. Under the natural distinction between branes sharing one vs. two dimensions, the model yields a two-component effective dark energy: a transient early-dark-energy-like contribution from two-dimensional overlaps, and a slowly evolving late-time component from one-dimensional overlaps. This framework provides a statistical origin for the “coincidence problem” and offers testable predictions for the dark energy equation of state evolution, which can be probed by DESI, Euclid, and other surveys.