ASingle-Parameter Cosmology Unifying Dark Energy, Dark Matter, and the Cyclic Universe

This paper presents a new cosmological model that explains the dynamics of the universethrough a single order parameter. The central equation of the model is ΨD = xn+xD−n, where xrepresents the physical energy of the system (continuously positive, measurable quantity) and nrepresents the geometric dimension state (continuously varying between 0+ and D = 3). Theterm xn denotes the n-dimensional geometric form of energy, while x(D−n) denotes the energydistribution across the remaining D−n dimensions; their sum ΨD can never reach zero. Theuniverse begins as dimensionless pure energy (n → 0+); as it acquires dimension, energy isreleased and space expands. The energy trapped and released during the n : 2 → 3 transitionincreases the universe’s expansion rate, constituting the physical origin of the acceleratingexpansion measured in observations as dark energy. The n = 3 boundary is an insurmountableand unsustainable geometric wall: a universe approaching this boundary sufficiently closelynecessarily begins to contract. During contraction, black hole mergers, Hawking radiation,and form reduction continue to produce entropy — the Big Crunch does not reduce entropy,it accumulates it. When contraction reaches the bounce point ρ = ρc, a new expansion cyclebegins; singularity never forms at any stage. Dark matter is the gravitational effect of incompletedimensional transition. Time is not an independent dimension but displacement measurementinformation derived from n variation. Singularity has been shown to be impossible through threeindependent arguments; conservation of energy and entropy have been proven mathematically.