Cosmological Expansion from Machian Phase Normalization by Horizon Constraints

We argue that cosmological expansion is governed by Machian phase normalization of the gravitational path integral, fixed by causal horizon boundary conditions rather than by local dynamics. In this formulation, the cosmological conformal factor is not a propagating degree of freedom but a global gauge variable fixed by the Hamiltonian constraint, rendering the conventional conformal-factor problem inapplicable. Thermal equilibrium at cosmological turning points uniquely fixes the equilibrium phase density ($\mathrm{\Lambda }=R\mathrm{/}6$) as the integrating factor that renders the horizon Clausius relation exact. Controlled departures from equilibrium are encoded by a single variance parameter governing non-adiabatic background evolution. The resulting framework clarifies the conceptual status of $\mathrm{\Lambda }$CDM, explains the emergence of effective $w$CDM behavior–including phantom regimes without new degrees of freedom–and provides a natural origin for late-time cosmological tensions, arising from global constraints that preclude a stable de Sitter state.