Strict Gravitational-Radius Cosmology

Abstract We present a cosmological framework based on a strict gravitational-radius postulate, ( R_g = GM/c^2 ), applied globally to the Universe as a whole. In this approach, cosmology is formulated as a boundary-value problem defined by the causal horizon rather than as a superposition of independently evolving components. The postulate leads uniquely to a modified Friedmann relation, linear cosmic expansion ( a(t) \propto t ), a global effective equation of state ( w = -1/3 ), and the absence of both acceleration and deceleration at all epochs. A consistent treatment of linear scalar perturbations demonstrates that density growth freezes immediately after horizon entry, resulting in constant growth functions and time-independent gravitational potentials. Consequently, major cosmological observables—including Type Ia supernovae, baryon acoustic oscillations, the cosmic microwave background angular scale, weak lensing, redshift-space distortions, and cosmic chronometers—acquire a predominantly geometric rather than dynamical interpretation. We further examine the empirical status of the numerical coefficient in the gravitational radius. An analysis based on Planck units, kinematic criteria, and clock-comparison experiments indicates that the commonly assumed factor of two in the Schwarzschild radius is not uniquely fixed by fundamental principles. A terrestrial experiment employing modern optical atomic clocks is proposed to discriminate between physically self-consistent scenarios. It is emphasized that the operational success of global navigation satellite systems does not constitute a direct experimental confirmation of the Schwarzschild radius coefficient. The resulting framework is covariant, parameter-free apart from ( H_0 ), and sharply falsifiable by current and near-future observations.