Linear-Expansion Cosmology Based on a Strict Gravitational Radius

Abstract We investigate a cosmological model based on a strict identification of the gravitational radius,[R_g = \frac{GM}{c^2},]and the corresponding modification of gravitational dynamics on large scales. Within this framework, the cosmological equations admit a linear expansion law, (a(t)\propto t), corresponding to an effective equation of state (w=-1/3). The resulting cosmology is fully determined up to an overall normalization of the Hubble scale and does not require vacuum energy or late-time accelerated expansion. We derive the background dynamics and show that the luminosity distance has a closed analytic form,[D_L(z)\propto (1+z)\ln(1+z),]yielding a rigid, parameter-free prediction for the distance–redshift relation. A numerical comparison with the spatially flat (\Lambda)CDM model demonstrates near degeneracy at low redshift and a characteristic deviation at (z\gtrsim1), rendering the model strictly falsifiable using high-redshift standard candles or standard sirens. We further analyze the evolution of linear perturbations and show that structure growth generically “freezes out” once the (w=-1/3) component dominates the expansion. As a result, large-scale gravitational potentials remain approximately constant in time, leading to a strong suppression of the late Integrated Sachs–Wolfe (ISW) effect. This provides an observational test largely orthogonal to distance measurements. We demonstrate that the familiar factor of two in weak-field gravity has a kinematic origin, associated with post-Newtonian metric potentials and null geodesics, and does not uniquely fix the geometric or quasi-local mass–radius relation relevant for cosmology. A clear separation between the post-Newtonian sector and the large-scale mass postulate, together with the allowance for screening mechanisms in dense environments, permits consistency with Solar-System tests while maintaining the strict gravitational-radius postulate on cosmological scales. Taken together, these results define a minimal and predictive alternative to vacuum-driven cosmic acceleration. Linear (R_g) cosmology provides a sharply defined baseline against which the physical necessity of a cosmological constant can be critically tested using distance data, structure growth, and correlations between the cosmic microwave background and large-scale structure. ---