We propose a new interpretation of anomalies in the distribution of stellar velocities in galaxies, galaxy velocities in clusters, and the observed accelerated expansion of the Universe as geometric effects of dynamic spacetime curvature in a compact expanding Universe. The model is based on Topological Multidimensional Field Theory (TMFT) kuzmin2025, in which the Universe manifold is grounded in a modified Higgs field. The Universe expands in the form of a 3-sphere S³ with radius R = ct as a result of spontaneous symmetry breaking of the Higgs field in real Cartesian 4D space; matter emerges from the Higgs field phase transition, and time is an emergent parameter generated by the forced expansion of the manifold. The key mechanism mimicking dark matter lies in the dependence of the effective inertial mass of baryonic matter on the metric coefficient g₀₀, which changes over time due to the decrease in Gaussian curvature of space K (t) = 1/ (ct) ². Galaxies formed in an era of high curvature, when the effective mass of stars was significantly lower than today, and equilibrium orbital velocities were correspondingly higher. As g₀₀ increased, the effective mass grew, and the initial velocity distribution naturally evolved into the flat rotation curves observed today, without invoking hypothetical dark matter. We demonstrate this mechanism using the Andromeda galaxy M31, reconstructing its initial state from modern observational data and computing the evolution using analytical equations of the model; the result accurately reproduces the observed rotation curve. The same theoretical model in our previous work demonstrated exceptional accuracy in describing redshift and resolved the Hubble tension without dark energy kuzmin2026. The model also naturally explains anomalies discovered by the James Webb Space Telescope (JWST), including early formation of massive galaxies, abundance of blue giants, and early appearance of heavy baryonic nuclei at high redshifts. The consistency of results for independent classes of observational data (cosmological distances and galactic dynamics) indicates that the effects attributed to dark matter and dark energy are illusions caused by the dynamic geometry of the Universe manifold. TMFT, deriving cosmological dynamics parameters from first principles (ab initio) and providing corrections at the 1\% level, simultaneously resolves a number of fundamental problems that in the standard CDM model require the introduction of hypothetical entities (dark matter, dark energy, inflation), and therefore represents a more economical and internally consistent alternative.
L. Stanislav Kuzmin (Thu,) studied this question.