Covariant Modified Gravity Reconstructs Exact Galactic Rotation Curves and Lensing Without Dark Matter

The authors first construct a fully covariant spherically symmetric static metric ansatz that encodes flat rotation curves and lensing data by construction. They then insert this metric into a minimally coupled action containing power-law terms in the Ricci scalar and matter Lagrangian, solve the resulting trace equation, and obtain metric coefficients that match any required Tully-Fisher index. This yields analytic expressions for circular velocities and deflection angles that fit data without additional mass components. The approach differs from MOND by remaining fully covariant and from f(R) gravity by tying the functional form directly to galactic observables rather than cosmic expansion.

Evidence rests on exact analytic reconstruction rather than numerical fits; the model reproduces the observed baryonic Tully-Fisher relation with slope 4 and matches lensing deflection angles to within measurement precision for the sample galaxies examined. Because the action parameters are fixed by galactic phenomenology alone, the same functional form automatically extends to cluster scales where dark-matter halos are usually invoked. No free functions remain after the power-law indices are chosen to satisfy the trace equation.

Contextually the work revives the empirical success of modified-gravity approaches while addressing the covariance objection that sank earlier MOND-like proposals. It also highlights a methodological gap in standard dark-matter searches: rotation-curve data are still the highest-signal-to-noise probe of the low-acceleration regime, yet most particle searches assume Newtonian gravity holds. If the model survives further tests it would redirect observational resources toward precision weak-lensing surveys at 10–100 kpc scales.

Next steps require confronting the same action against cluster weak-lensing profiles and the cosmic microwave background power spectrum; any deviation larger than 5 percent at 1 Mpc would falsify the power-law choice within two years of upcoming Euclid and Rubin data releases.