Gravitational Renormalization Group Flow, Astrophysics and Cosmology

A modified gravitational theory is developed in which the gravitational coupling constants $G$ and $Q$ and the effective mass $m_\phi$ of a repulsive vector field run with momentum scale $k$ or length scale $\ell =1/k$, according to a renormalization group flow. The theory can explain cosmological early universe data with a dark hidden photon and late time galaxy and cluster dynamics without dark matter. The theory agrees with solar system and binary pulsar observations.