Tensor-vector-scalar-modified gravity: from small scale to cosmology

The impressive success of the standard cosmological model has suggested to many that its ingredients are all one needs to explain galaxies and their systems. I summarize a number of known problems with this program. They might signal the failure of standard gravity theory on galaxy scales. The requisite hints as to the alternative gravity theory may lie with the MOND paradigm which has proved an effective summary of galaxy phenomenology. A simple nonlinear modified gravity theory does justice to MOND at the nonrelativistic level, but cannot be consistently promoted to relativistic status. The obstacles were first sidestepped with the formulation of TeVeS, a covariant modified gravity theory. I review its structure, its MOND and Newtonian limits, and its performance in face of galaxy phenomenology. I also summarize features of TeVeS cosmology and describe the confrontation with data from strong and weak gravitational lensing