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Observational Constraints on the Rastall gravity from Rotation Curves of Low Surface Brightness Galaxies

The Rastall gravity is a modification of Einstein's general relativity, in which the energy-momentum conservation is not satisfied and depends on the gradient of the Ricci curvature. It is in dispute whether the Rastall gravity is equivalent to the general relativity (GR). In this work, we constrain the theory using the rotation curves of Low Surface Brightness (LSB) spiral galaxies. Through fitting the rotation curves of LSB galaxies, we obtain the parameter $β$ of the Rastall gravity. The $β$ values of LSB galaxies satisfy Weak Energy Condition (WEC) and Strong Energy Condition(SEC). Combining the $β$ values of type Ia supernovae and gravitational lensing of elliptical galaxies on the Rastall gravity, we conclude that the Rastall gravity is equivalent to the general relativity.