Constraining the Rastall parameters in static space-times with galaxy-scale strong gravitational lensing

Recently, Rastall gravity has undergone a significant surge in popularity. We obtain a power-law total mass-density profile for the inner region (within several effective radius) of early-type galaxies (ETGs) from the space-time structures which are described by the static spherically symmetric solutions of Rastall gravity under the assumption of perfect fluid matter. We find that in the inner region of ETGs, the Rastall dimensionless parameter beta = kappa lambda determines the mass distribution. We then use 118 galaxy-galaxy strong gravitational lensing systems to constrain the Rastall dimensionless parameter beta. We find that the mean value of beta for the total 118 ETGs is beta = 0.163 +/- 0.001(68 per cent CL) with a minor intrinsic scatter of delta = 0.020 +/- 0.001. Our work observationally illustrates the physical meaning of the Rastall dimensionless parameter at the galaxy scale. From the Newtonian approximation of Rastall gravity, we also find that an absolute isothermal mass distribution for ETGs is not allowed in the framework of Rastall gravity.