# Constraining the Rastall parameters in static spacetimes with galaxy-scale strong gravitational lensing

## TL;DR

This paper uses strong gravitational lensing data from 118 galaxies to constrain the Rastall gravity parameter, revealing its physical significance at galaxy scales and challenging the isothermal mass distribution assumption.

## Contribution

It provides the first observational constraints on the Rastall gravity parameter using galaxy-scale lensing data and explores its implications for galaxy mass profiles.

## Key findings

- Mean Rastall parameter β = 0.163 ± 0.001 (68% CL)
- Inner galaxy mass profiles follow a power-law distribution influenced by β
- Isothermal mass distribution is incompatible with Rastall gravity framework

## Abstract

Recently, Rastall gravity is undergoing 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 total 118 ETGs is $\beta=0.163\pm0.001$(68\% CL) with a minor intrinsic scatter of $\delta=0.020\pm 0.001$. Our work observationally illustrates the physical meaning of the Rastall dimensionless parameter in 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.