Observational test for $f(Q)$ gravity with weak gravitational lensing

Understand

In this article we confront a class of $f(Q)$ gravity models with observational data of galaxy-galaxy lensing.

• Specifically, we consider the $f(Q)$ gravity models containing a small quadratic correction when compared with General Relativity (GR), and quantify this correction by a model parameter $\alpha$.
• To derive the observational constraints, we start by extracting the spherically symmetric solutions which correspond to the deviations from the Schwarzschild solution that depends on the model parameter in a two-fold way, i.e., a renormalized mass and a new term proportional to $r^{-2}$.
• Then, we calculate the effective lensing potential, the deflection angle, the shear component, and the effective Excess Surface Density (ESD) profile.