Observational Test of f(Q) Gravity with Weak Gravitational Lensing

In this article we confront a class of f(Q) gravity models with observational data of galaxy-galaxy lensing. Specifically, we consider 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 spherically symmetric solutions, which correspond to deviations from the Schwarzschild solution that depends on the model parameters in a twofold 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 profile. After that, we employ a group catalog and a shape catalog from the Sloan Digital Sky Survey Data Release 7 for the lens and source samples, respectively. Moreover, we handle the off-center radius as a free parameter and constrain it using a Markov Chain Monte Carlo method. Concerning the deviation parameter from GR we derive alpha=1.202(-0.179)(+0.277)x10-6Mpc(-2) at the 1 sigma confidence level, and then compare the fitting efficiency with the standard Lambda cold dark matter paradigm by applying the Akaike information criterion and Bayesian information criterion. Our results indicate that the f(Q) corrections alongside the off-center effect yield a scenario that is slightly favored.