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

Abstract

Abstract 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, α . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.202</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.179</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.277</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.33em"/> <mml:msup> <mml:mrow> <mml:mi>Mpc</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> at the 1 σ confidence level, and then compare the fitting efficiency with the standard Λ 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.