Solar system tests in covariant f(Q) gravity

Abstract

We study the Solar System constraints on covariant $f(Q)$ gravity. The covariant $f(Q)$ theory is described by the metric and affine connection, where both the torsion and curvature vanish. Considering a model including a higher nonmetricity-scalar correction, $f(Q)=Q+\hat{I}\pm Q^n-2\hat{I}›$, we derive static and spherically symmetric solutions, which represent the Schwarzschild-de Sitter solution with higher-order corrections, for two different ansatz of the affine connection. On the obtained spacetime solutions, we investigate the perihelion precession, light deflection, Shapiro delay, Cassini constraint, and gravitational redshift in the $f(Q)$ gravity. We place bounds on the parameter $\hat{I}\pm$ with $n=2,3$ in our model of $f(Q)$ gravity, using various observational data in the Solar System.

27 pages, 1 figures, 2 tables