We derive the affine tensor associated with the energy and momentum densities of both gravitational and matter fields, the complex pseudotensor, for $f(Q)$ nonmetric gravity, the straightforward extension of the symmetric teleparallel equivalent of general relativity (STEGR), characterized by a flat, torsion-free, nonmetric connection. The local conservation of energy-momentum complex on shell is satisfied through a continuity equation. An important analogy is pointed out between gravitational pseudotensor of teleparallel $f(T)$ gravity, in the Weitzenböck gauge, and the same object of symmetric teleparallel $f(Q)$ gravity, in the coincident gauge. Furthermore, we perturb the gravitational pseudotensor ${{\tau }^{\alpha }}_{\lambda }$ in the coincident gauge up to the second order in the metric perturbation, obtaining a useful expression for the power carried by the related gravitational waves. We also present an application of the gravitational pseudotensor, determining the gravitational energy density of a Schwarzschild spacetime in STEGR gravity, adopting the concident gauge. Finally, analyzing the conserved quantities on manifolds, the Stokes theorem can be formulated for generic affine connections.

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• Alternative gravity theories