On the viability of f(Q) gravity models

In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in f (R) theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally f (Q) model specific. We further prove that the energy conservation criterion is equivalent to the affine connection's field equation of f (Q) theory, and except the f(Q) = alpha Q+ ss model, the nonlinear f (Q) models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless Q itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support.