On the viability of f(Q) gravity models

Abstract

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 $f(Q)=\alpha Q+\beta$ model, the non-linear 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.