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.

Accepted in CQG

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• Neutron Star in Covariant $f(Q)$ gravity
• Cosmological reconstruction and $\Lambda$CDM universe in $f(Q,C)$ gravity
• Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
• Geometry and covariance of symmetric teleparallel theories of gravity
• Spatial curvature in coincident gauge $f(Q)$ cosmology
• Influence of pressure anisotropy and non-metricity parameter on mass-radius relation and stability of millisecond pulsar in $f(Q)$ gravity
• Cosmological dynamics and observational constraints on a viable $f(Q)$ non-metric gravity model
• Modeling and Analyzing Stability of Hybrid Stars within $f(Q)$ Gravity
• Emergent Universe in f(Q) gravity theories
• A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity
• Observational constraints using Bayesian statistics and Deep Learning in $f(Q)$ gravity
• Reconstructing modified and alternative theories of gravity
• Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in $f(Q)$ cosmology
• Polytropic Stars in $f(Q)=Q+\xi Q^2$ covariant formulation
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• Probing symmetric teleparallel gravity in the early universe
• Phase space structure of symmetric teleparallel theory of gravity
• Vulnerability of f(Q) gravity theory and a possible resolution
• Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity