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arXiv · 2212.08304

On the viability of $f(Q)$ gravity models

Avik De·Tee-How Loo
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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.

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Avik De, Tee-How Loo. 2022-12-16. On the viability of $f(Q)$ gravity models. https://doi.org/10.1088/1361-6382/accef7

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