On the viability of <i>f</i>(<i>Q</i>) gravity models
Avik De, Tee‐How Loo
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:mi>Q</mml:mi> <mml:mo>+</mml:mo> <mml:mi>β</mml:mi> </mml:math> 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.