General covariant symmetric teleparallel cosmology

Abstract

Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to the nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been a topic of growing interest in recent studies. Numerous works study the cosmology of symmetric teleparallel gravity assuming a flat Friedmann-Lemaître-Robertson-Walker metric, while working in the so-called "coincident gauge", further assuming that the connection coefficients vanish. However, little attention has been paid to the fact that both of these assumptions rely on the freedom to choose a particular coordinate system in order to simplify the metric or the connection, and that they may, in general, not be achieved simultaneously. Here we construct the most general symmetric teleparallel geometry obeying the conditions of homogeneity and isotropy, without making any assumptions on the properties of the coordinates, and present our results in both the usual cosmological coordinates and in the coincident gauge. We find that in general these coordinates do not agree, and that assuming both to hold simultaneously allows only for a very restricted class of geometries. For the general case, we derive the energy-momentum-hypermomentum conservation relations and the cosmological dynamics of selected symmetric teleparallel gravity theories. Our results show that the symmetric teleparallel connection in general contributes another scalar quantity into the cosmological dynamics, which decouples only for a specific class of theories from the dynamics of the metric, and only if the most simple geometry is chosen, in which both assumed coordinate systems agree. Most notably, the $f(Q)$ class of theories falls into this class.

18 pages, no figures

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• Cosmology in $f(Q)$ gravity: A unified dynamical system analysis at background and perturbation levels
• New models and Big Bang Nucleosynthesis constraints in $f(Q)$ gravity
• Revisiting Cosmologies in Teleparallelism
• Cosmological Inflation in f(Q, T) Gravity
• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Forecasting constraints on deviations from general relativity in $f(Q)$ gravity with standard sirens
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• Possible consistent model of parity violations in the symmetric teleparallel gravity
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• Symmetric Teleparallel Horndeski Gravity
• Symmetric Teleparallel Geometries
• Teleparallel gravity
• Conserved quantities in STEGR and applications
• Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
• Bulk viscous fluid in symmetric teleparallel cosmology: theory versus experiment
• Viscous fluid cosmology in symmetric teleparallel gravity
• Effects of the matter Lagrangian degeneracy in $f(Q,T)$ gravity
• Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity