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Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
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abstract
We formulate $f(Q,C)$ gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar $Q$ we incorporate in the Lagrangian the boundary term $C$ of its difference form the standard Levi-Civita Ricci scalar $\mathring R$. We extract the general metric and affine connection field equations, we apply them at a cosmological framework, and adopting three different types of symmetric teleparallel affine connections we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.
Forward citations
Cited by 4 Pith papers
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Degenerate and connection-dependent cosmological sectors in f(Q,C) gravity
Connection field equations force a degenerate f(R)-equivalent sector of f(Q,C) cosmology in which three geometric connections coincide, and only nonzero integration constants make the connections physically distinct.
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Alleviating the Hubble Tension with Smooth Sign-Switching Dark Energy: Full CMB Constraints with DESI and PantheonPlus
Smooth ECDM dark energy remains compatible with Planck+ACT+SPT, DESI DR2 and Pantheon+/SH0ES while alleviating the Hubble tension through a controlled late-time density transition.
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Atomic clocks and gravitational waves as probes of non-metricity
The paper claims existing gravitational-wave data already bound Weyl non-metricity, α²ω̄0<10⁻⁶⁹ GeV, via backreaction of a Planck-scale Weyl field, but a dropped kinetic term numerically exceeds the assumed sensitivity.
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Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the impact on the $\sigma_8$ tension
A sqrt(Q) correction in f(Q) gravity suppresses structure growth without altering the expansion history; fitted to RSD/DESI data it can bring sigma8 into agreement with Planck, at the cost of a sigma8-M degeneracy.
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