Hypersurface-deformation algebroids and effective space-time models

Abstract

In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same space-time structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can in some cases map the space-time structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective space-time, and is shown here to be a new quantum space-time phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions prove the existence of classical space-time structures assumed elsewhere in models of loop quantum cosmology, but also shows the existence of additional quantum corrections that have not always been included.

30 pages

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Cited by in corpus (8)

• Multifractional theories: an unconventional review
• A no-go result for covariance in models of loop quantum gravity
• Constraining the loop quantum gravity parameter space from phenomenology
• General Covariance from the Quantum Renormalization Group
• Effective Field Theory of Loop Quantum Cosmology
• Lorentzian wormhole in the framework of loop quantum cosmology
• Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity
• Problem of Time and Background Independence: classical version's higher Lie Theory