TY - JOUR
T1 - Hypersurface-deformation algebroids and effective spacetime models
AU - Bojowald, Martin
AU - Büyükçam, Umut
AU - Brahma, Suddhasattwa
AU - D'Ambrosio, Fabio
N1 - Funding Information:
This work was supported in part by NSF Grants No. PHY-1307408 and No.PHY-1607414.
Publisher Copyright:
© 2016 American Physical Society.
PY - 2016
Y1 - 2016
N2 - 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 spacetime structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can, in some cases, map the spacetime 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 spacetime, and it is shown here to be a new quantum spacetime phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions not only prove the existence of classical spacetime structures assumed elsewhere in models of loop quantum cosmology, they also show the existence of additional quantum corrections that have not always been included.
AB - 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 spacetime structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can, in some cases, map the spacetime 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 spacetime, and it is shown here to be a new quantum spacetime phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions not only prove the existence of classical spacetime structures assumed elsewhere in models of loop quantum cosmology, they also show the existence of additional quantum corrections that have not always been included.
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U2 - 10.1103/PhysRevD.94.104032
DO - 10.1103/PhysRevD.94.104032
M3 - Article
AN - SCOPUS:84995527342
VL - 94
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 10
M1 - 104032
ER -