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Effective actions from loop quantum cosmology: Correspondence with higher curvature gravity. (English) Zbl 1166.83018

Summary: Quantum corrections of certain types and relevant in certain regimes can be summarized in terms of an effective action calculable, in principle, from the underlying theory. The demands of symmetries, local form of terms and dimensional considerations limit the form of the effective action to a great extent leaving only the numerical coefficients to distinguish different underlying theories. The effective action can be restricted to particular symmetry sectors to obtain the corresponding, reduced effective action. Alternatively, one can also quantize a classically (symmetry) reduced theory and obtain the corresponding effective action. These two effective actions can be compared. As an example, we compare the effective action(s) known in isotropic loop quantum cosmology with the Lovelock actions, as well as with more general actions, specialized to homogeneous isotropic spacetimes and find that the \(\bar{\mu} \)-scheme is singled out.

MSC:

83F05 Relativistic cosmology
83C45 Quantization of the gravitational field
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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