Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity

TL;DR

This paper compares effective actions derived from loop quantum cosmology with higher curvature gravity theories, highlighting the unique role of the  scheme in the correspondence.

Contribution

The paper establishes a connection between effective actions in loop quantum cosmology and higher curvature gravity, particularly identifying the  scheme as special.

Findings

The  scheme is uniquely singled out.

Effective actions in loop quantum cosmology can be matched with Lovelock and more general higher curvature actions.

Symmetry considerations significantly constrain the form of the effective action.

Abstract

Quantum corrections of certain types and relevant in certain regimes can be summarised 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, {\em 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 space-times and find that the $\bar{\mu}$-scheme is singled out.