Quantum Gravity and Higher Curvature Actions

TL;DR

This paper discusses the derivation of effective equations with higher curvature terms in quantum gravity, emphasizing Hamiltonian methods, degrees of freedom, and the role of symmetries, with applications to loop quantum gravity and string theory.

Contribution

It introduces a general scheme for computing effective equations perturbatively in a Hamiltonian formalism, applicable around any quantum state, not just the vacuum.

Findings

Effective equations include higher derivative and curvature terms.

The scheme allows expansion around arbitrary quantum states.

It highlights the role of symmetries and free parameters in effective descriptions.

Abstract

Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.