Quantum Cosmology With R+R^2 Gravity

TL;DR

This paper develops a quantum cosmology framework for R+R^2 gravity, demonstrating that including curvature squared terms and properly applying auxiliary variable techniques yields a consistent quantum description with a probability interpretation.

Contribution

It introduces a novel approach to quantize R+R^2 gravity in cosmology, ensuring correct auxiliary variable use and deriving a quantum probability interpretation.

Findings

First-time derivation of a quantum probability interpretation in R+R^2 cosmology

Effective potential extremization reproduces Einstein's equations

Proper removal of total derivatives is crucial for unique quantum dynamics

Abstract

Canonical quantization of an action containing curvature squared term requires introduction of an auxiliary variable. Boulware etal[1] prescribed a technique to choose such a variable, by taking derivative of an action with respect to the highest derivative of the field variable, present in the action.It has been shown that[2] this technique can even be applied in situations where introduction of auxiliary variables are not at all required, leading to wrong Wheeler-deWitt equation. It has also been pointed out that[2] Boulware etal's[1] prescription should be taken up only after removing all removable total derivative terms from the action. Once this is done only a unique description of quantum dynamics would emerge. For curvature squared term this technique yields, for the first time, a quantum mechanical probability interpretation of quantum cosmology, and an effective potential, whose extremization leads to Einstein's equation. We conclude that Einstein-Hilbert action should essentially be modified by at least a curvature squared term to get a quantum mechanical formulation of quantuum cosmology and hence extend our previous work[2] for such an action along with a scalar field.