Gravity as an effective theory

TL;DR

This paper reviews the effective field theory approach to quantum gravity, discussing quantum corrections, their observability in cosmology, and proposing a toy model to explore dynamical geometry.

Contribution

It introduces an effective field theory framework for gravity, analyzes quantum corrections to classical gravity, and proposes a novel two-dimensional toy model with dynamical zweibein.

Findings

Quantum corrections to Newton's law are tiny but theoretically significant.

Non local quantum effects in gravity could be observable in early universe cosmology.

A two-dimensional toy model demonstrates dynamical zweibein generation without a metric.

Abstract

Using as inspiration the well known chiral effective lagrangian describing the interactions of pions at low energies, in these lectures we review the quantization procedure of Einstein gravity in the spirit of effective field theories. As has been emphasized by several authors, quantum corrections to observables in gravity are, by naive power counting, very small. While some quantities are not predictable (they require local counterterms of higher dimensionality) others, non local, are. A notable example is the calculation of quantum corrections to Newton's law. Albeit tiny these corrections are of considerable theoretical importance, perhaps providing information on the ultaviolet properties of gravity. We then try to search for a situation where these non local corrections may be observable in a cosmological context in the early universe. Having seen that gravity admits an effective treatment similar to the one of pions, we pursue this analogy and propose a two-dimensional toy model where a dynamical zwei-bein is generated from a theory without any metric at all.