Abundance of local actions for the vacuum Einstein equations

TL;DR

This paper introduces numerous local actions for the vacuum Einstein equations, highlighting how matter coupling or quantum effects can lead to inequivalent theories with multiple parameters.

Contribution

It demonstrates the existence of large classes of local actions for Einstein's equations and explores their implications for matter coupling and quantum theories.

Findings

Existence of large classes of local actions for vacuum Einstein equations

Matter coupling introduces inequivalent equations with arbitrary parameters

Quantum theories depend on these parameters

Abstract

We exhibit large classes of local actions for the vacuum Einstein equations. In presence of fermions, or more generally of matter which couple to the connection, these actions lead to inequivalent equations revealing an arbitrary number of parameters. Even in the pure gravitational sector, any corresponding quantum theory would depend on these parameters.