Constraints on Gravitation from Causality and Quantum Consistency

TL;DR

This paper explores how causality and quantum mechanics constrain theories of gravity, comparing different spin-2 particle interactions, and discusses the quantum consistency of scalar-tensor modifications like $F(R)$ models.

Contribution

It identifies the limitations of certain gravitation theories based on causality and quantum consistency, highlighting differences from general relativity and analyzing scalar-tensor models.

Findings

General relativity requires an infinite tower of terms for consistency.

Certain spin-2 theories with finite terms fail causality when coupled to photons.

$F(R)$ models lack the necessary counterterms for quantum consistency.

Abstract

We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of terms for consistency, which is known to lead uniquely to general relativity. The second class only requires a finite number of terms for consistency, which appears as another class of theories of massless spin 2. We recap the causal consistency of general relativity and show how this fails in the second class for the special case of coupling to photons, exploiting related calculations in the literature. In a companion paper [1] this result is generalized to a much broader set of theories. Then, as a causal modification of general relativity, we add light scalar particles and recap the generic violation of universal free-fall they introduce and its quantum resolution. This leads to a discussion of a special type of scalar-tensor theory; the $F(\mathcal{R})$ models. We show that, unlike general relativity, these models do not possess the requisite counterterms to be consistent quantum effective field theories. Together this helps to remove some of the central assumptions made in deriving general relativity.