Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

TL;DR

This paper examines the initial value problem in scalar-tensor and f(R) gravity theories, clarifying the nature of singularities and demonstrating the equivalence of Jordan and Einstein frames in this context.

Contribution

It provides a detailed analysis of singularities in scalar-tensor and f(R) gravity, and shows the physical equivalence of conformal frames regarding the initial value problem.

Findings

Singularities in scalar-tensor and f(R) gravity are clarified.

Jordan and Einstein frames are equivalent for the initial value problem.

Toy models illustrate the theoretical points.

Abstract

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini f(R) gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.