Gravitational wave constraints on the Paneitz operator

TL;DR

This paper explores the role of the Paneitz operator in four-dimensional conformal gravity, linking it to mimetic gravity theories and deriving gravitational wave constraints.

Contribution

It demonstrates that the Paneitz operator aligns with extended mimetic gravity and derives observational constraints from gravitational wave propagation.

Findings

Paneitz operator behaves like extended mimetic gravity with associated instabilities.

Constraints on the operator are obtained from gravitational wave speed measurements.

Assumption of higher derivative terms to cure instabilities is considered.

Abstract

The Paneitz operator is a dimension-4 conformally invariant fourth-order differential operator that has recently attracted attention for possible cancellations of the vacuum energy. We show that, in four dimensions, the Paneitz operator acting on a scalar field falls within the class of extended mimetic gravity theories. Thus, it exhibits the usual instabilities of mimetic gravity. Assuming such instabilities are cured by higher derivative terms, we derive constraints on the Paneitz operator from a modified propagation speed of gravitational waves, after including the Einstein-Hilbert action in the mimetic gravity formulation.