Exorcising ghosts with gravitational waves: cases of ghostful and ghost-free fourth-order gravity

TL;DR

This paper compares ghostful and ghost-free fourth-order gravity theories by analyzing gravitational wave emissions and observational data, establishing new astrophysical bounds on their parameters and addressing theoretical consistency issues.

Contribution

It provides the first astrophysical constraints on ghostful and ghost-free fourth-order gravity theories using gravitational wave observations.

Findings

Ghostful theory exhibits non-unitarity and phenomenological inconsistencies.

Ghost-free theory reproduces GR predictions when coupling constants vanish.

GW observations constrain the mass of modes and coupling constants, setting new bounds.

Abstract

General Relativity (GR) is an effective field theory valid in the infrared regime. Quadratic curvature extensions intended to probe ultraviolet physics generically propagate a massive spin-$2$ ghost and are therefore non-unitary. One route to remove ghost is by enlarging the geometric sector (torsion, non-metricity). We investigate the infrared phenomenology of both the standard (ghostful) and ghost-free fourth-order gravity theories by computing Gravitational Wave (GW) emission and confronting the results with observations such as the orbital-period decay of quasi-stable binaries such as PSR B1913+16 and PSR J1738+0333 and the chirp-mass evolution of GW170817. In the ghostful theory, besides the theoretical inconsistency due to non-unitarity, there are also phenomenological problems: the massless spin-$2$ GW flux cancels the combined GW fluxes of the massive spin-$2$ ghost and massive spin-$0$ scalar in the vanishing-mass limit, so the GR quadrupole formula is not recovered at the leading order. As a result, we obtain the GW constraint on the ghostful theory as $m\gtrsim 10^{-11}~\mathrm{eV}$, where $m$ is the mass of the massive modes. By contrast, the ghost-free theory smoothly reproduces the Newtonian potential and GR quadrupole formulae when the two coupling constants $\alpha_1$ and $\alpha_2$ vanish, independently of the mass $m$. Therefore, GW observations put mass-dependent upper bounds on the size of the coupling constants. For example, if we assume $\alpha_1\simeq\alpha_2$ for simplicity, then we obtain $\alpha_{1,2}\lesssim 4.2\times 10^{83}$ for $m\sim 3\times 10^{-16}\,\mathrm{eV}$ and $\alpha_{1,2}\lesssim 1.3\times 10^{75}$ for $m\sim 10^{-11}\,\mathrm{eV}$. To our knowledge, these are the first astrophysical-scale bounds reported for ghostful and ghost-free fourth-order gravity.