Exorcising ghosts with gravitational waves: cases of ghostful and ghost-free fourth-order gravity
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2025
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| author | Lambiase, Gaetano Mukohyama, Shinji Poddar, Tanmay Kumar Rescigno, Anna Chiara |
| author_facet | Lambiase, Gaetano Mukohyama, Shinji Poddar, Tanmay Kumar Rescigno, Anna Chiara |
| contents | 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 $α_1$ and $α_2$ 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 $α_1\simeqα_2$ for simplicity, then we obtain $α_{1,2}\lesssim 4.2\times 10^{83}$ for $m\sim 3\times 10^{-16}\,\mathrm{eV}$ and $α_{1,2}\lesssim 1.3\times 10^{75}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_17789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exorcising ghosts with gravitational waves: cases of ghostful and ghost-free fourth-order gravity Lambiase, Gaetano Mukohyama, Shinji Poddar, Tanmay Kumar Rescigno, Anna Chiara General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology 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 $α_1$ and $α_2$ 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 $α_1\simeqα_2$ for simplicity, then we obtain $α_{1,2}\lesssim 4.2\times 10^{83}$ for $m\sim 3\times 10^{-16}\,\mathrm{eV}$ and $α_{1,2}\lesssim 1.3\times 10^{75}$ 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. |
| title | Exorcising ghosts with gravitational waves: cases of ghostful and ghost-free fourth-order gravity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2510.17789 |