dorsal/arxiv
View SchemaParameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints
| Authors | Jie Zhu, Hao Li |
|---|---|
| Categories | |
| ArXiv ID | 2601.05750vv1 |
| URL | https://arxiv.org/abs/2601.05750 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
This work systematically investigates the post-Newtonian behavior of general quadratic gravity in the weak-field regime. By extending the Einstein-Hilbert action to include quadratic curvature terms as $\mathcal{L}\propto R-\lambda C^2+\mu R^2$, the theory introduces two massive modes: a scalar mode and a ghost tensor mode. Using the post-Newtonian expansion method, we derive the explicit expressions for the metric for a general source up to 1.5PN order. Furthermore, for a point-mass source, we extend the solution to 2PN order and evaluate the effective Parameterized Post-Newtonian parameters $\gamma(r)$ and $\beta(r)$. The results show that deviations from General Relativity are exponentially suppressed. The theory has the feature $\gamma(r)\equiv 1$ when $m_R=m_W$, and to ensure that gravity remains attractive, we have $m_W>m_R/4$. The leading correction to $\beta(r)$ exhibiting a characteristic $\mathcal{O}(r \ln (r)e^{-mr})$ dependence. Based on the Solar System experiments, we derive preliminary constraints on the theory's parameters: $m_R,m_W\gtrsim23~\mathrm{AU}^{-1}$, corresponding to $\lambda\lesssim2.1\times10^{19}~\mathrm{m}^2$ and $\mu\lesssim 7.1\times 10^{18}~\mathrm{m}^2$. This study provides a theoretical foundation for future tests of quadratic gravity using pulsar timing arrays, gravitational-wave observations, and laboratory-scale short-range gravity experiments.
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"abstract": "This work systematically investigates the post-Newtonian behavior of general quadratic gravity in the weak-field regime. By extending the Einstein-Hilbert action to include quadratic curvature terms as $\\mathcal{L}\\propto R-\\lambda C^2+\\mu R^2$, the theory introduces two massive modes: a scalar mode and a ghost tensor mode. Using the post-Newtonian expansion method, we derive the explicit expressions for the metric for a general source up to 1.5PN order. Furthermore, for a point-mass source, we extend the solution to 2PN order and evaluate the effective Parameterized Post-Newtonian parameters $\\gamma(r)$ and $\\beta(r)$. The results show that deviations from General Relativity are exponentially suppressed. The theory has the feature $\\gamma(r)\\equiv 1$ when $m_R=m_W$, and to ensure that gravity remains attractive, we have $m_W\u003em_R/4$. The leading correction to $\\beta(r)$ exhibiting a characteristic $\\mathcal{O}(r \\ln (r)e^{-mr})$ dependence. Based on the Solar System experiments, we derive preliminary constraints on the theory\u0027s parameters: $m_R,m_W\\gtrsim23~\\mathrm{AU}^{-1}$, corresponding to $\\lambda\\lesssim2.1\\times10^{19}~\\mathrm{m}^2$ and $\\mu\\lesssim 7.1\\times 10^{18}~\\mathrm{m}^2$. This study provides a theoretical foundation for future tests of quadratic gravity using pulsar timing arrays, gravitational-wave observations, and laboratory-scale short-range gravity experiments.",
"arxiv_id": "2601.05750",
"authors": [
"Jie Zhu",
"Hao Li"
],
"categories": [
"gr-qc"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints",
"url": "https://arxiv.org/abs/2601.05750",
"version": "v1"
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