{"paper":{"title":"Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Quadratic gravity produces exponentially suppressed deviations from general relativity at solar system scales.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Hao Li, Jie Zhu","submitted_at":"2026-01-09T12:05:09Z","abstract_excerpt":"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 "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Deviations from General Relativity are exponentially suppressed. The theory has the feature gamma(r) identical to 1 when m_R equals m_W, and to ensure gravity remains attractive we have m_W greater than m_R over 4. Solar System experiments give preliminary constraints m_R, m_W greater than or equal to 23 AU inverse, corresponding to lambda less than or equal to 2.1 times 10 to the 19 square meters and mu less than or equal to 7.1 times 10 to the 18 square meters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The post-Newtonian expansion remains valid for the quadratic gravity theory in the weak-field regime around solar-system sources, and the ghost tensor mode does not produce instabilities or negative-energy issues that would invalidate the classical metric solution at these scales.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quadratic gravity with Weyl-squared and Ricci-squared terms produces PPN parameters that equal their GR values except for exponentially decaying corrections, with gamma identically 1 when the two mode masses are equal, yielding solar-system lower bounds m_R, m_W greater than or equal to 23 per AU.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quadratic gravity produces exponentially suppressed deviations from general relativity at solar system scales.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7a7176f8eed68b016553e8dd17bccd235939cdc3218dde3d70f74324a7f4bf53"},"source":{"id":"2601.05750","kind":"arxiv","version":3},"verdict":{"id":"c65659a3-d383-400c-ade2-96d828aee46e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T16:16:07.669671Z","strongest_claim":"Deviations from General Relativity are exponentially suppressed. The theory has the feature gamma(r) identical to 1 when m_R equals m_W, and to ensure gravity remains attractive we have m_W greater than m_R over 4. Solar System experiments give preliminary constraints m_R, m_W greater than or equal to 23 AU inverse, corresponding to lambda less than or equal to 2.1 times 10 to the 19 square meters and mu less than or equal to 7.1 times 10 to the 18 square meters.","one_line_summary":"Quadratic gravity with Weyl-squared and Ricci-squared terms produces PPN parameters that equal their GR values except for exponentially decaying corrections, with gamma identically 1 when the two mode masses are equal, yielding solar-system lower bounds m_R, m_W greater than or equal to 23 per AU.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The post-Newtonian expansion remains valid for the quadratic gravity theory in the weak-field regime around solar-system sources, and the ghost tensor mode does not produce instabilities or negative-energy issues that would invalidate the classical metric solution at these scales.","pith_extraction_headline":"Quadratic gravity produces exponentially suppressed deviations from general relativity at solar system scales."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.05750/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":51,"sample":[{"doi":"","year":2014,"title":"The Confrontation between General Relativity and Experiment","work_id":"acffb50a-b7d3-471f-b146-9e457bb1183f","ref_index":1,"cited_arxiv_id":"1403.7377","is_internal_anchor":true},{"doi":"","year":2009,"title":"Experimental Tests of General Relativity: Recent Progress and Future Directions","work_id":"3aa3b634-ee00-40bb-9802-7e9779bda200","ref_index":2,"cited_arxiv_id":"0809.3730","is_internal_anchor":true},{"doi":"","year":2015,"title":"Testing General Relativity with Present and Future Astrophysical Observations","work_id":"219087d7-5726-4967-bc19-af2ca31335c7","ref_index":3,"cited_arxiv_id":"1501.07274","is_internal_anchor":true},{"doi":"","year":2016,"title":"Observation of Gravitational Waves from a Binary Black Hole Merger","work_id":"ab878228-151c-4a29-8026-a4308b076d30","ref_index":4,"cited_arxiv_id":"1602.03837","is_internal_anchor":true},{"doi":"","year":2019,"title":"First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole","work_id":"090661bf-d0e6-4cf3-a7b6-39cd0420cf87","ref_index":5,"cited_arxiv_id":"1906.11238","is_internal_anchor":true}],"resolved_work":51,"snapshot_sha256":"7eb37543107cf8b04f7bf25a4aac3b9d0cf70214e2419d63216ce65c1cdb047d","internal_anchors":23},"formal_canon":{"evidence_count":2,"snapshot_sha256":"77e9aba31986a89a1283de40b3a237c7ab15e7792c67df9f0608b8f8c5a865cf"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}