{"paper":{"title":"The Amplitude-Growth Degeneracy and Implied $A_s$ Diagnostic for Background-Inert Modified Gravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Background-inert f(Q) gravity couplings degenerate with σ80 through a deeper As-D0(λ) link when CMB distance priors are used.","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Ameya Kolhatkar, P. K. Sahoo","submitted_at":"2026-05-13T09:41:26Z","abstract_excerpt":"We prove that any background-inert perturbative coupling $ \\lambda $ in coincident $ f(Q) $ gravity exhibits a degeneracy with the clustering amplitude $ \\sigma_{80} $, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a more deeper $ A_s-D_0(\\lambda) $ degeneracy between the primordial amplitude $ A_s $ and the present day growth factor $ D_0(\\lambda) $. We outline a consistency check scheme, applicable to models even outside the $ f(Q) $ class, by computing $ A_s $ needed to reproduce the $ \\sigma_{80} $ predicted by the sampler. We perform o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that any background-inert perturbative coupling λ in coincident f(Q) gravity exhibits a degeneracy with the clustering amplitude σ80, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a more deeper As-D0(λ) degeneracy between the primordial amplitude As and the present day growth factor D0(λ).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the perturbative coupling remains strictly background-inert and that compressed CMB distance priors capture the full information needed to expose the degeneracy without full likelihood analysis.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Any background-inert λ in coincident f(Q) gravity degenerates with σ80 via an As-D0(λ) link, inflating σ80 to unphysical levels and raising As by 20-30% in tension with Planck unless fixed by As priors.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Background-inert f(Q) gravity couplings degenerate with σ80 through a deeper As-D0(λ) link when CMB distance priors are used.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"885791288d140da748ba4092faa8fa74380aaade3cc33cca35078e9680adf891"},"source":{"id":"2605.13914","kind":"arxiv","version":1},"verdict":{"id":"a8d76fdc-f1de-4558-a2f6-8d996f1f17df","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:44:00.521574Z","strongest_claim":"We prove that any background-inert perturbative coupling λ in coincident f(Q) gravity exhibits a degeneracy with the clustering amplitude σ80, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a more deeper As-D0(λ) degeneracy between the primordial amplitude As and the present day growth factor D0(λ).","one_line_summary":"Any background-inert λ in coincident f(Q) gravity degenerates with σ80 via an As-D0(λ) link, inflating σ80 to unphysical levels and raising As by 20-30% in tension with Planck unless fixed by As priors.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the perturbative coupling remains strictly background-inert and that compressed CMB distance priors capture the full information needed to expose the degeneracy without full likelihood analysis.","pith_extraction_headline":"Background-inert f(Q) gravity couplings degenerate with σ80 through a deeper As-D0(λ) link when CMB distance priors are used."},"references":{"count":57,"sample":[{"doi":"10.1103/revmodphys.88.015004","year":2015,"title":"Big Bang Nucleosynthesis: 2015","work_id":"7016372a-8738-4b92-9883-79f92f2687da","ref_index":1,"cited_arxiv_id":"1505.01076","is_internal_anchor":true},{"doi":"10.1051/0004-6361/201833910","year":2018,"title":"Planck 2018 results. VI. Cosmological parameters","work_id":"eeae0089-7b56-4c63-ace2-a31de468f6c5","ref_index":2,"cited_arxiv_id":"1807.06209","is_internal_anchor":true},{"doi":"10.3847/1538-4357/ab1422","year":2019,"title":"Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the De- termination of the Hubble Constant and Stronger Evi- dence for Physics beyond ΛCDM","work_id":"087325a7-4da4-4cf5-8830-e9bdc1b1615d","ref_index":3,"cited_arxiv_id":"1903.07603","is_internal_anchor":true},{"doi":"10.1103/physrevd.103.083533","year":2021,"title":"Physical Review D , author =","work_id":"09a332ec-9eba-4e16-987d-8d114ec8573d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1051/0004-6361/202039063","year":2021,"title":"2021, , 646, A140, 10.1051/0004-6361/202039063","work_id":"b42935af-fa9e-44a7-9251-bafa847cbeb1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":57,"snapshot_sha256":"0c928cc7f26d8db90bc2039d69582bba0763e8e1f29311f1751e37fb38574778","internal_anchors":21},"formal_canon":{"evidence_count":2,"snapshot_sha256":"35a3df27be724babb24fe7b1d7e55ac2a34e740970dc67a98223771dcdc248fd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}