{"paper":{"title":"Cosmological perturbations in the theory of gravity with non-minimal derivative coupling. I. Modes of perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In gravity with non-minimal derivative coupling, all cosmological perturbation modes including vectors amplify during the early quasi-de Sitter stage, unlike in standard Friedmann cosmology.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"R. I. Kamalitdinov, S. V. Sushkov","submitted_at":"2026-05-13T16:11:44Z","abstract_excerpt":"We consider perturbations in the isotropic and homogeneous cosmological model with the spatially flat Friedmann-Lemaitre-Robertson-Walker metric in the framework of the theory of gravity with non-minimal derivative coupling. The Lagrangian of the theory contains the coupling term $\\eta G^{\\mu\\nu}\\nabla_\\mu\\phi \\nabla_\\nu\\phi$ and represents the particular example of a general Horndeski Lagrangian, which results in second-order field equations. It is known that the non-minimal derivative coupling crucially changes scenarios of the Universe evolution on early times. In particular, the $\\eta$-ter"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that all modes, including vector ones, are amplified in the quasi-de Sitter (inflationary) stage, and such the behavior is cardinally distinct from that in Friedmann cosmology.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The non-minimal derivative coupling term dominates at early times and produces a primary quasi-de Sitter stage without fine-tuned potential; the background evolution is taken as given and the linear perturbation analysis assumes the validity of the second-order Horndeski equations throughout.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In gravity with non-minimal derivative coupling, scalar, vector, and tensor perturbation modes are all amplified during the early quasi-de Sitter stage, unlike in standard Friedmann cosmology.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In gravity with non-minimal derivative coupling, all cosmological perturbation modes including vectors amplify during the early quasi-de Sitter stage, unlike in standard Friedmann cosmology.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7f83205ea7dbf73bdab3956561afee9cb6471f65ec59198402062067d71ce27a"},"source":{"id":"2605.13732","kind":"arxiv","version":1},"verdict":{"id":"62b72d1e-acca-4bbc-a2f3-12c05d5f3a13","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:45:19.136975Z","strongest_claim":"We show that all modes, including vector ones, are amplified in the quasi-de Sitter (inflationary) stage, and such the behavior is cardinally distinct from that in Friedmann cosmology.","one_line_summary":"In gravity with non-minimal derivative coupling, scalar, vector, and tensor perturbation modes are all amplified during the early quasi-de Sitter stage, unlike in standard Friedmann cosmology.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The non-minimal derivative coupling term dominates at early times and produces a primary quasi-de Sitter stage without fine-tuned potential; the background evolution is taken as given and the linear perturbation analysis assumes the validity of the second-order Horndeski equations throughout.","pith_extraction_headline":"In gravity with non-minimal derivative coupling, all cosmological perturbation modes including vectors amplify during the early quasi-de Sitter stage, unlike in standard Friedmann cosmology."},"references":{"count":76,"sample":[{"doi":"","year":null,"title":"Scalar modes in the post-inflationary stage In this case one can neglect theη-terms in Eqs. (4.5)–(4.7). Then, the equation (4.7) gives that Φ = Ψ,(4.8) 7 and Eqs. (4.5), (4.6) reduce to 3H(Ψ′ +HΨ) +k","work_id":"353a0cfc-11cb-478c-864f-9f2b2d6976fc","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Scalar modes in the quasi-de Sitter (inflationary) stage First, let us rewrite Eq. (4.7) as follows (1−4πηa −2ϕ′2)Ψ−(1 + 4πηa −2ϕ′2)Φ = 8πηa −2ϕϕ′′δφ.(4.15) Taking into account that in the quasi-de Si","work_id":"c9e82bba-583c-4635-bea8-fc4751e06b4c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Results are presented graphically in Fig","work_id":"506b2198-a104-4167-9686-7afb6e3febb7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Tensor modes in the post-inflationary stage Neglecting theη-terms in Eq. (4.24) and substitutingH= 1/2τ, we obtain the following equation for tensor modes in the post-inflationary stage: h′′ + 1 τ h′ ","work_id":"9f29c72f-b6e9-4bdf-9109-27268fa3923b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"(4.24) the background expressions for a(τ), H(τ),ϕ(τ) given by Eq","work_id":"24663358-23d4-4e7f-92c7-5b4fd89f83b2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":76,"snapshot_sha256":"f3cb5514334773bd6ed5c1a3f2896e42fc9bd5e0ce5ae9aeeffef1daaf06c9b5","internal_anchors":4},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5fefd87db037f9db9492f9c9b4ca41ab42d57079a6dfa0bb028c00397228a891"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}