{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7Z4463W563L7Y6RTGUPVU2MMHF","short_pith_number":"pith:7Z4463W5","schema_version":"1.0","canonical_sha256":"fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed","source":{"kind":"arxiv","id":"2605.13732","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.13732","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-13T16:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"7d97e47246246ece37b7738ffa4f8e01e3f8a4ca5000e68b274dbf1d2c014613","abstract_canon_sha256":"e647f60ec100cc00f9dd05afa28755bf3a3aea8698cb19e9d5a201bd8f843979"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:16.551488Z","signature_b64":"ddSHQiYpfiVaMzUlgOW1bvhWmUPz1eT6GatTdQwxaJCR9g3qGGzxIgC1ZEFss11tYu/ROjFVVCIYuD5G2yy9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed","last_reissued_at":"2026-05-18T02:44:16.550897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:16.550897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.13732","created_at":"2026-05-18T02:44:16.550986+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13732v1","created_at":"2026-05-18T02:44:16.550986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13732","created_at":"2026-05-18T02:44:16.550986+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Z4463W563L7","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Z4463W563L7Y6RT","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Z4463W5","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF","json":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF.json","graph_json":"https://pith.science/api/pith-number/7Z4463W563L7Y6RTGUPVU2MMHF/graph.json","events_json":"https://pith.science/api/pith-number/7Z4463W563L7Y6RTGUPVU2MMHF/events.json","paper":"https://pith.science/paper/7Z4463W5"},"agent_actions":{"view_html":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF","download_json":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF.json","view_paper":"https://pith.science/paper/7Z4463W5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13732&json=true","fetch_graph":"https://pith.science/api/pith-number/7Z4463W563L7Y6RTGUPVU2MMHF/graph.json","fetch_events":"https://pith.science/api/pith-number/7Z4463W563L7Y6RTGUPVU2MMHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF/action/storage_attestation","attest_author":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF/action/author_attestation","sign_citation":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF/action/citation_signature","submit_replication":"https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF/action/replication_record"}},"created_at":"2026-05-18T02:44:16.550986+00:00","updated_at":"2026-05-18T02:44:16.550986+00:00"}