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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","authors_text":"R. I. Kamalitdinov, S. V. Sushkov","cross_cats":[],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-13T16:11:44Z","title":"Cosmological perturbations in the theory of gravity with non-minimal derivative coupling. I. Modes of perturbations"},"references":{"count":76,"internal_anchors":4,"resolved_work":76,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"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","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"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","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Results are presented graphically in Fig","work_id":"506b2198-a104-4167-9686-7afb6e3febb7","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"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","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"(4.24) the background expressions for a(τ), H(τ),ϕ(τ) given by Eq","work_id":"24663358-23d4-4e7f-92c7-5b4fd89f83b2","year":null}],"snapshot_sha256":"f3cb5514334773bd6ed5c1a3f2896e42fc9bd5e0ce5ae9aeeffef1daaf06c9b5"},"source":{"id":"2605.13732","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T17:45:19.136975Z","id":"62b72d1e-acca-4bbc-a2f3-12c05d5f3a13","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"62b72d1e-acca-4bbc-a2f3-12c05d5f3a13"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f04f8f9c381d7bb8fb0f583dbfa8e7cea0f4fc073a9c80da69553665b7c6e5d","target":"record","created_at":"2026-05-18T02:44:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e647f60ec100cc00f9dd05afa28755bf3a3aea8698cb19e9d5a201bd8f843979","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-13T16:11:44Z","title_canon_sha256":"7d97e47246246ece37b7738ffa4f8e01e3f8a4ca5000e68b274dbf1d2c014613"},"schema_version":"1.0","source":{"id":"2605.13732","kind":"arxiv","version":1}},"canonical_sha256":"fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed","first_computed_at":"2026-05-18T02:44:16.550897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:16.550897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ddSHQiYpfiVaMzUlgOW1bvhWmUPz1eT6GatTdQwxaJCR9g3qGGzxIgC1ZEFss11tYu/ROjFVVCIYuD5G2yy9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:16.551488Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f04f8f9c381d7bb8fb0f583dbfa8e7cea0f4fc073a9c80da69553665b7c6e5d","sha256:5ce2ba31bf1aeeeac2eb52bde913a02b5ae63fa0d284489b66eb120368174aa1"],"state_sha256":"7e1a41d9992bdac9d6356d09573ede6bd5b879667ee39e27cfe9384af9c10a32"}