Pith Number

pith:7Z4463W5

pith:2026:7Z4463W563L7Y6RTGUPVU2MMHF

not attested not anchored not stored refs resolved

Cosmological perturbations in the theory of gravity with non-minimal derivative coupling. I. Modes of perturbations

R. I. Kamalitdinov, S. V. Sushkov

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.

arxiv:2605.13732 v1 · 2026-05-13 · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Z4463W563L7Y6RTGUPVU2MMHF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

76 extracted · 76 resolved · 4 Pith anchors

[1] 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

[2] 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

[3] Results are presented graphically in Fig

[4] 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′

[5] (4.24) the background expressions for a(τ), H(τ),ϕ(τ) given by Eq

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:16.550897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed

Aliases

arxiv: 2605.13732 · arxiv_version: 2605.13732v1 · doi: 10.48550/arxiv.2605.13732 · pith_short_12: 7Z4463W563L7 · pith_short_16: 7Z4463W563L7Y6RT · pith_short_8: 7Z4463W5

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7Z4463W563L7Y6RTGUPVU2MMHF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fe79cf6eddf6d7fc7a33351f5a698c3961ce5150675efb0a7f1b6b9ea30262ed

Canonical record JSON

{
  "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
  }
}