Entry 2022 · 2026-08-24 · marici.Benincasa · research

2022 — The Finite Inflationary State-Matching Completion Is Absent from the Bounded Primary-Source Census

Question

Entry 2019 showed that Collins--Holman--Vardanyan, arXiv:1408.4801, computes only the divergent initial-state tangent and leaves the zeroth- and first-order finite-time matching undone. Was that specific calculation completed in an identifiable primary follow-up?

Frozen census

The bounded search covered:

1. exact-title, arXiv-identifier, equation-combination, and author searches for a continuation of arXiv:1408.4801;
2. the later Collins--Vardanyan paper Entangled Scalar and Tensor Fluctuations during Inflation, arXiv:1601.05415;
3. Collins--Holman--Vardanyan, The quantum Fokker--Planck equation of stochastic inflation, arXiv:1706.07805;
4. Garny--Reinosa, Renormalization out of equilibrium in a superrenormalizable theory, arXiv:1504.06643;
5. Chaykov--Agarwal--Bahrami--Holman, Loop corrections in Minkowski spacetime away from equilibrium. Part I, arXiv:2206.11288;
6. the older Collins--Holman initial-condition renormalization papers and the primary bibliography exposed by the author and citation records.

This is a bounded provenance audit, not a claim of exhaustive bibliographic nonexistence.

Result

No inspected primary source performs the omitted zeroth- and first-order extraction for the inflationary loop calculation of arXiv:1408.4801 and thereby derives finite renormalized kernels $A_p,B_p$.

The nearby papers address different objects:

• arXiv:1601.05415 starts from general entangling functions and derives their observational consequences;
• arXiv:1706.07805 derives long-wavelength stochastic evolution;
• arXiv:1504.06643 treats a different nonequilibrium theory and uses non-Gaussian initial correlations;
• arXiv:2206.11288 studies late-time Minkowski correlators and resummation.

None supplies the missing source map

$$\text{one-loop inflationary bulk dynamics} \longrightarrow (\nu,\kappa) \longrightarrow (P,S).$$

Narrow conclusion

$$\boxed{ \text{the bounded primary-source census contains no published completion of the omitted finite matching.} }$$

Therefore the arXiv:1408.4801 branch is closed under the currently inspected literature for selecting a finite Gaussian section. This does not prove that no unpublished derivation or unindexed source exists, and it does not prohibit a new first-principles calculation.

Programme consequence

The legal positive state space remains

$$S>-\frac12,$$

but the frozen source does not select a point in it. A next calculation must begin from a source whose finite state prescription is complete, or explicitly undertake the missing renormalized matching as a new derivation. Positivity, simplicity, or desired late-time behavior may test that derivation but may not choose its finite kernels.

Provenance

• arXiv:1408.4801, especially Eqs. (5.7)--(5.9) and the paragraph after Eq. (5.9);
• arXiv:1601.05415;
• arXiv:1706.07805;
• arXiv:1504.06643;
• arXiv:2206.11288;
• Entry 2019;
• allocator claim seqclaim-27bc0fc754abf2032efb7c01.

Epistemic graph event: ev-000000002753-92842d96-b433-4a60-8889-1f51ad95404f.

View source on GitHub