eokahya / claude-audits-quantum-gravity

# Claude Audits Quantum Gravity
*An AI re-derived a published one-loop quantum gravity calculation step by step. It found a sign error and a missing term, and confirmed the physical conclusion.*
> **The paper:** E. O. Kahya, *Auditing a quantum gravity calculation with an AI model: corrected scalar self-mass and
> unchanged late-time mode functions during inflation* (submitted to arXiv, 2026). PDF ·
> LaTeX source
This repository re-derives, step by step, a published one-loop quantum gravity calculation during inflation:
the graviton correction to a massless, minimally coupled scalar on de Sitter space
(Paper I, Phys. Rev. D 76, 124005 (2007)), and its use in the scalar's late-time field equation
(Paper II, arXiv:0710.5282). The re-derivation was carried out with Claude (Anthropic's AI model,
Claude Opus 5.5) as a checking tool. It was published by E. O. Kahya, one of the authors of both papers.
Each step, from the Feynman rules (I.6)–(I.8) to the renormalized self-mass (I.167) and the late-time analysis of Paper II,
was derived again from the inputs stated in the papers, keeping the dimension $`D`$ general wherever the paper does, and
cross-checked with independent SymPy/mpmath code. (The bookkeeping tables of Paper I's appendix were audited rather than
redone; see Limitations.) Every difference from the printed papers is classified: **4 substantive
findings (S1–S4), 6 finite errors absorbed into counterterms (B1–B6) and 23 typographical errors (C1–C23)**. The
complete list of findings gives each one with its evidence.
**Bottom line:** the main physical conclusion of Paper II survives. The scalar's mode function receives no significant
one-loop correction at late times. However, the printed self-mass-squared is $`-1`$ times the one defined by Paper I's own
(I.168) (the 4-point and 3-point parts are both reversed, so their relative sign is consistent), and two entries of its
final table, Table X, need correcting.
**Contents:**
The question ·
What was done ·
Main results ·
Read it in order ·
The paper ·
Complete list of findings ·
Full derivations ·
Reproduce the checks ·
How Claude was used ·
Papers ·
Citation
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## The question in one picture
 [code] 
Inflation pulls long-wavelength quanta of massless fields that are not conformally invariant out of the vacuum.
Gravitons are such fields, so as inflation goes on the universe fills with an ever-growing sea of infrared gravitons.
The question is whether this sea changes how a massless, minimally coupled scalar (a stand-in for a very flat inflaton)
propagates. All quantum corrections at one loop are contained in the scalar self-mass-squared $`M^2(x;x')`$, which enters
the linearized effective field equation (Paper I, Eq. (I.168)):
 [code] 
At tree level the plane-wave mode function freezes to a constant once the mode has left the horizon:
 [code] 
Write $`M^2=\kappa^2M^2_1+O(\kappa^4)`$ and $`\Phi=u+\kappa^2\Phi_1`$, with $`\kappa^2=16\pi G`$; $`\Phi_1`$ is sourced by
$`M^2_1`$, so $`\kappa^2`$ is