Experiment V2.85: KMS Equilibrium from Adiabatic FRW

Status: COMPLETE

Goal

Show that standard QFT in curved spacetime (adiabatic vacuum) produces near-thermal horizons, establishing consistency with the equilibrium framework. Quantify the KMS deviation epsilon_KMS and derive the implied bound on N.

Key Results

Background	epsilon_KMS (a=1)	epsilon_KMS (avg)
de Sitter	~0	~0
LCDM	1.34e-02	3.54e-02
Non-adiabatic	Large	Large

• QFT-derived N bound: N <= 8.16e-02
• QFT consistency: YES (horizons are near-thermal)

The Chain of Logic

Standard QFT + Adiabatic Vacuum
            |
Near-KMS Thermal Horizons (epsilon_KMS ~ 10^{-2})
            |
Near-Clausius: delta_Q ~ T dS
            |
Bounded d_iS: |d_iS| <= epsilon_KMS |dS|
            |
QFT bound: N <= 0.1   <-- This experiment

+ Holographic/observational constraints
            |
Full bound: N <= 10^{-3}   <-- Requires additional arguments

Part A: KMS Deviation Measures

Defined two complementary measures of KMS deviation:

1. Wightman-function KMS deviation (theoretical)
2. Detector-response thermal deviation (operational)

Part B: Analytic Adiabatic Estimates

Derived the scaling relation: epsilon_KMS ~ O(|H_dot|/H^2, |H_dotdot|/H^3)

For slowly varying H(t):

• LCDM: epsilon_KMS << 1
• de Sitter: epsilon_KMS = 0 exactly
• Non-adiabatic: epsilon_KMS ~ O(1)

Part C: Unruh-DeWitt Detector Numerics

For LCDM:

• epsilon_KMS (max) = 4.24e-02
• epsilon_KMS (mean) = 2.86e-02

Part D: Connection to d_iS and N Bound

Established the key relation:

|d_iS| <= C_1 * epsilon_KMS * |dS_geo|
N <= C_1 * integral(epsilon_KMS(a) d ln a)

Background	epsilon_KMS (avg)	N_bound	Threshold?
de Sitter	~0	~0	PASS
LCDM	3.54e-02	8.16e-02	PASS
Non-adiabatic	Large	Large	FAIL (expected)

Important Caveat

QFT alone gives N <= 0.1, not N <= 10^{-3}. The tighter threshold comes from:

1. Holographic arguments (V2.82 Part B): d_iS < 0.1% of horizon entropy
2. Observational constraints (V2.79): Planck CMB constrains GR departures
3. Jacobson’s derivation: horizons must be near-equilibrium for gravity to emerge

Modules

Module	Purpose
adiabatic_modes.py	Adiabatic mode functions
frw_backgrounds.py	FRW background cosmologies
kms_diagnostics.py	KMS deviation diagnostics
thermo_bridge.py	Bridge to thermodynamic framework
udw_detector.py	Unruh-DeWitt detector response