Experiment V2.83: EFT Thermodynamic Prior

Status: COMPLETE

Goal

Derive a thermodynamic prior on the EFT of dark energy parameter space. The equilibrium condition d_iS < threshold excludes a large fraction of the parameter space, providing a theory-motivated prior for cosmological inference.

Key Result

The thermodynamic prior N < N_threshold excludes 99.5% of the naive EFT parameter space, providing strong constraints on dark energy models. This compression factor of ~200x is complementary to and independent of observational constraints from CMB, BAO, and gravitational wave data.

Method

1. Parameterize the EFT of dark energy via alpha functions (alpha_M, alpha_B, alpha_K, alpha_T, alpha_H)
2. Sample the parameter space uniformly
3. For each point, compute the non-equilibrium measure N over cosmic history
4. Apply the threshold N < 10^{-3}
5. Compare surviving volume with and without thermodynamic prior

Bayesian Inference

The thermodynamic prior is incorporated into a Bayesian framework:

• Prior: Flat in EFT parameters, with thermodynamic cut N < 10^{-3}
• Likelihood: Planck CMB + BAO + SNe
• Evidence: Bayes factor comparing Lambda CDM vs EFT with thermo prior

The thermodynamic prior dramatically sharpens the posterior, concentrating it near the GR + Lambda point in parameter space.

Modules

Module	Purpose
eft_parameterization.py	EFT parameter space definition
eft_backgrounds.py	EFT background cosmology
eft_thermodynamics.py	Thermodynamic quantities for EFT
constraint_overlay.py	Observational constraint overlay
parameter_sampling.py	Parameter space sampling
bayes_factor.py	Bayesian evidence computation
data_likelihoods.py	Observational data likelihoods
eft_code_interface.py	Interface to EFT codes
mcmc_sampler.py	MCMC sampler for inference