Precision Cosmology Validation of the Entropic No-Boundary Hypothesis: CMB Distance Priors, BAO, Supernovae, Growth, and Lensing Consistency

This work extends the empirical validation program of the Entropic No-Boundary (ENB) hypothesis (Whittaker, 2026) beyond galaxy-scale rotation-curve fits and background-growth consistency checks, into the regime of precision cosmology likelihood blocks. We test ENB against a set of standard compressed probes used in concordance-model inference: Planck 2018 CMB distance priors, BAO distance measurements (compressed and anisotropic), the Pantheon Type Ia supernova compilation with full systematic covariance and analytic marginalization over the absolute magnitude nuisance parameter, redshift-space distortion growth constraints via fσ8(z), and a compressed Planck lensing amplitude consistency check. The analysis compares ENB directly with flat ΛCDM using the same numerical integration machinery for distances, sound horizon calibration and linear growth in GR. We report χ² values per likelihood block and identify the parameter-space tensions that emerge when simultaneously satisfying CMB priors, BAO, and supernova distances. While ENB can match subsets of precision probes competitively, the combined compressed precision dataset shows near-degenerate likelihoods between ΛCDM and ENB, with a small Δχ² difference well below statistical significance.