Doubly Logarithmic Corrections to Radiation Domination from CET {\Omega}: Theory and Planck/BBN Constraints

Abstract

We present the CET Omega framework, a causal-informational extension of standard cosmology that predicts a universal doubly logarithmic correction to the radiation energy density in the early Universe. This correction arises naturally from scale-invariant spectral sectors with logarithmically-running infrared scales and represents a low-energy manifestation of the full CET Omega theory. We derive the doubly logarithmic form from two complementary perspectives -- spectral integration and renormalization group flow -- and perform a full Markov Chain Monte Carlo analysis jointly varying six LambdaCDM parameters and alpha_log, using Planck 2018 TT, TE, EE + lowE likelihoods and BBN constraints. The result, alpha_log = -0.008 +/- 0.006 (68\% C.L.), is consistent with zero. We identify the expected N_eff degeneracies with H0 and n_s, establish the first observational bound |alpha_log| <= 0.006, and demonstrate that future CMB-S4 measurements can probe |alpha_log| ~ 10^{-3}.