Doubly logarithmic corrections to radiation domination from CET Ω: Theory and Planck/BBN constraints

We present the CET Ω framework, a causal-informational extension of standard cosmology that predicts a universal doubly logarithmic correction to the radiation energy density in the early Universe: ρ Ω ( a ) = ρ r ( a ) [ 1 + α log log log ( a / a i ) ] . This correction arises naturally from scale-invariant spectral sectors with logarithmically-running infrared scales and represents a low-energy manifestation of the full CET Ω 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 ΛCDM parameters and α log , using Planck 2018 TT,TE,EE+lowE likelihoods and BBN constraints. The result, α log = − 0.008 ± 0.006 (68% C.L.), is consistent with zero. We identify the expected N eff degeneracies with H 0 and n s , establish the first observational bound | α log | ≲ 0.006, and demonstrate that future CMB-S4 measurements can probe | α log | ∼ 10 − 3 .