RLMT: Reading the Primordial Fossils of RLMT-lite: Spectral Shape with ACT DR6, Non-Gaussianity, and the Tensor-to-Scalar Ratio

Abstract

RLMT-lite is the phenomenological form of R-layer Mode Theory (RLMT) for the primordial curvature spectrum: a softmax mixture of three modes, P(k) = Σ_n w_n(k) P_n(k), whose weights follow from an SU(2) mode map. We ask what the three observable "fossils" of the early universe (the shape of the scalar spectrum, its non-Gaussianity, and the tensor-to-scalar ratio r) can say about it today. (1) Shape. With Planck 2018 low-ℓ TT and EE (SRoll2), the Planck high-ℓ spectra restricted to the range that complements ACT, and the ACT DR6 CMB-only likelihood, a two-pass minimizer gives Δχ² = −3.6 for RLMT-lite relative to ΛCDM with seven extra parameters, i.e. ΔAIC = +10.4. The small gain comes from the high-ℓ Planck and ACT likelihoods and is partly cancelled by low-ℓ TT. Over the ACT range the best-fit spectrum has the same mean tilt as ΛCDM (0.9719 vs 0.9716), with a sub-percent running; the data do not call for the mode mixture. H0 does not rise. (2) Non-Gaussianity. Under either reading of the mixture (a sum of independent Gaussian modes, or a stochastic selection of one mode) the bispectrum vanishes, f_NL = 0. Selection leaves an excess kurtosis that raises the variance of C_ℓ by at most a few per cent of cosmic variance for ℓ ≳ 14 and by at most 9% at the quadrupole, far below what a single sky can detect. (3) Tensors. The most direct reading of the SU(2) scale factor as a horizon-exit map gives a blue tensor spectrum with n_t → 2 but violates the null energy condition with Ḣ/H² = (k/k*)², beyond any known stable violation; we reject it. RLMT therefore makes no prediction for r at present. We conclude that current fossil data neither exclude nor support RLMT-lite, and state what the theory must supply before they can: parameters fixed by the Lindblad dynamics, the dynamics that produces ζ from the three modes, and a stable expansion law for cosmogenesis. Code to reproduce all tables is included. A Japanese translation of the paper is included.