Thermal cosmology tracks energy exchange; we introduce an algebra-resolved “record economy” for pair-labeled coherence loss and, in receptive fragment environments, distinguishable records. A cumulative depth for a chosen pointer algebra and alternative pair classifies scalar-sector dynamics into visible, mute, frozen, and monitored-frozen regions using m/H and Γfine/H. For axion-like particles (ALPs), the framework reproduces the Primakoff thermalization boundary, resolves the early-plasma decoherence kernel, and separates mean-field damping from macroscopically enhanced branch decoherence in cold condensates. At a QCD-like benchmark, opposite-phase branch visibility is highly protected electromagnetically, whereas coarse gravitational monitoring rapidly classicalizes parsec-scale density profiles across a surface-to-volume bracket. Two scalar-portal propositions show that monitored-frozen behavior is alternative-resolved: single-quantum monitoring is incompatible with freeze-out for an unprotected sub-Planckian scalar, whereas Hubble-scale dephasing of coarse field-value branches, derived from the finite-temperature noise kernel, remains compatible with it. The framework separates objective record formation, coherence loss without which-branch records, and observables that remain unread.
We develop a discrete model to study the effects of inhomogeneities on the redshift of photons propagating on cosmological scale. Inhomogeneities are modeled with independent discrete random variables at different positions along the propagation path, and the probability distribution of the cumulative effect on the redshift is computed using the moment generating function. We find that the dispersion of the distribution is proportional to the square root of the comoving distance. We then discuss what are the implications for the estimation of background cosmological parameters, giving some examples for quantities related to the luminosity distance.
