Cosmology from Two Axioms 9; Information Potential Difference as the Order Parameter for Cosmological Phase Transitions

This paper, based on the two axioms of ”information conservation” and ”computability,” proposes the information potential difference ∆µ as the order parameter for cosmological phase transitions, used to unify the description of the evolutionary process from structureless failed universes, critical universes with emerging local structures, to completely self-referentially closed successful universes. Themagnitude of ∆µ determines whether the system can continuously drive structuralevolution, establish global causality, and form continuous mathematical structures.Within this framework, this paper derives the observable characteristics of threetypes of cosmic states, including the delay time of gravitational wave echoes, thesign and amplitude of CMB non-Gaussianity, and the cutoff behavior of the largescale structure power spectrum. These predictions are compatible with existingcosmological observations (e.g., Planck, LIGO-Virgo) and can be tested within 5years by next-generation observational facilities (e.g., Einstein Telescope, CMB-S4,SKA).