Scale-Invariant Hierarchical Quantum Cosmology (SIHQC): A Rigorous Framework for Quantum Cosmology

This paper proposes a self-consistent and rigorous framework for quantum cosmology—Scale-Invariant Hierarchical Quantum Cosmology (SIHQC). Its core dynamical mechanism isenvironment-induced decoherence driven by energy flow. When the energy flow is zero, theUniverse as a closed quantum system resides in a pure coherent superposition state, where allmoments, spatial positions, and quantum branches coexist completely. When the energy flowexceeds the critical threshold, the decoherence process projects the Universe onto anobservable classical effective spacetime, naturally emerging a single "present", a single spatialposition, and a definite classical history.This framework postulates that the Universe originated from a scale-invariant hierarchicalquantum initial state with a strictly self-similar hierarchical structure. This state is rigorouslydefined via the inductive limit of Hilbert spaces, which completely circumvents the divergenceproblem caused by infinite tensor products in traditional quantum cosmology. Based on thetheory of open quantum systems and the mechanism of environment-induced decoherence,this paper systematically addresses fundamental issues in quantum cosmology, including thestructure of the initial singularity, the origin of the arrow of time, and the quantum-to-classicaltransition, using energy flow as the sole driving variable. It also discusses its implications for thedynamics of cosmic expansion.A universal and constant global decoherence threshold of the Universe ε0 = 1/τP exists in theframework, uniquely determined by the Planck time. The current temperature of the CosmicMicrowave Background (CMB) is a natural manifestation of this threshold in the low-energyUniverse, rather than an artificially input parameter. This model is fully compatible withstandard quantum mechanics, open system dynamics, thermodynamics, the classical limit ofgeneral relativity, and the ΛCDM cosmological model. It only introduces two free parametersconstrained by observations (the branch number and the hierarchy activation exponent ),and provides four physical inferences with clear falsifiability