The_Formation_Mechanism_of_the_Cosmic_Singularity_Bang

This paper recasts the “big bang singularity” from the beginning of time into a saturation phase transition of apressure field, and gives a closed mechanism with a single dynamical variable and no new fields. Exactly onedynamical assumption is added: the gravitational response to energy saturates at a critical density, ρeff= ρ(1 − ρ/ρc),which is the mathematical form of “when things reach an extreme, they reverse”. Four results follow rigorously.First, as ρ → ρc, H = 0 while Ḣ = 4πG(ρ+P) > 0: the bounce is inevitable and requires no exotic matter. Second, theeffective fluid at the bounce satisfies ρeff+ Peff= −(ρ+P) < 0, so the effective null energy condition is violated whilethe primordial matter still satisfies ρ + P > 0; the premises of HawkingPenrosetype theorems therefore fail in thebounce neighbourhood, and the curvature singularity is replaced by a turning point of finite density. Third, in termsof the effective scale factor Aeff≡ √n·a (eq. 7), the solution near the bounce is Aeff/Aeff,b= 1 + 4πGρc(t−tb)2(for w =1): the geometry is C2, and the energy density is bounded, ρ ≤ ρc. Fourth, the interface current J = −3HPV sendsenergy from the yang sheet to the yin sheet during expansion, back during contraction, and vanishes and reverses atthe bounce, while the total energy E++ E−= 0 holds identically. This is the mathematical content of the “Taijiballenergy cycle”, and the bookkeeping reading of “a universe out of nothing”. Observationally, ρ/ρc≈ 4×10−88at BBN,so the model is numerically identical to ΛCDM over the entire observed thermal history; its fate depends only onthe primordial perturbations left by the prebounce contracting phase. Seven criteria, the current data position, andfour explicitly open items are given.