Chapter 43: The Big Bang as Regime: Same Laws, Extreme Parameters

What is the Big Bang? Orthodox cosmology treats it as a singular event — a point of infinite density, infinite temperature, and zero volume — from which spacetime itself emerged. The singularity theorems of Penrose and Hawking guarantee that under mild energy conditions, a past-incomplete geodesic must exist: the universe “began” in a singularity. But a singularity is not a physical state. It is a signal that the theory has broken down. General relativity predicts its own failure.

In Category τ, the Big Bang is not a singularity and not a creation event. It is a regime — the pre-hadronic regime of the same τ-Einstein equation that governs the present epoch. The equation R^H = κ_τ · T does not change. The boundary characters that enter it take extreme values at early refinement depths, but the equation itself is regime-invariant.

The absence of a singularity follows from the profinite structure of τ¹. The base circle has a well-defined first element α_a = α₁: the beginning of the α-orbit is a legitimate structural point, not a limit or a blow-up. The “Planck epoch” is not an era of unknown physics but the first few α-ticks, where the boundary characters are close to their maximal values.