The Multiverse Hypothesis: Physics, Mathematics, and Cosmology

If space is infinite ($V \to \infty$) and matter is roughly uniformly distributed, then everything that can happen must happen. The observable universe has a radius of about $4.6 \times 10^{10}$ light-years, defined by the distance light has traveled since the Big Bang. Beyond this cosmological horizon, other identical or slightly different 'bubble' volumes must exist due to the limited arrangements of matter configurations .

Driven by the theory of chaotic eternal inflation. Space undergoes exponential expansion ($e^{Ht}$), but stops in certain regions while continuing in others. Each region where inflation stops becomes a distinct bubble universe. The physical constants (such as the mass of the electron $m_e$ or the fine-structure constant $\alpha$) can vary between bubbles because they are determined by different spontaneous symmetry-breaking events .

Based on the Many-Worlds Interpretation (MWI) of quantum mechanics proposed by Hugh Everett III. When a quantum measurement occurs, the global wave function $\Psi$ does not collapse. Instead, the universe splits into decoherent branches. Every possible outcome of a quantum measurement is realized in a separate branch of the quantum multiverse .

The ultimate multiverse hypothesis, proposed by Tegmark. It posits that mathematical existence is equivalent to physical existence. Any self-consistent mathematical structure corresponds to a physical universe. In this level, not only physical constants vary, but the fundamental equations of physics themselves (e.g., the Einstein field equations or Schrödinger's equation) do not apply, replaced by other mathematical structures .