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First-Order Phase Transition

The Big Bang model describes the universe originating from an extremely hot, dense state undergoing a first-order phase transition, analogous to water freezing.
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The statement of the theorem

For a first-order phase transition involving a scalar field ϕ\phi, the dynamics are governed by the potential energy density V(ϕ)V(\phi). The transition occurs when the free energy functional F(ϕ)F(\phi) develops multiple minima. The transition rate Γ\Gamma is determined by the barrier height ΔV\Delta V and the vacuum expectation value ϕ0\phi_0. The transition proceeds via bubble nucleation, characterized by the action S3S_3: \ndΓdt=Ae−S3/ℏ\frac{d\Gamma}{dt} = A e^{-S_3/\hbar}where S3=1H4ΔV(ϕfalse)−1H2σS_3 = \frac{1}{H^4} \Delta V(\phi_{false}) - \frac{1}{H^2} \sigma, and σ\sigma is the bubble wall tension.