False Vacuum Decay as Dynamical Conformal Degeneration: Attractor Dynamics and CCC Application

We study the late-time dynamics of scalar fields inside Coleman-De Luccia bubble interiors with degenerate terminal minima. In an expanding background the scalar energy decreases monotonically, and the field relaxes dissipatively toward the terminal minimum. For k>=3 the interior evolution approaches a universal scaling regime where curvature invariants decay rapidly and the field settles through attractor dynamics. This regime is selected by the stability of the dominant-balance fixed point. At k=2 the picture changes: the fixed point is non-hyperbolic, logarithmic oscillations develop, and the conformal factor acquires corrections that suggest an obstruction to smooth boundary regularity. Near the crossover the conformal geometry simplifies considerably. Regularity selects a linear relation between the conformal factor and the scalar potential, and the result is a multi-step relaxation mechanism, a possible dynamical trigger for the type of conformal crossover discussed in conformal cyclic cosmology. Bubble wall collisions acquire a modulation set by k. Candidate signatures have been reported in CMB data; numerical simulations in full general relativity show that collision outcomes depend sensitively on the scalar potential. Existing templates assume exponential wall profiles. The algebraic decay delta_phi ~ tau^{-1/(k-1)} produces a k-dependent power-law structure instead. No existing template search covers this regime.