Emergent Spacetime Geometry from Condensate Entanglement: A de Sitter Realisation of the ER=EPR Conjecture

The ER=EPR conjecture — that spacetime geometry emerges from quantum entanglement — has been developed extensively in Anti-de Sitter (AdS) space, but its realisation in de Sitter (dS) space, the geometry of our own Universe, remains an open problem. We show that the Cosmological Braking Theory (CBT) provides a concrete, self-consistent realisation of this programme in de Sitter space through a temporal holographic boundary.

The quantum rebound surface z_c = 6.539 of the cosmological EM condensate plays the role of the holographic boundary: at this surface, the condensate is in a pure coherent state (S_vN = 0, D(z_c) = 1 exactly), and all holographic boundary conditions are simultaneously satisfied. For z < z_c, the tachyonic Jeans instability of the conformal field δΦ generates entangled pairs, producing a von Neumann entropy S_vN(z) = 2 ln G(z), where G(z) is the growth factor of δΦ. Numerically: G(0) = 5.09, S_vN(0) = 3.26, effective central charge c_CBT = 36.9.

Three results are established. First, the holographic boundary is temporal rather than spatial, resolving the absence of a spatial boundary in de Sitter holography. Second, the Wick rotation L_dS = i L_AdS maps the AdS spatial boundary to the CBT temporal boundary; both are real forms of SO(5,C). Third, CBT is a self-consistent hologram: the tachyonic squeezing that drives S_vN = 2 ln G is itself the geometric deformation of the bulk, making entanglement and geometry dual manifestations of the same dynamical object.

New in v2: The condition S_vN(z_c) = 0 is shown to derive the magnetic equipartition relation rho_B = Omega_m alpha rho_m (previously Postulate 1 of CBT, now Theorem 1), closing a self-consistent logical loop: ESG establishes the holographic boundary, which implies the pure coherent state, which implies the QED equipartition, which implies CBT, which implies ESG. The sole external input is alpha = 1/137.036. A growth factor formula G(0) = [(sqrt(105)+3)/(2*sqrt(105))] x (Omega_m alpha)^(-(sqrt(105)-3)/12) is derived analytically in the matter-dominated limit.