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.

Three results are established. First, the holographic boundary of CBT is temporal rather than spatial, resolving the well-known absence of a spatial boundary in de Sitter holography. Second, the de Sitter and AdS holographic structures are related by the Wick rotation L_dS = i × L_AdS, which exchanges the spatial and temporal directions of the boundary; both are real forms of the complex group 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.

The effective central charge is c_CBT = r_0 / N_eff = 36.9, where r_0 = ln G(0) = 1.63 is the squeezing parameter and N_eff = 0.044 is the number of unstable modes — a minimal holographic theory with a single dominant mode. The physical consequence is a four-level causal chain: quantum entanglement → emergent geometry → temporal dilation → apparent cosmic acceleration, all derived without additional parameters from α = 1/137 and the standard cosmological observables.