Communications in Mathematical Physics Non-local Backreaction from 5D Bulk-Brane Entanglement: Mathematical Foundations and Cosmological Implications

Source abstract

We present a rigorous mathematical derivation of non-local corrections to fourdimensional Einstein gravity arising from quantum entanglement between a 4D spacetime brane and a 5D Anti-de Sitter bulk, within the ER=EPR correspondence. Starting from the Schmidt decomposition of the bulk-brane pure state, we explicitly construct the integral kernel K(X,x) and prove its exponential decay in AdS_5. We demonstrate dynamical stability of the extra dimension via a Goldberger-Wise radion potential and prove a classical decoupling theorem showing exact recovery of General Relativity as M_5-> infinity. As a mathematical application, we show that the resulting modified growth law provides a consistent description of high-redshift structure formation and large-angle CMB anomalies. All derivations are performed at the level of mathematical rigor required for self-consistent gravitational theories.