Geometry-information duality: Quantum entanglement contributions to gravitational dynamics

We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields, specifically through the entanglement entropy of quantum states. By establishing a correspondence between geometric invariants and informational measures, we introduce an informational stress–energy tensor T μ ν info , derived from quantum entanglement entropy, into Einstein’s field equations. This framework modifies spacetime geometry, particularly in regimes of strong gravitational fields, such as near black holes. Our approach provides explicit corrections to Newton’s constant G , incorporating entanglement entropy contributions from various quantum fields with explicit dependence on fundamental constants ħ , c , and k B , ensuring dimensional consistency. These corrections have implications for black hole thermodynamics, leading to entropy and temperature modifications, and extend to cosmology, influencing inflationary dynamics, Big Bang nucleosynthesis, and the nature of dark energy. Our findings suggest that quantum information fundamentally shapes spacetime structure, offering testable predictions in gravitational and cosmological phenomena and shedding new light on challenges in quantum gravity. • Introduces a duality between spacetime geometry and quantum information content. • Shows how entanglement entropy contributes to spacetime curvature. • Modifies Einstein’s equations using an informational stress–energy tensor. • Demonstrates effects on black hole thermodynamics and early universe cosmology. • Calculates quantum corrections to Newton’s constant from entanglement entropy.