Emergent Gravity, Cosmological Constant, and Friedmann Dynamics from Discrete Network Entanglement in Granular Entropic Physics

This paper presents a thermodynamic and information-theoretic framework for emergent gravity based on a discrete network model of spacetime called Granular Entropic Physics (GEP). The fundamental degrees of freedom reside on network links with a Z2 gauge structure, and gravitational dynamics arise from their collective behavior. The central result is that Newton's gravitational constant G emerges from the entanglement entropy of boundary links, including edge mode contributions from relaxed Gauss constraints, yielding G proportional to the square of the fundamental lattice scale. The Planck length is not a fundamental input but an emergent quantity. Combining this entropy with the Clausius relation and local energy conservation derived from microscopic network dynamics, the Friedmann equation is obtained without assuming the Einstein field equations explicitly. The cosmological constant is shown to arise from holographic constraints and gravitational stability conditions at the largest scales, giving Lambda proportional to the square of the Hubble parameter, independent of ultraviolet details. The product Lambda times G is a scale-independent combined consequence of both derivations. Independently, integrating out microscopic network excitations generates an effective gravitational action of the Sakharov type, reproducing the Einstein-Hilbert structure in the infrared and confirming the G scaling through a second independent route. The Z2 gauge structure itself is shown to emerge dynamically from the transport term of the microscopic action via a cosine potential selecting two stable minima. The paper includes explicit statements of all assumptions, open problems, and limitations, and does not claim a complete microscopic derivation of gravity. An anticipated response to referee is included as an appendix.