Structural Foundations for an Entropic Field Theory of Gravity

Abstract We propose a field-theoretic framework in which the Bekenstein-Hawking entropy of spacetime geometry is promoted to a dynamical scalar field φ(x) = S(x)/k₂. This field couples to the Einstein-Hilbert action through a dimensionally consistent kinetic term controlled by a new constant Λₛ (entropy per unit length), and contributes a stress-energy source to the modified Einstein field equations. The framework reduces to general relativity in the limit of vanishing entropic field gradients and provides a candidate structure for quantum gravity via three legitimate decoherence mechanisms. Three falsifiable predictions are identified: (1) a short-range modification to Newtonian gravity scaling as (lₚ/r)⁴, (2) a modified Friedmann equation in the early universe with entropic corrections to the Hubble parameter, and (3) a decoherence rate for quantum systems proportional to ∇²S. Current experimental bounds do not exclude these predictions, and dedicated experiments at nanometer scales could test them. The framework remains incomplete in several respects: the potential V(φ) is unspecified, quantum renormalizability has not been established, and the relationship to string theory or loop quantum gravity is not yet determined. This work presents structural foundations for an entropic field theory of gravity, not a completed theory.