Informational Scalar-Tensor Gravity: A Covariant Effective Field Theory for MOND Phenomenology

This work introduces Informational Scalar-Tensor Gravity (ISTG), a covariant effective field theory in which spacetime geometry is coupled to a dimensionless scalar field encoding the local informational state of the vacuum. The scalar field is defined in terms of renormalized entanglement entropy and interpreted as a measure of physical negentropy. The theory is formulated within a restricted Horndeski framework, ensuring second-order field equations and compatibility with the observed luminal propagation of gravitational waves. Stability conditions and consistency requirements are explicitly analyzed. In the weak-field regime, nonlinear scalar dynamics modify the gravitational potential. A central result of the model is the emergence of Modified Newtonian Dynamics (MOND) phenomenology as a scaling regime of the field equations. Both the MOND interpolating function and the characteristic acceleration scale a₀ ~ cH₀ arise dynamically from the theory, rather than being introduced phenomenologically. A screening mechanism ensures recovery of General Relativity in high-density environments, maintaining compatibility with local gravity tests. ISTG therefore provides a conceptually unified and testable alternative to dark matter at galactic scales, linking gravitational dynamics to the informational structure of spacetime.