Informational Scalar-Tensor Gravity (ISTG): A Covariant EFT Framework with Weak-Field Phenomenology

The idea that gravity may emerge from underlying quantum informational or thermodynamic principles has attracted significant attention in recent decades Jacobson1995, Verlinde2011. In these approaches, spacetime dynamics are not fundamental, but arise from coarse-grained degrees of freedom associated with entropy, entanglement, or holographic bounds. Despite these conceptual advances, a major challenge remains: the construction of a consistent, covariant field-theoretic framework capable of reproducing known gravitational physics while allowing for controlled deviations in appropriate regimes. Many emergent gravity proposals lack a well-defined variational principle or cannot be embedded into an effective field theory (EFT) satisfying observational constraints, particularly those arising from Solar System tests and gravitational wave propagation. In this work, we introduce Informational Scalar-Tensor Gravity (ISTG), a covariant scalar-tensor framework in which gravitational dynamics are coupled to an effective informational scalar field N (x). This field is interpreted as a dimensionless measure of the local saturation of an informational bound, admitting both a quantum formulation in terms of renormalized entanglement entropy and a thermodynamic interpretation in terms of normalized physical negentropy. The theory is formulated within a restricted subclass of Horndeski models, ensuring second-order field equations and luminal propagation of gravitational waves. Within this setting, ISTG can be consistently interpreted as an effective field theory valid below a cutoff scale, in which the informational sector provides a dynamical correction to standard gravitational interactions. At the phenomenological level, we analyze the weak-field limit of the theory and show that it admits modified gravitational dynamics through an additional scalar contribution to the Poisson equation. Under a suitable scaling regime—introduced here at a phenomenological level—the framework can reproduce MOND-like behavior with an emergent acceleration scale potentially linked to the cosmological background. We emphasize that this regime is not derived from first principles in the present work, but serves as an indication of possible non-linear dynamics of the scalar sector. The paper is organized as follows. In Section 2 we define the informational scalar field N (x) from both operational and microscopic perspectives. In Section 3 we introduce the action and derive the field equations. Section 4 is devoted to consistency and stability conditions. In Section 5 we analyze the weak-field limit and discuss phenomenological implications. Section 6 addresses screening mechanisms and observational constraints. In Section 7 we clarify the domain of validity of the EFT, and Section 8 concludes.