Spacetime Densification Theory and the Newtonian limit

Abstract We develop an effective scalar-field theory for a coherent spacetime substrate whose long-wavelength response reproduces Newtonian gravity. The substrate is represented at macroscopic scales by a scalar density field coupled universally to standard matter through an effective metric whose leading conformal sector generates the Newtonian limit and whose disformal sector defines higher-gradient viability constraints, . The microscopic equation of state of the substrate is taken from companion work and is not derived here. We obtain the linearized field equation for the density perturbation around a homogeneous background, identify a Poisson-like source law , and show that the gradient of the substrate density acts on matter through an effective force . The Newtonian limit is recovered exactly when the two response coefficients satisfy the calibration condition . A benchmark thermodynamic closure for maps these coefficients to substrate parameters, reducing the calibration to a constraint on one microscopic combination rather than an arbitrary split of . The tensorial Einstein–Hilbert sector is not derived, but imposed as an infrared matching condition required for relativistic consistency. We formulate the matching prescription that prevents double counting: the densification potential and the infrared Newtonian potential are identified as the same object, not additive. Disformal and higher-derivative corrections, together with post-Newtonian and multi-messenger constraints, are characterized as viability conditions on the effective parameter space rather than as derived predictions. No claims are made in this paper concerning post-Newtonian observables, gravitational waves, galactic phenomenology, or strong-field dynamics; these are deferred to companion work. Keywords: emergent gravity; effective field theory; disformal coupling; Newtonian limit; induced gravity; infrared matching; scalar–tensor theories.