We present an effective scalar framework in which the observed low-acceleration anomalies of galaxies emerge from gravitational coherence rather than from particle dark matter halos. The theory combines a nonlinear kinetic sector with environmental screening, allowing local recovery of General Relativity while generating modified dynamics in diffuse galactic environments.
A characteristic acceleration scale naturally appears as
g_crit = cH0 / (4π²√3),
linking galactic phenomenology to cosmological expansion. In the weak-field, low-acceleration regime, the model yields the effective radial acceleration law
a = a_N + √(a_N g_crit),
which reproduces asymptotically the baryonic Tully-Fisher relation
v⁴ = G M_bar g_crit.
At high densities, thin-shell screening suppresses scalar forces and preserves Solar-System bounds. The framework therefore interpolates between screened local gravity and emergent large-scale galactic dynamics within a single effective description.
We discuss implications for galaxy rotation curves, gravitational lensing, cluster-scale offsets, and redshift evolution of the baryonic Tully-Fisher relation. The model provides a falsifiable alternative to particle dark matter scenarios based on emergent infrared gravitational physics.
The dynamical structure of disk galaxies continues to present one of the central open problems of modern astrophysics. Across a wide range of masses, morphologies, and surface brightnesses, observed rotation curves display systematic departures from the expectations of Newtonian gravity sourced solely by the visible baryonic component. In particular, many galaxies exhibit an extended velocity plateau at large radii, where standard Keplerian decline would predict (V \propto r^{-1/2}).
High-quality compilations such as the SPARC database have shown that these deviations are not random, but follow remarkably tight scaling relations linking baryonic matter and orbital dynamics. Among them, the baryonic Tully-Fisher relation (BTFR),
[V^4 \propto M_{\rm bar},]
suggests the existence of an acceleration scale governing the transition between Newtonian and non-Newtonian regimes.
Motivated by this empirical structure, we re-examine galactic rotation data from the perspective of regime separation. A characteristic flattening threshold appears near
[ g_{\rm crit} \approx 10^{-11}\ {\rm m\,s^{-2}}, ]
with broad stability across independent systems once inner baryon-dominated points and outer low-signal tails are treated separately. This scale lies close to the cosmological quantity (cH_0), suggesting that galactic dynamics may retain sensitivity to infrared properties of the expanding universe.
This observation motivates an alternative framework in which the low-acceleration behavior of galaxies is not produced by particle dark matter halos, but by an emergent modification of the effective gravitational response below a critical acceleration threshold. Rather than postulating a phenomenological interpolation law alone, we formulate a scalar effective theory capable of reproducing galactic anomalies while remaining screened in dense environments.
The resulting model combines three desirable properties:
(i) Newtonian recovery at high acceleration,
(ii) modified collective behavior at galactic scales, and
(iii) a cosmologically linked critical scale.
In this work we develop the theoretical structure of this framework, derive its galactic limit, recover the BTFR, discuss screening constraints, and present observationally testable consequences.