The Cosmic Flow-Gradient Field 

A Falsifiable Field Hypothesis for Residual Peculiar Velocities in the Great Attractor Region

The Great Attractor was originally introduced to explain coherent galaxy motions that could not be described by simple cosmic expansion. Over time, observations revealed substantial conventional structure in this region, including the Norma cluster, large galaxy walls, voids, and the influence of more distant structures such as Shapley. Modern peculiar-velocity reconstructions now describe the local Universe as a network of interacting flow basins rather than as matter falling toward a single hidden object.

This paper asks a more specific question: after the strongest available conventional reconstruction of the matter distribution and gravitational flow is applied, does a reproducible component of galaxy motion remain?

To address that question, the paper introduces the Cosmic Flow-Gradient (CFG) field as a new falsifiable phenomenological field hypothesis.

The CFG field is proposed as an additional peculiar-velocity vector field associated with the geometry of large-scale cosmic flow gradients rather than with matter density alone. The hypothesis predicts that the field becomes most observable near basin separatrices—the boundaries between neighboring regions whose matter flows toward different large-scale gravitational destinations.

Its primary mathematical form is \[ \mathbf v_{\mathrm{CFG}}(\mathbf x) = \beta H_0\ell_B g_B(\mathbf x) \mathbf\Sigma_0(\mathbf x)\mathbf n_B(\mathbf x), \]

where \(\beta\) is a dimensionless coupling coefficient, \(H_0\ell_B\) establishes the velocity scale, \(g_B\) localizes the field near a basin boundary, \(\mathbf\Sigma_0\) represents the independently reconstructed velocity-shear geometry, and \(\mathbf n_B\) gives the oriented boundary direction. The null hypothesis is \(\beta=0\).

The proposal therefore predicts more than an unexplained residual near the Great Attractor. It predicts where the additional motion should occur, the direction it should follow, how its strength should depend on local flow geometry, and where it should disappear.

The test architecture compares four possibilities: conventional cosmology alone; a generic spatial residual; a simple boundary-proximity effect; and the full directional CFG field. Testing requires independent density and peculiar-velocity data, spatially blocked hold-out analysis, realistic ΛCDM mock universes, false-boundary controls, Zone-of-Avoidance tests, injection-recovery sensitivity analysis, and independent replication.

No detection of the CFG field is claimed. If conventional reconstruction removes the residual, if the predicted directional relationship is absent, or if simpler models explain the data equally well, the hypothesis fails. If standard ΛCDM simulations reproduce the same effect, the CFG relation may represent an effective description of conventional nonlinear dynamics rather than new physics.

Only a reproducible field signature that survives those tests would justify investigation of genuinely missing dynamics.