AGL-EFT and Cosmic Void Peculiar Velocities: A Matched-Filter Analysis with CosmicFlows-4 and VAST

We present the rst application of the Adiabatic Geometric Leveling eective eld theory(AGL-EFT) to cosmic void peculiar velocities. The AGL-EFT predicts that the axion-like condensate, which accumulates preferentially in underdense regions, amplies the radialoutow velocity of void galaxies by a factor μeff (z, Q0, n) = 1 + 2nQ0/(3ΩM ) · an+3 relativeto the ΛCDM prediction. Using the VoidFinder catalog of 817 voids from the SDSS NSAsurvey [6] (VAST; z ∈ [0.006, 0.076], Rv ∈ [14, 32] Mpc) and the CosmicFlows-4 reconstructedvelocity eld on a 643 grid of 1000 Mpc/h [8, 7], we apply a radial matched lter to measurethe amplitude Aopt = μeff at zmed = 0.057. We obtain Aopt = −0.0053 ± 0.0026 (SNR=−2.0), consistent with zero and incompatible with both ΛCDM (A = 1) and AGL-EFT(A = μeff > 1). We show that this null result is a resolution artefact: the grid cell size ofthe CosmicFlows-4 eld (22.3 Mpc/cell) is larger than the typical void radius (17.5 Mpc),causing the outow signal to be smoothed below the detection threshold. We derive theresolution criterion ∆x < Rv /3 ≈ 6 Mpc as the requirement for a direct measurement ofμeff from void peculiar velocities. This work establishes the methodology and identies theobservational requirement for Paper VI, which will apply the matched lter to individualCF4 group velocities.