Line-of-Sight Integrated Radio Emission in Underdense Regions: A Multi-Scale Test of a Density-Dependent Scalar Field Model

We present a multi-scale observational analysis of radio residuals in underdense cosmic environments using NVSS (1.4 GHz) and LoTSS DR2 (144 MHz) data. Main Results NVSS stacking and individual sightline tests reveal a suggestive environmental hierarchy: positive radio excesses are strongest and most consistent in the cleanest underdense regions (cosmic voids and South Galactic Pole) and are suppressed in high-density environments (galaxy clusters). In contrast, a rigorous Monte Carlo analysis of LoTSS DR2 residuals in the Boötes and Lockman Hole deep fields yields a clean null detection, with negligible effect sizes and distributions statistically indistinguishable from background controls. This GHz–MHz spectral tension is the central observational finding of the work.