3.2 The “Excess” Cosmic Radio Background: Raising the Floor Without Hidden Point Sources

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Terminology. We interpret the “excess diffuse radio floor” as Tensor Local Noise (TBN) produced when Generalized Unstable Particles (GUP) deconstruct or annihilate and inject energy into the medium. The spatial mean of Statistical Tensor Gravity (STG) provides a weak co-varying “terrain.” After these first mentions, we use the full terms only: Generalized Unstable Particles, Tensor Local Noise, Statistical Tensor Gravity, and Cosmic Microwave Background (CMB), thereafter Cosmic Microwave Background. We likewise write pulsar timing arrays (PTA) once, thereafter pulsar timing arrays.

I. Phenomenon and Puzzle

1. A surplus, floor-like layer.
2. After subtracting resolvable radio sources—galaxies, quasars, jets, supernova remnants—an all-sky residual remains systematically high, as if a broad underlay supports the map.
3. Smooth and broadband.
4. The floor is angularly smooth with weak small-scale grain; its spectrum is broadband and lineless, unlike a choir driven by one engine class.
5. Why “more tiny sources” fails.
   • The number–flux distribution needed to mimic the floor would add excessive small-scale power, contradicting observations.
   • The required source counts and evolution disagree with ultra-deep surveys.
6. Supplementary traits.
   • Strong isotropy, with only slight uplift in highly active environments.
   • Low net polarization, as unaligned phases cancel.
   • Temporal stability consistent with a long-term diffuse baseline.

Takeaway: the signal behaves like a truly diffuse base, not a pile of unseen point lights.

II. Physical Interpretation

1. Root picture: the “coming-and-going” of Generalized Unstable Particles.
2. In the Energy Sea, Generalized Unstable Particles are drawn out, live briefly, then deconstruct or annihilate. Each deconstruction releases a weak, broadband, low-coherence packet; individually tiny, collectively numerous.
3. Tensor Local Noise: stacking packets into a floor.
4. Myriad independent packets add statistically across space and time to form a diffuse, broadband, low-coherence floor—Tensor Local Noise. It naturally matches the excess:
   • Brighter yet not dazzling: the sum raises the floor without creating dense bright knots.
   • Smooth spectrum: irregular packets, not fixed transitions or a common metronome.
   • Strong isotropy: birth and death occur nearly everywhere and average uniformly over cosmic time.
   • Weak co-variance with structure: emission is not tied to a single oriented family; it only weakly follows the Statistical Tensor Gravity terrain.
5. Why radio is the most sensitive band.
6. Radio interferometers best integrate broadband, low-coherence power, accumulating many weak, distant packets into a measurable floor. At higher frequencies, dust and scattering more easily mask such sums.
7. Weak—but real—co-variance with Statistical Tensor Gravity.
8. Generalized Unstable Particle activity tracks mergers, jets, and strong shear. The mean Tensor Local Noise amplitude therefore undulates slightly with the Statistical Tensor Gravity terrain: mildly brighter in more active regions, yet smooth when averaged on large scales.
9. Balancing the ledgers: energy and image.
   • Energy: the brightness surplus is powered by continual injection during deconstruction or annihilation of Generalized Unstable Particles.
   • Image: the appearance is a raised, smooth, broadband, isotropic floor—Tensor Local Noise.
   • Conclusion: one side accounts for power, the other for what we see.
10. Expected details: spectrum, polarization, variability.
    • Spectrum: nearly smooth power law or gentle curvature, with small regional differences and no narrow lines.
    • Polarization: low net polarization from many uncorrelated contributors; mild rises only where shear aligns fields.
    • Variability: long-term stability, with faint delayed uplifts after major merger or jet events (the “noise-first” radiative side).

III. Testable Predictions and Cross-Checks

• P1 | Angular power-spectrum test.
• Prediction: small-scale power is well below unresolved point-source models; large scales show a smooth ramp.
• Check: compare deep-map CℓC_\ellCℓ​ with point-source extrapolations; smoother small scales favor Tensor Local Noise.
• P2 | Spectral smoothness test.
• Prediction: sky-averaged spectra are lineless and gently curved; spectral indices vary little across regions.
• Check: multi-band fits should prefer “smooth and gradual” over mixtures of narrow mechanisms.
• P3 | Weak co-variance with Statistical Tensor Gravity.
• Prediction: the diffuse floor shows a small positive cross-correlation with lensing ϕ/κ\phi/\kappaϕ/κ maps and cosmic shear.
• Check: cross-correlate with ϕ/κ\phi/\kappaϕ/κ and shear; a weak positive coefficient that strengthens in active zones matches expectations.
• P4 | Event sequencing: noise-first, pull-second.
• Prediction: along merger axes, shock fronts, and jet environments, a slight Tensor Local Noise uplift precedes a later deepening of Statistical Tensor Gravity.
• Check: multi-epoch monitoring to compare diffuse-radio changes with dynamical and lensing lags.
• P5 | Low net polarization.
• Prediction: all-sky net polarization stays low, rising slightly only in geometrically brightened edge stripes.
• Check: wide-field polarization maps should show “low–stable–edge-lift” as a triad.

IV. Contrast with Traditional Accounts

• Not “a hidden sea of tiny bulbs.”
• A pure sum of unresolved sources would over-grain the map and contradict deep number counts and realistic evolution.
• Not a single unified engine.
• A single mechanism usually leaves spectral lines or polarized fingerprints; here the broadband, lineless, low-polarization floor fits a superposition of countless irregular packets.
• One picture, many features.
• The same medium–statistical process explains brightness uplift, spectral smoothness, strong isotropy, weak granularity, and weak co-variance—more economical than patchwork fixes.

V. Modeling and Fitting (Operational Guide)

1. Steps.
   • Foreground cleaning: consistently remove Galactic synchrotron, free–free, dust, and ionospheric effects.
   • Two-component spatial model: an isotropic floor plus a template that weakly co-varies with the Statistical Tensor Gravity terrain.
   • Spectral priors: smooth power law or gentle curvature; forbid dominant narrow-line components.
   • Small-scale constraint: use the angular power spectrum to suppress point-source granularity and bound the unresolved tail.
   • Cross-checks: co-map and co-epoch with lensing ϕ/κ\phi/\kappaϕ/κ, cosmic shear, and merger samples to verify spatial–temporal coupling.
2. Quick-look diagnostics.
   • Is small-scale CℓC_\ellCℓ​ smoother than point-source extrapolations?
   • Are multi-band spectra smooth and gradual?
   • Is the cross-correlation weakly positive and stronger in active zones?
   • Is net polarization low, with only edge lifts?

VI. Analogy

Distant city traffic. You do not hear one engine; you hear the low rumble of countless cars. The noise floor rises, it is not piercing, and it is steady. The diffuse radio “excess” behaves the same way.

VII. Conclusions

• Physical cause: the “excess” radio background is best read as a raised diffuse floor from Tensor Local Noise, sourced by the long-term statistical sum of weak, broadband packets released during deconstruction or annihilation of Generalized Unstable Particles.
• Spatial relation: Tensor Local Noise weakly co-varies with the Statistical Tensor Gravity terrain—slightly higher in more active regions, yet smooth across the sky.
• Shift of question: not “how many unseen point sources remain,” but “what diffuse floor does the medium naturally build under continuous birth and death?”
• Consistent picture: together with Section 3.1 and 2.1–2.5, we close the same loop: during life, Generalized Unstable Particles pull the Sea (Statistical Tensor Gravity); at deconstruction, they add noise (Tensor Local Noise). Two faces, one origin, weak co-variance, and testable unity.