14 Corroborating “Path Redshift” in the Cosmic Microwave Background Cold Spot: Frequency-Shift Bias of Background Sources

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. For general readers: the Cosmic Microwave Background (CMB) “Cold Spot” is a sky region with an unusually low CMB temperature. We use background sources seen through this corridor to test whether their spectral features show band-insensitive shifts consistent with a path redshift, rather than with foregrounds or pipelines.

I. One-Sentence Goal

Center the analysis on the CMB Cold Spot and perform an environment-forward test using background objects along its line of sight (for example, quasars, absorption systems, molecular-line galaxies). After unified de-motion and frequency referencing, compare the relative zero-point offsets of lines or narrow features between the Cold-Spot corridor and matched control regions. The claim is supported if the offsets in the corridor are same-direction, band-insensitive (non-dispersive), monotonic with environment strength (for example, Cold-Spot temperature drop, void–filament metrics, external convergence), and reproducible across institutions/pipelines. If foregrounds, pipelines, or selection explain the offsets—or no environmental link appears—the claim is disfavored.

II. What to Measure

• Relative zero-point offset (text interval): After removing observer/antenna motion, known medium dispersion, and instrumental chains, measure for each background source the residual shift of representative line families (molecular rotational ladders; atomic fine/hyperfine; narrow/maser lines; narrow absorbers) relative to source-internal references (see Chapter 3) or population baselines. Grade strength (strong/medium/weak) and direction (uplift/depression).
• Cross-band consistency: Check whether direction and rank order of the offset agree across radio/millimeter/optical–near-infrared for the same object/patch. Within each object, verify the “rigid shift with ratio invariance” of same-source multilin es to separate source/pipeline terms.
• Spatial gradient and annular profile: Define concentric annuli centered on the Cold Spot (core–inner ring–outer ring). Compare offset amplitude and direction by annulus and test for the pre-registered monotonic profile (for example, core > inner ring > outer ring). Use lat/long/coverage-matched control annuli in parallel.
• Environment linkage: Summarize correlations (plain language) between offsets and CMB temperature decrement, weak-lensing convergence (κ), void/filament metrics, distance to nodes, and other environment proxies; report their rank ordering.
• Frequency independence (non-dispersion): Offsets must not flip with band or rescale with wavelength; λ² or 1/ν-type behaviors are attributed to medium/pipeline and excluded from path-redshift evidence.

III. How to Do It

1. Sky tiling and samples:
   • Tiling: Build a Cold-Spot-centered mosaic with core + two outer rings, each matched to a control ring for latitude, foreground brightness, and survey strategy.
   • Background sources: Prefer targets with multi-line and multi-band coverage: high-z quasars (broad/narrow lines), molecular-line galaxies (CO ladders plus fine/hyperfine), quasar absorption systems (multi-ion/isotopologue), and bright narrow-line masers.
2. Environment templates and forward predictions:
   • Construct a two-layer template: a line-of-sight layer (CMB drop, κ, void–filament–node skeleton and node distance) and a neighborhood layer (local group/cluster context).
   • The environment team, without spectra, issues prediction cards: per annulus, state direction, strength tier, and spatial ordering (for example, core > inner ring > outer ring), with no access to measurements.
3. Acquisition and processing (blinded and independently reproduced):
   • Unified line list and referencing: Use a common line catalog across radio/millimeter/optical–near-infrared and an absolute frequency/time reference. Independent institutions perform de-motion and chain calibration without sharing code/parameters.
   • Same-source multi-line calibration: Within each source, test “rigid shift, ratio-invariant” behavior and treat any common offset as the path candidate.
   • Arbitration: A third party aligns prediction cards with measured offsets under pre-registered rules, computing hit/wrong/null rates and stratifying by core–outer rings–controls and environment grade.
4. Control designs:
   • Rotation test: Randomly rotate the Cold-Spot annuli to latitude-matched longitudes to test for spurious “hits.”
   • Foreground-equivalent controls: Repeat the analysis in regions matched for dust/synchrotron/free–free levels to remove Galactic coupling.
   • Survey-strategy controls: Re-run in areas with similar scan coverage and noise floors to avoid strategy-induced zero-point bias.

IV. Positive/Negative Controls and Removal of Artifacts

1. Positive controls:
   • Background sources in the core/inner ring show same-sign zero-point offsets larger than in outer/control rings, with monotonic growth versus environment proxies.
   • Offsets are direction-consistent across bands and, within sources, appear as a common shift with line-ratio invariance.
   • Results replicate across institutions/pipelines, and the annular profile matches the prediction cards.
2. Negative controls:
   • Rotating the annulus template or shuffling environment labels drives hit rates toward chance.
   • Foreground/scan-strategy surrogate templates that reproduce the signal identify foreground/strategy coupling, not path redshift.
   • Intra-band sub-channels that follow λ²/1/ν laws, or signals confined to one band or one pipeline, are excluded.

V. Systematics and Safeguards (Three Items)

• Galactic foregrounds and atmospheric/local-oscillator residues: Dust lanes, airglow, and LO image lines can shift centroids. Safeguard: parallel foreground solutions, strong masks and sky-reference subtraction; dual references/dual chains with LO-swap/playback-order repeats.
• Sample-composition and redshift-distribution bias: Different source classes or redshifts by annulus can fake profiles. Safeguard: re-weight by redshift/brightness/class, stratify statistics, and report post-matching robustness.
• Source-side kinematics and radiative transfer: Outflows/self-absorption shift line centers. Safeguard: favor narrow lines/absorption pairs and combine multi-depth lines; down-weight/hold out lines with strong self-absorption.

VI. Execution and Transparency

Pre-register annulus boundaries, environment proxies, line/reference strategy, prediction-card schema, scoring and exclusion rules. Keep hold-out subsets in each annulus and control ring for final confirmation. Replicate across surveys and teams (for example, ALMA/VLA/MeerKAT and SDSS/DESI/4MOST). Publicly release environment-template summaries, prediction cards, text intervals and direction orderings by annulus, cross-band consistency summaries, and key intermediate artifacts. This chapter forms a closed loop with Chapters 3 (same-source multi-line calibration), 5 (radio-background floor), 6 (CMB μ/y deconstruction–injection), and 27 (path-redshift tomography); cross-references are required.

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more annuli and two or more environment grades, environment-forward predictions of direction and strength achieve significantly above-chance hit rates, with a core/inner > outer/control spatial monotonicity.
   • Offsets are direction-consistent across bands, manifest as common shifts within same-source multi-line sets, and remain non-dispersive.
   • Results replicate across institutions/pipelines and survive foreground/scan-strategy equivalence tests.
2. Refutation (fails):
   • Hit rates near chance or non-monotonic spatial profiles.
   • Band flips/wavelength rescaling (dispersive behavior) or signals driven primarily by foreground/scan/pipeline.
   • Signals vanish after re-weighting/matching, or appear only in one data source/pipeline.