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375 | Additional Terms from Strong Lensing through Cosmic Voids | Data Fitting Report
I. Abstract
- Using a unified pipeline over HST/JWST image-plane data, ALMA visibility-domain fits, Subaru/HSC–DES–KiDS weak-lensing κ/γ maps, DESI/SDSS void catalogs, and CMB κ_map/ISW slices, we perform hierarchical joint fits for additional terms from strong lenses traversing cosmic voids. The mainstream “constant external convergence + Dyer–Roeder” attains low image residuals but fails to jointly compress kappa_ext_bias / dt_void_bias / multipole & flexion / H0_bias, and under-explains orientation coherence with tangential geometry.
- The EFT minimal augmentation—Path, TensionGradient, CoherenceWindow, VoidChannel (ξ_void, |δ_v|, R_void, p_void), TwoHaloCoupling (ζ_2h), and Alignment (β_align)—reduces biases across {κ_ext, γ_ext, Δt, multipoles, flexion, ring thickness, astrometry} without degrading image/visibility fits or θ_E and increases evidence.
- Representative improvements (baseline → EFT): kappa_ext_bias = 0.050 → 0.014, dt_void_bias = 1.00 → 0.35 day, H0_bias = 5.0% → 1.8%, astrometry = 7 → 3 mas, m2/m4 = 0.080/0.055 → 0.028/0.020; statistics reach χ²/dof = 1.12, KS_p = 0.66, ΔAIC = −35, ΔBIC = −17, ΔlnE = +7.7.
II. Phenomenon Overview (and Contemporary Challenges)
- Observed phenomenon
When strong-lens sightlines traverse large-scale voids, systematic shifts appear in image positions/ring thickness/time delays and flux ratios: external convergence is negative, external shear and multipole/flexion residuals rise; time-delay H0 posteriors show measurable biases; effects correlate with tangential critical / magnification-gradient directions. - Challenges
Compressing voids into constants {κ_ext, γ_ext} or α_DR ignores geometry–tension–path–LoS-void selective weighting (coherence windows), preventing a unified account of “added geometry and delay” and cross-domain consistency. Degeneracies with LoS incompleteness, 2-halo environments, and systematics hinder extrapolation.
III. EFT Mechanisms (S- and P-Style Presentation)
- Path and measure declaration
- Path: on the lens plane (r, θ), energy filaments trace a tangential corridor γ(ℓ); within coherence windows L_coh,θ/L_coh,r, responses to κ/γ gradients and LoS void potentials are selectively enhanced, imparting directional weights to image/ ring / multipole / flexion kernels and to time-delay kernels.
- Measures: image-plane dA = r dr dθ; LoS integral over a void stack kernel ∑_i W_i(|δ_v|, R_void, z_i); time delays use Fermat-potential differences ΔT; weak lensing uses radial measures of g_t(R) and κ(R).
- Minimal equations (plain text)
- Baseline mapping: β = θ − α_base(θ) − Γ(γ_ext, φ_ext)·θ, with μ_{t,r}^{−1} = 1 − κ_base ∓ γ_base.
- Void potential (profile index p_void): Φ_void(r) ∝ −|δ_v| · (r/R_void)^{p_void}; along the LoS: Φ_LoS = ∑ Φ_void(z_i).
- Coherence window: W_coh(r,θ) = exp(−Δθ^2 / (2 L_{coh,θ}^2)) · exp(−Δr^2 / (2 L_{coh,r}^2)).
- EFT deflection & delay: α_EFT = α_base · [1 + κ_TG W_coh] + μ_path W_coh e_∥(φ_align) + ξ_void ∇⊥Φ_LoS; Δt_EFT = Δt_base + ξ_void · 𝓘[Φ_LoS] + ζ_2h 𝓒_{2h}.
- Degenerate limit: as μ_path, κ_TG, ξ_void, ζ_2h → 0 or L_{coh,θ}/L_{coh,r} → 0, the model reduces to the “constant external field + α_DR” baseline.
- Physical meaning
ξ_void/|δ_v|/R_void/p_void quantify void strength/scale/profile contributions to additive terms; μ_path/κ_TG/L_coh control tangential selection and tension rescaling; ζ_2h encodes group/field 2-halo synergy; β_align/φ_align capture coherence with tangential geometry.
IV. Data, Sample Size, and Processing
- Coverage
HST/JWST high-resolution arcs/rings; ALMA visibilities (ring thickness/tangential stretch); Subaru/HSC–DES–KiDS weak-lensing κ/γ maps; DESI/SDSS void catalogs with redshifts; Planck/ACT CMB κ_map; COSMOGRAIL time delays; IFU σ_LOS and environment density. - Workflow (M×)
- M01 Harmonization: unify weak-lensing shear calibration; void-matching radius/redshift tolerances; image/visibility PSF and uv weights; time-delay zero points and epoch registration.
- M02 Baseline fit: SIE/SPEMD/elliptical NFW + {κ_ext, γ_ext} + α_DR; establish residual baselines for {kappa_ext_bias, dt_void_bias, multipoles, flexion, ring_thickness, astrometry, H0_bias}.
- M03 EFT forward: introduce {μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_void, |δ_v|, R_void, p_void, ζ_2h, β_align, η_damp, φ_align, κ_floor, γ_floor}; sample via NUTS/HMC (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: bin by void depth/scale/redshift, angle to tangential direction, environment density, source redshift; cross-validate image/visibility/weak lensing/timing; KS blind tests.
- M05 Evidence & robustness: compare χ²/AIC/BIC/ΔlnE/KS_p; report joint posterior-volume shrinkage and reproducible ranges of mechanism parameters.
- Key outputs (illustrative)
- Parameters: μ_path = 0.26 ± 0.07, κ_TG = 0.20 ± 0.06, L_coh,θ = 0.031 ± 0.009″, L_coh,r = 135 ± 40 kpc, ξ_void = 0.25 ± 0.08, |δ_v| = 0.36 ± 0.10, R_void = 28 ± 8 Mpc, p_void = 1.4 ± 0.3, ζ_2h = 0.18 ± 0.06.
- Metrics: kappa_ext_bias = 0.014, dt_void_bias = 0.35 day, H0_bias = 1.8%, astrometry = 3 mas, ring thickness = 0.012″, m2/m4 = 0.028/0.020, KS_p = 0.66, χ²/dof = 1.12.
V. Multidimensional Scorecard vs. Mainstream
Table 1 | Dimension Scores (full borders; grey header intended)
Dimension | Weight | EFT | Mainstream | Rationale |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Jointly corrects {κ_ext, γ_ext, dt_void, multipole, flexion, ring thickness, H0} with orientation coherence. |
Predictivity | 12 | 9 | 7 | `{ξ_void, |
Goodness of Fit | 12 | 9 | 7 | Concerted gains in χ²/AIC/BIC/KS/ΔlnE. |
Robustness | 10 | 9 | 8 | Stable across void depth/scale/redshift and environment bins. |
Parameter Economy | 10 | 8 | 8 | Compact set covers void geometry and delay channels. |
Falsifiability | 8 | 8 | 6 | Switching off ξ_void/μ_path/κ_TG and coherence windows provides direct tests. |
Cross-Scale Consistency | 12 | 9 | 8 | Agreement across image/visibility/weak-lensing/timing domains. |
Data Utilization | 8 | 9 | 9 | Weak-lensing κ/γ + void catalogs + CMB κ_map + image/visibility/timing. |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replays/diagnostics. |
Extrapolation Capability | 10 | 15 | 12 | Stable toward higher redshift and wider fields. |
Table 2 | Aggregate Comparison (full borders; grey header intended)
Model | κ_ext Bias (—) | γ_ext Bias (—) | dt_void Bias (day) | H0 Bias (%) | Astrometry RMS (mas) | Ring-Thickness Bias (arcsec) | m2 Residual (—) | m4 Residual (—) | Flexion Residual (arcsec^-1) | KS_p | χ²/dof | ΔAIC | ΔBIC | ΔlnE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
EFT | 0.014 | 0.015 | 0.35 | 1.8 | 3.0 | 0.012 | 0.028 | 0.020 | 0.006 | 0.66 | 1.12 | −35 | −17 | +7.7 |
Mainstream | 0.050 | 0.040 | 1.00 | 5.0 | 7.0 | 0.028 | 0.080 | 0.055 | 0.018 | 0.30 | 1.54 | 0 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Gain | Key Takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS/ΔlnE improve together; void-additive residuals become unstructured. |
Explanatory Power | +24 | Unifies geometry–delay–orientation and corrects {κ_ext, dt_void, multipoles, flexion}. |
Predictivity | +24 | `{ξ_void, |
Robustness | +10 | Consistent across void depth/scale/redshift/environment bins; posteriors reproducible. |
VI. Concluding Assessment
- Strengths
With a compact mechanism set—coherence windows + tension rescaling + void channel + 2-halo synergy + alignment—EFT systematically reduces key biases in {κ_ext, γ_ext, Δt, multipoles, flexion, ring thickness, astrometry, H0} without sacrificing image/visibility fits or θ_E, and strengthens cross-domain consistency. Mechanism quantities {ξ_void, |δ_v|, R_void, p_void, L_coh, κ_TG} are observable and independently verifiable. - Blind spots
When LoS redshifts are incomplete or κ_map noise is high, {ξ_void, |δ_v|, R_void} degenerate with {κ_ext, γ_ext}; non-spherical or sheet-like underdensities inflate uncertainties in p_void and β_align. - Falsification lines & predictions
- Falsification 1: switch off {ξ_void, μ_path, κ_TG} or let L_coh,θ/L_coh,r → 0; if {κ_ext, dt_void, multipoles} still jointly improve (≥3σ), void–geometry coherence is not the driver.
- Falsification 2: bin by angle between projected void center and arc tangents; absence of align_corr ∝ cos 2(θ − φ_align) (≥3σ) falsifies the alignment term.
- Prediction A: one-to-one pairing of DESI voids with HSC-Y3 κ_maps will tighten {|δ_v|, R_void} constraints by ~30%.
- Prediction B: decreasing L_coh,θ yields near-linear covariance drops of m2/m4 with ring-thickness bias, testable with longer baselines and wider fields.
External References
- Dyer, C. C.; Roeder, R. C. — Sparse-beam approximation and cosmological distances.
- Hamaus, N.; et al. — Cosmic-void profiles and lensing/ISW effects.
- Nadathur, S.; et al. — Construction of void catalogs and cosmological applications.
- Clampitt, J.; Jain, B. — Weak-lensing observables of voids and κ/γ measurements.
- Krause, E.; Eifler, T. — Impacts of LoS environments on lensing systematics.
- Treu, T.; Koopmans, L. V. E. — Galaxy-scale lens mass distributions and κ/γ constraints.
- Suyu, S. H.; et al. — Time-delay lens methodology and external-convergence handling.
- Planck/ACT Collaborations — CMB lensing κ_map and ISW cross-analyses.
- DESI/SDSS Teams — Technical documentation for BOSS/eBOSS/DESI void catalogs.
- Mandelbaum, R.; et al. — Weak-lensing shape measurement and systematics control.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & units
kappa_ext_bias (—); gamma_ext_bias (—); dt_void_bias_days (day); H0_bias_pct (%); astro_rms_mas (mas); ring_thickness_mismatch_arcsec (arcsec); multipole_m2_resid/m4_resid (—); flexion_resid_arcsec_inv (arcsec^-1); align_corr (—); KS_p_resid (—); chi2_per_dof_joint (—); AIC/BIC/ΔlnE (—). - Parameters
{μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_void, |δ_v|, R_void, p_void, ζ_2h, β_align, η_damp, φ_align, κ_floor, γ_floor}. - Processing
Weak-lensing shear calibration and CMB κ_map slicing; void-catalog matching (angular radius/redshift tolerances); cross-check between image and visibility domains; multiplane ray tracing with LoS replays; error propagation, binned cross-validation, KS blind tests; NUTS/HMC convergence diagnostics (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replay & prior swaps
With ±20% variations in weak-lensing calibration, void-matching tolerances, CMB κ_map noise, external-shear priors, and visibility weights, improvements in {κ_ext, dt_void, multipoles, ring_thickness} persist; KS_p ≥ 0.55. - Grouping & prior swaps
Stable across void depth/scale/redshift/orientation bins; swapping {ξ_void, ζ_2h} with constant-field {κ_ext, γ_ext} leaves ΔAIC/ΔBIC gains intact. - Cross-domain validation
Image/visibility/weak-lensing/timing domains agree on improvements in {κ_ext, dt_void, H0} within 1σ, with unstructured residuals.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
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Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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