Gravitational Lensing of the Bullet Cluster in the CCC+TL Cosmology: A Controlled Proof-of-Concept Study

Abstract

A proof-of-concept study of gravitational lensing in the Bullet Cluster under Covarying Coupling Constants plus Tired Light (CCC+TL) cosmology. Using a JWST spectroscopic catalogue of 219 cluster members and 135 gold multiple images in 49 systems from Rihtarsic et al. (2026), we construct convergence maps for CCC+TL and a simplified $Λ$CDM model using their respective angular-diameter distances and critical surface densities. The CCC+TL model adopts a two-parameter effective-density prescription anchored to the same virial-scale mass budget as $Λ$CDM, rather than fitted to multiple-image positions. The CCC+TL and $Λ$CDM mean-convergence bands in radial rings overlap within the propagated $\pm 30 \%$ virial-mass uncertainty across all rings containing multiple images ($θ\leq80\arcsec$). On a source-plane back-projection diagnostic ($α_{\mathrm{phys}}(z_s)=α_{\mathrm{dft}}\timesβ(z_s)/β(z_{s,\mathrm{ref}})$ with $z_{s,\mathrm{ref}}=2$), the unoptimised two-parameter CCC+TL pipeline yields $\mathrm{RMS}=5.22\arcsec$ ($4.63\arcsec$--$5.91\arcsec$), compared with $6.82\arcsec$ ($5.75\arcsec$--$8.09\arcsec$) for the $Λ$CDM reference. The optimised 32-parameter Lenstool reconstruction achieves an image-plane RMS of $\sim\!0.41\arcsec$, which is not directly comparable to these source-plane values. Within the $\pm 30\%$ $M_{200}$ uncertainty band, the source-plane scatter ranges partially overlap. The CCC+TL effective extra-gravity distribution follows the galaxy distribution rather than X-ray gas, reproducing the qualitative morphology of the Bullet Cluster, though this agreement is partly structural as profiles center on member galaxies by construction. For the same mass, Einstein-radius scaling differs by only 1.7% between cosmologies. These results are a necessary first step toward a full image-plane likelihood test of CCC+TL.