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

We present a controlled proof-of-concept study of gravitational lensing in the Bullet Cluster (1E 0657-56, zd=0.296) under the Covarying Coupling Constants plus Tired Light (CCC+TL) cosmology. Using a JWST spectroscopic catalogue of 219 confirmed cluster members and the 135 gold multiple images in 49 systems from Rihtaršič et al. (2026), we construct independent convergence maps for CCC+TL and a simplified ΛCDM reference 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 the ΛCDM reference by construction, rather than fitted to the multiple-image positions themselves. Three comparisons are presented: First, the CCC+TL and ΛCDM mean-convergence bands in radial rings overlap within the propagated ±30% virial-mass uncertainty across all rings containing multiple images (θ≤80′′). Secondly, on the source-plane back-projection diagnostic (convention αphys(zs)=αdft×β(zs)/β(zs,ref) with zs,ref=2), the unoptimised two-parameter CCC+TL pipeline gives RMS=5.22′′ (4.63′′–5.91′′ across the mass band), compared with 6.82′′ (5.75′′–8.09′′) for the equivalent two-parameter ΛCDM reference. For context, the fully optimised 32-parameter Lenstool reconstruction of Rihtaršič et al. (2026) achieves an image-plane RMS of ∼0.41′′ on this gold catalogue; this is a different quantity than the source-plane values quoted above and is not directly comparable. Within the ±30%M200 uncertainty band the two source-plane scatter ranges partially overlap, which is a statement about two model predictions, not a test of either model against the observed multiple-image positions. Thirdly, the CCC+TL effective extra-gravity distribution follows the galaxy distribution rather than the X-ray gas, reproducing the qualitative morphological feature that defines the Bullet Cluster; we stress that this agreement is partly structural, since the galaxy-scale and cluster-scale CCC profiles are centred on the member galaxies by construction. For the same cluster mass, the Einstein-radius scaling in arcseconds differs by only 1.7% between the two cosmologies. These results are a necessary first step toward a full image-plane likelihood test of CCC+TL on the Bullet Cluster, but not a sufficient one; the full pipeline reproducing the numerical results of this paper is available at a dedicated website.