Beyond Peak Statistics: Searching for Topological Folds in the Space Between Galaxies Using Dome Template Matching in Weak Lensing Tomography

Abstract

Abstract Modern weak lensing surveys (Euclid, LSST, DES) are optimized to detect dark matter through "peak statistics" — identifying local maxima in the convergence map corresponding to dark matter halos around galaxies. This paradigm treats the space between galaxies as a smooth background. We propose a methodological shift: instead of searching for point-like mass concentrations, we search for the periodic geometry of the spacetime fabric in the space between galaxies. Using template matching with strong Bayesian priors, we propose fitting dome-shaped profiles (upward ridges and downward troughs) to the cosmic shear field at a characteristic scale of L ≈ 150 Mpc. This approach transforms dark matter detection from a search for discrete objects into a search for the continuous topological curvature of spacetime itself. We also address the critical degeneracy with Baryon Acoustic Oscillations (BAO) and propose a geometric criterion for distinguishing the two signals.