Radion Leakage in a 5D Gauss-Bonnet Braneworld: Power Law Transfer Function and Resolution of S₈, Lyman-α, and Dark-Galaxy Abundances

This record presents a refined treatment of radion leakage in five-dimensional Gauss-Bonnet braneworld gravity and its consequences for the matter power spectrum. Earlier formulations that employed a steep exponential transfer function successfully addressed the S8S_8S8 and Lyman-α tensions but produced an unacceptably strong suppression of small-scale structure, in conflict with the observed abundance of dark-matter-dominated dwarf galaxies.

A systematic survey of alternative transfer-function forms identifies a shallow power-law suppression that simultaneously accommodates current constraints on the amplitude of matter fluctuations, the Lyman-α forest, and dwarf-galaxy counts, while preserving consistency with CMB, BAO, and primordial nucleosynthesis results. The emergence of the power-law behaviour is discussed in terms of holographic renormalisation-group flow. The work updates earlier phenomenological constructions and provides a more observationally viable realisation of scale-dependent gravitational leakage.