The Seashell-Universe Model: A Non-Metric Cosmological Model Based on a Conical Helicoidal Trajectory with Variable Speed of Light

In this work, an alternative cosmological framework is introduced wherein macroscopic cosmicexpansion is attributed not to a dynamic spacetime metric (expansion of space itself), but to thepropagation of photons along a confined geodesic path within a three-dimensional hypersurfaceexhibiting a conical helicoidal geometry (conical spiral). Under this approach, a Variable Speedof Light (VSL) model is postulated, linearly coupled to the local radius of the cone, v(R) ∝ R,which vanishes at the initial singularity. We mathematically demonstrate that integrating the lineelement differential along this helicoidal trajectory exactly cancels the geometric scale factor ofthe spiral, converging on an absolute age of the universe independent of the spiral’s turn density,yielding exactly T = Rf /c ≈ 46,500 million years. Finally, we discuss how this physical mechanismreinterprets the cosmological redshift phenomenon and resolves the Cosmic Microwave Background(CMB) horizon paradox through purely geometric means.