Relativity and Cosmology

    

A Closed, Expanding Universe with a Radial Curvature Gradient

Authors: Alaa H. Kheder

We propose a novel cosmological model in which the universe is spatially closed and expanding, yet features a radial gradient in curvature that intensifies near its outermost regions. Unlike the standard closed FLRW universe with constant positive spatial curvature, our model introduces a smooth radial deformation of the angular part of the metric. This curvature profile bends geodesics inward as they approach the outer regions, yielding a finite yet unbounded spatial geometry. Notably, unlike many inhomogeneous cosmologies or big bang-type models, the proposed geometry permits geodesic completeness without encountering singularities, due to the regulating effect of the radial curvature gradient. We derive the spacetime metric, compute the Ricci scalar and Einstein tensor, and analyze the physical implications of the associated energy-momentum distribution.

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[v1] 2025-07-20 20:27:16

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