Cosmological Evolution in the $GL(4,\mathbb{R})$ Yang-Mills Theory of Gravity: Resolving the JWST Early Galaxy Crisis and Late-Time Acceleration

Abstract

We investigate the cosmological implications of the $GL(4,\mathbb{R})$ Yang-Mills gauge theory of gravity. A long-standing theoretical challenge in standard cosmology is the reliance on ad hoc rolling scalar fields (e.g., the inflaton or quintessence) to drive early-time inflation and late-time acceleration, despite their unknown particle physics origins. In this work, by treating the affine connection as a gauge field and the world metric as a non-dynamical background, we derive an exact expansion history that strictly eliminates the need for any rolling scalar fields or a cosmological constant. The dynamics are governed solely by the Yang-Mills field strength squared. We demonstrate that the early Universe exhibits a singularity-free coasting expansion $a(t) \propto t$, resolving the JWST high-redshift galaxy crisis by granting significantly more time for early structure formation. As radiation dilutes, the Universe naturally transitions into a Weitzenb\"ock vacuum state, where a residual, topologically non-trivial constant torsion locks the spacetime kinematics to drive a late-time exponential acceleration $a(t) \propto \exp(\xi t)$. This framework establishes a purely geometric and gauge-theoretic origin for the cosmological evolution.