A G_2G2-Holonomy Model for Late-Time Cosmic Acceleration in M-theory: Alleviating the Hubble Tension through Geometric Vacuum Energy

A framework is developed within an eleven-dimensional M-theory scenario where dynamical geometric moduli, originating from a $G_2$-holonomy compactification, generate an evolving cosmological term, $\mathrm{\Lambda }(z)$. This ``Geometric Vacuum Energy’’ (GVE) is shown to be consistent across both cosmological and astrophysical scales. We demonstrate that a natural attractor solution alleviates the Hubble tension, yielding an inferred $H_0\approx 69.4\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ and a suppressed structure growth parameter $S_8\approx 0.67$, while remaining in excellent agreement with cosmic chronometer data (${\chi }^2\mathrm{/}N\approx 0.44$). Its predictions in the strong-gravity regime profoundly strengthen the framework’s self-consistency. We show that this model supports stable, hairy black hole solutions whose existence conditions are congruent with the cosmological attractor (${\mathrm{\Phi }}_{\text{horizon}}\leftrightarrow {\mathrm{\Phi }}_{\text{cosmology}}$). Furthermore, these objects exhibit a rich, falsifiable phenomenology, including (i) the definitive breaking of isospectrality in their gravitational-wave quasi-normal modes, (ii) a suppressed Integrated Sachs-Wolfe effect, and (iii) unique thermodynamic and electromagnetic accretion signatures. These interconnected findings highlight a pathway where a single, theoretically-motivated framework can naturally reconcile multiple observational puzzles.