The Dilaton: A Natural Resolution to the Hubble Tension via Spontaneous Scale Symmetry Breaking

Abstract

The statistical tension between early and late universe measurements of the Hubble constant ($H_0$) suggests that the dark sector is dynamical rather than static. We propose that this dynamics arises from a fundamental symmetry principle: the Spontaneous Breaking of Scale Invariance. We introduce the Dilaton ($\chi$), a Pseudo-Nambu-Goldstone Boson (PNGB) associated with dilatation symmetry breaking. We demonstrate that a simple quadratic mass term in the fundamental theory transforms, via conformal coupling to gravity, into a ''thawing'' exponential potential $V(\phi) \propto e^{-\lambda\phi}$ in the Einstein frame. Using recent Bayesian reconstructions of dark energy dynamics from Planck, Pantheon+, and SH0ES data, we constrain the potential slope to be $\lambda \approx 0.056$. We show that this observational value is not arbitrary but corresponds to a fundamental non-minimal coupling strength of $\xi \approx 7.8 \times 10^{-4}$. The Dilaton mechanism naturally generates the late-time equation of state evolution ($w_0 \approx -0.85$) required to alleviate the Hubble tension while protecting the field mass $m \sim H_0$ through approximate shift symmetry.