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

TL;DR

The paper tackles the Hubble tension by proposing that late-time cosmic acceleration is driven by a Dilaton, the PNGB of spontaneously broken scale invariance in a non-minimally coupled gravity sector. A simple quadratic mass term in the Jordan frame maps to a thawing exponential potential in the Einstein frame, with the slope $λ$ determined by the coupling $ξ$; this relation is tested against Bayesian reconstructions of dark energy dynamics from Planck, Pantheon+, and SH0ES data. The analysis finds $λ_{obs} ≈ 0.056$ and infers $ξ ≈ 7.8 × 10^{-4}$, yielding a present equation of state $w_0 ≈ -0.85$ and a natural mass scale $m ∼ H_0$, protected by approximate shift symmetry. The mechanism links a fundamental symmetry to cosmological evolution, offering a physically motivated resolution to the Hubble tension and making testable predictions for future surveys and local gravity tests through screening behaviors and thawing dynamics.

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 ($χ$), 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 $V(φ) \propto e^{-λφ}$ 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 $λ\approx 0.056$. We show that this observational value is not arbitrary but corresponds to a fundamental non-minimal coupling strength of $ξ\approx 7.8 \times 10^{-4}$. 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.

Figures (3)

• Figure 1: The Dilaton Mechanism. (a) In the fundamental Jordan frame, the field is trapped in a steep symmetry-breaking potential $V \sim \chi^2$. (b) The conformal transformation to the Einstein frame stretches this potential into a shallow exponential slope $U \sim e^{-\lambda\phi}$, naturally generating a "thawing" dark energy candidate. The arrow indicates the mapping via the conformal factor $\Omega^2(\chi)$.
• Figure 2: Constraint on Fundamental Coupling. The solid curve shows the theoretical prediction (Eq. \ref{['eq:master_lambda']}) relating the potential slope $\lambda$ to the non-minimal coupling $\xi$. The red star indicates the observational value derived from our previous analysis ($\lambda_{\text{obs}} \approx 0.056$), fixing the Dilaton coupling to $\xi \approx 7.8 \times 10^{-4}$. The tight correlation demonstrates that the "thawing" signal is consistent with a perturbative scalar-gravity interaction.
• Figure 3: Thawing History. The Dilaton model (blue) predicts $w(z) \to -1$ at high redshifts due to the curvature trap. It begins to thaw at $z \lesssim 1$, reaching $w_0 \approx -0.85$ today. This specific late-time trajectory alleviates the $H_0$ tension by modifying the low-redshift expansion history.