Hubble Sinks In The Low-Redshift Swampland

TL;DR

The paper investigates whether Quintessence, including a string-motivated exponential coupling to dark matter, can raise the local Hubble constant $H_0$ to alleviate the Hubble tension. It employs a model-independent, low-redshift Taylor expansion around $z=0$ for the scalar field and for $H(z)$, scanning a large space of $(\alpha,\beta,\gamma)$ while constraining a late-time coupling $f(\phi)=e^{-C(\phi-\phi_0)}$ with $C$ fixed near observational bounds, and tests these models against cosmic chronometer, BAO, and Pantheon data up to $z\le0.7$. The main result is that uncoupled Quintessence tends to lower $H_0$ relative to $\Lambda$CDM, and even with $C\approx0.1$ the coupling does not significantly raise $H_0$ within the low-$z$ window; only scenarios with early-universe coupling (matter-dominated era or dark ages) could alter the outcome, pointing toward a high-redshift completion as necessary. These findings place low-redshift Quintessence in tension with local $H_0$ measurements and imply that the swampland-inspired resolutions, if viable, require physics beyond $z\lesssim0.7$, potentially testable via future 21-cm observations for the dark ages.

Abstract

Local determinations of the Hubble constant $H_0$ favour a higher value than Planck based on CMB and $Λ$CDM. Through a model-independent expansion, we show that low redshift ($z \lesssim 0.7$) data comprising baryon acoustic oscillations (BAO), cosmic chronometers and Type Ia supernovae has a preference for Quintessence models that lower $H_0$ relative to $Λ$CDM. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save $H_0$ from sinking in the string theory Swampland.

Figures (4)

• Figure 1: Bounds on the CPL parametrisation Chevallier:2000qyLinder:2002et, $w(z) = w_0 + w_a z/(1+z)$, which are constructed directly from the chains of an MCMC exploration of cosmic chronometer, BAO and supernovae data restricted to $z \leq 0.7$.
• Figure 2: Distribution of our 87,675 models, which survive our cuts, as a function of $\chi^2$ versus $H_0$. Dashed green line highlights the $\chi^2$ for $\Lambda$CDM and all models that raise $H_0$ also increase the $\chi^2$ value. In contrast 53,744 models lower both $H_0$ and $\chi^2$.
• Figure 3: Distribution of 80,732 surviving models as a function of $\chi^2$ versus $H_0$ for the coupling $C=0.1$. Here all models that raise $H_0$ also raise the $\chi^2$, whereas 46,665 models lower $H_0$ and $\chi^2$.
• Figure 4: The $1$ and $2 \, \sigma$ intervals for the normalised potential $V/V_0$ corresponding to CPL models that are consistent with CMB, BAO and Pantheon. For illustrative processes we plot the simplest Quintessence model, $V/V_0 = e^{-\lambda \phi}$ for different values of $\lambda$.