Is Local $H_0$ At Odds With Dark Energy EFT?

TL;DR

This paper investigates whether dark energy models within effective field theories can reconcile the discrepancy between local and early universe measurements of the Hubble constant, finding limited potential for such models to resolve the tension.

Contribution

It demonstrates that standard dark energy EFT models cannot significantly increase the Hubble constant to match local measurements, highlighting limitations of these theories in resolving the Hubble tension.

Findings

EoS with $w_{DE}(z=0)<-1$ can raise $H_0$ modestly

Quintessence and K-essence do not satisfy conditions to increase $H_0$

Dark energy EFT models cannot outperform phenomenological two-parameter models in increasing $H_0$

Abstract

Local $H_0$ determinations currently fall in a window between $H_0 \sim 70$ km/s/Mpc (TRGB) and $H_0 \sim 76$ km/s/Mpc (Tully-Fisher). In contrast, BAO data calibrated in an early $\Lambda$CDM universe are largely consistent with Planck-$\Lambda$CDM, $H_0 \sim 67.5$ km/s/Mpc. Employing a generic two parameter family of evolving equations of state (EoS) for dark energy (DE) $w_{\textrm{DE}}(z)$ and mock BAO data, we demonstrate that if i) $w_{\textrm{DE}}(z=0) < -1$ and ii) integrated DE density less than $\Lambda$CDM, then $H_0$ increases. EoS that violate these conditions at best lead to modest $H_0$ increases within $1 \sigma$. Tellingly, Quintessence and K-essence satisfy neither condition, whereas coupled Quintessence can only satisfy ii). Beyond these seminal DE Effective Field Theories (EFTs), we turn to explicit examples. Working model agnostically in an expansion in powers of redshift $z$, we show that Brans-Dicke/$f(R)$ and Kinetic Gravity Braiding models within the Horndeski class can lead to marginal and modest increases in $H_0$, respectively. We confirm that as far as increasing $H_0$ is concerned, no DE EFT model can outperform the phenomenological two parameter family of the DE models. Evidently, the late universe may no longer be large enough to accommodate $H_0$, BAO and DE described by EFT.