Acoustic Dark Energy: Potential Conversion of the Hubble Tension

TL;DR

This work investigates Acoustic Dark Energy (ADE), a transient dark fluid that becomes relevant near matter-radiation equality, as a robust mechanism to alleviate the Hubble tension without compromising CMB fits. ADE perturbs the Weyl potential through its own acoustic oscillations, enabling a higher inferred H0 when combined with BAO and SN data, while observationally constraining its parameters via CMB polarization. A principal realization is a canonical scalar that converts potential energy to kinetic energy around equality (c_s^2 ≈ w_f ≈ 1), leading to a fit improvement of ∆χ^2_tot ≈ -12.7 over ΛCDM with 2 extra parameters, and a detectable finite ADE fraction around 8%. The authors further develop explicit canonical potentials and discuss how future polarization measurements can decisively test this scenario, distinguishing ADE from related early dark energy models.

Abstract

We discuss the ability of a dark fluid becoming relevant around the time of matter radiation equality to significantly relieve the tension between local measurements of the Hubble constant and CMB inference, within the $Λ$CDM model. We show that the gravitational impact of acoustic oscillations in the dark fluid balance the effects on the CMB and result in an improved fit to CMB measurements themselves while simultaneously raising the Hubble constant. The required balance favors a model where the fluid is a scalar field that converts its potential to kinetic energy around matter radiation equality which then quickly redshifts away. We derive the requirements on the potential for this conversion mechanism and find that a simple canonical scalar with two free parameters for its local slope and amplitude robustly improves the fit to the combined data by $Δχ^2 \approx 12.7$ over $Λ$CDM. We uncover the CMB polarization signatures that can definitively test this scenario with future data.

Figures (8)

• Figure 1: The joint marginalized distribution of the ADE parameters $c_s^2$ and $w_{\rm f}$, obtained using our combined datasets. The darker and lighter shades correspond respectively to the 68% C.L. and the 95% C.L. The markers indicate the maximum likelihood values for ADE (solid circle) from Tab. \ref{['tab:parameters']} and the intersection between canonical models $c_s^2=1$ (solid line) and models which convert potential to kinetic energy at the transition $c_s^2=w_{\rm f}$ (dashed line), i.e. $c_s^2 = w_{\rm f} =1$ (open circle) as in cADE.
• Figure 2: The Weyl potential evolution of the ML ADE model from Table \ref{['tab:parameters']} for two modes: $k=0.01$ and $0.04\;{\rm Mpc^{-1}}$. Lower subpanels show differences with respect to the baseline value of Weyl potential for the $\Lambda$CDM parameters of ML ADE but with no ADE ($f_c=0$), as displayed in the upper subpanels. Shown are ML ADE (red solid) and parameter variations around it: $c_s^2+$ (orange dashed) and $w_f+$ (dark blue dashed) mean $+0.4$ variations, while $\Omega_c h^2-$ (cyan dashed) means lowering it to the ML $\Lambda$CDM value in Table \ref{['tab:parameters']}. Relevant temporal scales (matter-radiation equality $a_{\rm eq}$, ADE transition $a_c$ and recombination $a_*$) are shown with vertical lines.
• Figure 3: The CMB model and Planck data residuals with respect to the ML $\Lambda$CDM model. Shown are the ML ADE model (red solid) and a $\Delta c_s^2=+0.4$ variation on it (orange dashed, see Fig. \ref{['fig:Weyl']}). The upper, middle, and bottom panels correspond to TT, EE, and TE residuals respectively and vertical lines denote their peaks in the ML $\Lambda$CDM model.
• Figure 4: Scalar field potential $V(\phi)$ match to the fractional ADE energy density $f_{\rm ADE}$ of the ML cADE parameters in Table \ref{['tab:parameters']}. Top: a locally quadratic potential with Eq. (\ref{['eqn:potential']}) compared with $p=1/2$ in Eq. (\ref{['eqn:eos']}); bottom: a locally quartic potential vs $p=1$.
• Figure 5: Canonical scalar field model and data residuals of ML cADE (orange solid) and ML EDE (dark blue solid) models with respect to the ML $\Lambda$CDM model as in Fig. \ref{['fig:residual']}. The model with $\Delta\Theta_i = -0.5$ from ML EDE (green dashed) is also shown.