Early dark energy, the Hubble-parameter tension, and the string axiverse

TL;DR

The paper tests an early dark energy (EE) scenario motivated by string-axiverse ideas, where an exotic energy density behaves like a cosmological constant before a critical redshift $z_c$ and decays thereafter, aiming to reconcile the CMB-inferred $H_0$ with local measurements. Using a Fisher-matrix analysis of Planck TT data with EE as a sixth parameter, the authors find that Planck TT strongly constrains the EE contribution around recombination to be $\rho_{ee}/\rho_{tot}\lesssim 2\%$ for $10\lesssim z_c\lesssim10^5$, and that the induced shift in $H_0$ is modest unless the reionization optical depth $\tau$ is allowed to be much larger than the Planck central value. When $\tau$ is fixed at Planck values, EE cannot fully resolve the $H_0$ tension, with maximum $H_0$ gains of a few tenths of a unit and broader $H_0$ uncertainties. Only with substantially larger $\tau$ (e.g., beyond $5\sigma$) does the EE scenario potentially bring the CMB $H_0$ into agreement with local measurements, highlighting that the tension’s resolution in this framework strongly hinges on the assumed $\tau$. Overall, EE remains a tightly constrained, small perturbation to $\Lambda$CDM under current Planck TT data, and its viability as a complete solution to the Hubble tension is limited without relaxing other Planck-derived priors.

Abstract

Precise measurements of the cosmic microwave background (CMB) power spectrum are in excellent agreement with the predictions of the standard $Λ$CDM cosmological model. However, there is some tension between the value of the Hubble parameter $H_0$ inferred from the CMB and that inferred from observations of the Universe at lower redshifts, and the unusually small value of the dark-energy density is a puzzling ingredient of the model. In this paper, we explore a scenario with a new exotic energy density that behaves like a cosmological constant at early times and then decays quickly at some critical redshift $z_c$. An exotic energy density like this is motivated by some string-axiverse-inspired scenarios for dark energy. By increasing the expansion rate at early times, the very precisely determined angular scale of the sound horizon at decoupling can be preserved with a larger Hubble constant. We find, however, that the Planck temperature power spectrum tightly constrains the magnitude of the early dark-energy density and thus any shift in the Hubble constant obtained from the CMB. If the reionization optical depth is required to be smaller than the Planck 2016 $2σ$ upper bound $τ\lesssim 0.0774$, then early dark energy allows a Hubble-parameter shift of at most 1.6 km~s$^{-1}$~Mpc$^{-1}$ (at $z_c\simeq 1585$), too small to fully alleviate the Hubble-parameter tension. Only if $τ$ is increased by more than $5σ$ can the CMB Hubble parameter be brought into agreement with that from local measurements. In the process, we derive strong constraints to the contribution of early dark energy at the time of recombination---it can never exceed $\sim2\%$ of the radiation/matter density for $10 \lesssim z_c \lesssim 10^5$.

Figures (13)

• Figure 1: Shown here are the evolutions of the energy densities of exotic energy (EE; dashed lines) for several critical redshifts $z_c$, matter (solid blue), radiation (solid green), and the cosmological constant (solid red). For each $z_c$ we choose the exotic-energy density $\Omega_{\rm ee}$ to be the $3\sigma$ upper limit we derive from the Planck temperature power spectrum assuming the reionization optical depth $\tau$ is fixed to the current Planck best-fit value. The energy densities are all shown, relative to the critical density $\rho_c$ today, as a function of the scale factor $a$.
• Figure 2: The shifts caused in the TT power spectrum due to the addition of EE are shown for various $z_c$. Here, the value of the reionization optical is fixed to the current Planck best-fit value $\tau=0.0596$. The other cosmological parameters are fixed at the values, shown in Table I, that provide the best fit to the TT power spectrum. Clearly the critical redshift of the EE is important in determining how the EE shifts the TT spectrum. In the upper figure, the value of $\Omega_{\rm ee}$ chosen for each $z_c$ is the $3\sigma$ upper limit of its best fit. In the lower figure, $\Omega_{\rm ee}$ is chosen such that it moves $\theta_*$ by 1%. $\Omega_{\rm ee}$ is approximately two orders of magnitude greater for the lower plot.
• Figure 3: Shown here are the partial derivatives of the TT spectrum with respect to the cosmological parameters, $H_0$ (dark blue), $\omega_{\rm b}$ (green), $\omega_{\rm c}$ (red), ln($10^{10}A_{\rm s}$) (light blue) and $n_{\rm s}$ (pink). These were derived at the best-fit values obtained by setting $\tau = \tau_{\rm Pl}$, shown in Table \ref{['best_fit_table']}.
• Figure 4: The partial derivatives of the TT spectrum with respect to $\Omega_{\rm ee}$ are shown here for various values of $z_c$.
• Figure 5: The best-fit values and errors on $\Omega_{\rm ee}$ are shown here. The optical depth $\tau$ was fixed at the best-fit Planck-16 value to obtain these constrains.