Why $w \ne -1$? Anthropic Selection in a $Λ$ + Axion Dark Energy Model

TL;DR

This work investigates a dark-energy model in which a negative bare cosmological constant and a single ultra-light axion together drive late-time acceleration. By imposing an anthropic condition that observers exist in a universe where acceleration begins after matter domination and persists to the present, the authors derive a conditional bound on the initial total dark-energy density and obtain nontrivial constraints on the axion mass $m$ and $ρ_Λ$. They show that the axion mass is typically $m \sim {\cal O}(10)\,H_0$ for a Planck-scale decay constant, and that the dark-energy equation-of-state parameter $w_0$ generically deviates from $-1$ by ${\cal O}(0.1)$, offering an anthropic explanation for $w_0 \neq -1$ and aligning with DESI hints of time-varying dark energy. The results also indicate that a slightly smaller decay constant can yield a present-day dark-energy density close to the observed value, reinforcing the viability of the Λ+axion framework within a string-theory landscape context.

Abstract

We study a dark energy model composed of a bare negative cosmological constant and a single ultra-light axion, motivated by the string axiverse. Assuming that intelligent observers arise and observe, as in our universe, the onset of dark-energy-driven acceleration following matter domination, and that this acceleration persists to the present, we derive nontrivial constraints on both the axion mass and the bare cosmological constant. The axion mass is bounded from above to avoid fine-tuning of the initial misalignment angle near the hilltop, and from below because too light axions cannot achieve accelerated expansion due to their limited energy budget. As a result, the anthropically allowed axion mass range typically lies around $m = \mathcal{O}(10)\, H_0$ for a decay constant close to the Planck scale, where $H_0$ is the observed value of the Hubble constant. In this framework, the dark energy equation-of-state parameter $w_0$ generically deviates from $-1$ by $\mathcal{O}(0.1)$, providing a natural explanation for why $w \ne -1$ may be expected. We also find that, for a decay constant slightly smaller than the Planck scale, the peak value of dark energy density is significantly smaller than the anthropic bound on the cosmological constant and can be close to the observed value. These outcomes are intriguingly consistent with recent DESI hints of time-varying dark energy, and offer a compelling anthropic explanation within the $Λ$ + axion framework.

Figures (8)

• Figure 1: Colored regions indicate the predicted values of $w_0$, and dashed lines show analytic estimates of the boundaries between them. The axion mass is taken to be $m = 100 H_0$, $10 H_0$, and $H_0$ from top to bottom. The gray-shaded region in each panel is excluded due to the requirement for the accelerated expansion to persist until the current time.
• Figure 2: Likelihood of $\ln m$ marginalized over $\theta_\mathrm{i}$ and $\rho_\Lambda$. The vertical axis is normalized by the maximum value. Lower masses are disfavored due to the limited range of $\rho_\Lambda$, while higher masses are suppressed due to fine tuning of $\theta_\mathrm{i}$.
• Figure 3: Histograms of $w_0$ for the three axion masses, $m = 100 H_0$, $10 H_0$, and $H_0$, are shown in different colors.
• Figure 4: Histogram of $\rho_\mathrm{DE,i}$ marginalized over $\theta_\mathrm{i}$, $\rho_\Lambda$, and $\ln m$.
• Figure 5: Same as Fig. \ref{['fig: mass likelihood']} except for $\rho_\Lambda^\mathrm{max} = 2 \rho_\mathrm{DE,obs}$.