Dark energy equation of state and anthropic selection

TL;DR

The paper argues that anthropic selection can explain the small present-day dark energy density by treating ρ_D as a random variable across a multiverse, and extends this idea to cases where the slope s of the dark-energy potential is also random.For a single-field, nearly flat potential the prior favors equiprobable ρ_D within the anthropic window, yielding late-time cosmology close to a cosmological constant; when the slope is allowed to vary, the slow-roll condition can be marginal, producing observable evolution in the equation of state w(z).In multi-field scenarios, the joint distribution of (ρ_D, s) is shaped by inflationary diffusion, differential expansion, and an observer-based selection that weighs regions by their number of civilizations, leading to a range of predictions from Λ-like behavior to detectable redshift dependence of dark energy and even future recollapse.The analysis identifies key regimes in parameter space (controlled by the prior exponent β for the slope distribution) that determine whether current observations align with a constant ρ_D or with appreciable evolution in w and potential signs of cosmic contraction.

Abstract

We explore the possibility that the dark energy is due to a potential of a scalar field and that the magnitude and the slope of this potential in our part of the universe are largely determined by anthropic selection effects. We find that, in some models, the most probable values of the slope are very small, implying that the dark energy density stays constant to very high accuracy throughout cosmological evolution. In other models, however, the most probable values of the slope are such that the slow roll condition is only marginally satisfied, leading to a re-collapse of the local universe on a time-scale comparable to the lifetime of the sun. In the latter case, the effective equation of state varies appreciably with the redshift, leading to a number of testable predictions.

Figures (8)

• Figure 1: Comparison of anthropic predictions with observations. The curves represent the boundaries of the 68% (solid) and 95% (dashed) confidence level regions predicted by the distribution (\ref{['nG']}). The cross represents the values inferred from WMAP observations, with $2\sigma$ error bars.
• Figure 2: Regions in the $s-\rho_D$ plane, illustrating the different behaviours of $\nu_{civ}$ with $s$.
• Figure 3: Sketch of $\nu_{civ}$ as a function of $s$ and $\rho_D$. For definiteness, we have used $t_*= 3 t_G$. The slope $s$ is in units of $\rho_G/M_p$, whereas $\rho_D$ is in units of $\rho_G$
• Figure 4: The distribution ${\cal P}(s,\rho_D)$ as a function of $s$ and $\rho_D$, for $\beta=0$. As in Fig. 3, $\rho_D$ is in units of $\rho_G$. For this and the following plots, we have taken $\rho_G\equiv (4/3) M_p^2 t_G^{-2}$, where $t_G= t_{rec} \sigma_{rec}^{-3/2}$. Here $\sigma_{rec}$ is the density contrast on the galactic scale at the time of recombination ($t_G$ is then the time it takes for the linearized density contrast to become equal to 1 in the absence of a dark energy component). With this choice, the variable $y$ which we used in section II is the same as $\rho_D/\rho_G$.
• Figure 5: The distribution $s \rho_D {\cal P}(s,\rho_D)$ as a function of $s$ and $\rho_D$, for $\beta=0$. Same conventions as in Fig. 4.