Testable anthropic predictions for dark energy

TL;DR

This paper develops an anthropic framework to address both the old cosmological constant problem and the time coincidence by treating the dark energy density as a random variable with an inflation-generated prior ${\cal P}_*(\rho_D)$ and an anthropic selection factor $n_{civ}(\rho_D)$. Under the generic, flat-in-the-anthropic-range prior and with civilizations likely arising in galaxies formed around $z\sim 1$, it yields concrete predictions: an effectively vacuum-like equation of state $p_D= w\rho_D$ with $w=-1\pm 10^{-5}$; a tendency for $\Omega_D$ to be higher than the conventional $0.7$ and $h$ to be lower; a strong bias for civilizations to emerge in massive, late-forming galaxies; and a recollapse timescale exceeding a trillion years. The work provides testable, quantitative forecasts that link the microphysics of $\rho_X$ to observable cosmological parameters and galactic evolution, offering a path to falsify or validate anthropic solutions with upcoming data.

Abstract

In the context of models where the dark energy density $\rD$ is a random variable, anthropic selection effects may explain both the "old" cosmological constant problem and the "time coincidence". We argue that this type of solution to both cosmological constant problems entails a number of definite predictions, which can be checked against upcoming observations. In particular, in models where the dark energy density is a discrete variable, or where it is a continuous variable due to the potential energy of a single scalar field, the anthropic approach predicts that the dark energy equation of state is $p_D=-ρ_D$ with a very high accuracy. It is also predicted that the dark energy density is greater than the currently favored value $Ω_D\approx 0.7$. Another prediction, which may be testable with an improved understanding of galactic properties, is that the conditions for civilizations to emerge arise mostly in galaxies completing their formation at low redshift, $z\approx 1$. Finally, there is a prediction which may not be easy to test observationally: our part of the universe is going to recollapse eventually. However, the simplest models predict that it will take more than a trillion years of accelerated expansion before this happens.

Figures (3)

• Figure 1: The distribution (\ref{['disy']}).
• Figure 2: Contours of the function $y_0(\Omega_D, h)$ given in (\ref{['y0']}), corresponding to the $1\sigma$ (lower curves) and $2\sigma$ (upper curves) predictions represented by Eqs. (\ref{['1sigma']}-\ref{['2sigma']}). The excluded region lies to the left of the curves. The thick solid lines assume that the dominant contribution to $n_{civ}$ is in galaxies of mass $M=M_{MW}=10^{12}M_\odot$. For comparison, we show the predictions for different choices of the mass. The short dashed curves correspond to the mass of the local group $M_{LG}=4\times 10^{12}M_\odot$, and the long dashed curves correspond to the mass of the bright inner part of our galaxy $M=10^{11}M_\odot$. A scale invariant spectrum of density perturbations is assumed.
• Figure 3: Effect of a tilt in the spectral index of density perturbations. As in Fig. 2, the thick solid lines correspond to a scale invariant spectrum $n=1$, and a mass $M=M_{MW}=10^{12}M_\odot$. The long dashed line and the short dashed lines correspond to tilted spectra, with $n=.95$ and $n=.9$ respectively.