Landscape Predictions from Cosmological Vacuum Selection

TL;DR

The study investigates cosmological selection in the string landscape using a holographic measure applied to a BP-like flux-vacua toy model with $J=\!250$ fluxes. By Monte Carlo sampling of decay chains and computing tunneling rates with instanton actions $B$, the authors show that cosmological dynamics drastically narrow the accessible small-$\lambda$ vacua: from ${\cal N}_{\lambda_0}^{\rm unselected} \approx 10^{121}$ to ${\cal N}_{\lambda_0} \approx 10^{80}$ (and ${\tilde{\cal N}}_{\lambda_0} \approx 10^{22}$ distinct values of $\lambda$ after accounting for degeneracies), constituting a dramatic thinning of the landscape. They find convergent, sharp predictions for the flux distributions $p_i(n)$, such as strong suppression of large $|n_i|$ and small-charge fluxes, and reveal that cosmological dynamics correlate with the decay structure across stages of the chain, yielding thousands of testable expectations while avoiding the staggering problem seen in alternative measures. The results suggest cosmological selection can meaningfully constrain the landscape, producing a dense, high-entropy distribution of accessible vacua and guiding expectations for low-energy parameters, while also offering a practical computational framework for studying large flux ensembles.

Abstract

In BP models with hundreds of fluxes, we compute the effects of cosmological dynamics on the probability distribution of landscape vacua. Starting from generic initial conditions, we find that most fluxes are dynamically driven into a different and much narrower range of values than expected from landscape statistics alone. Hence, cosmological evolution will access only a tiny fraction of the vacua with small cosmological constant. This leads to a host of sharp predictions. Unlike other approaches to eternal inflation, the holographic measure employed here does not lead to "staggering", an excessive spread of probabilities that would doom the string landscape as a solution to the cosmological constant problem.

Figures (6)

• Figure 1: A two-dimensional slice through the $J$-dimensional flux grid. Surfaces of constant $\lambda$ are $J-1$ dimensional spheres. Each dot represents a vacuum. Starting from initial vacua with $\lambda\approx 1$ (outermost shell), we simulate decay chains (blue lines) through the landscape, which terminate when a vacuum with $\lambda\leq 0$ is reached. Among the "penultimate" vacua with relatively small positive $\lambda$ (green/shaded region), only a small fraction is actually accessed by the decay chains, leading to a host of predictions. Vacua with $\lambda$ of order the tiny observed value lie in a much thinner shell (schematically shown as a black circle). A model can be ruled out if the selection effects render this shell inaccessible.
• Figure 2: The number of selected vacua with $\lambda\sim\lambda_0$, $\log{\cal N}_{\lambda_0}$, obtained from different initial ensembles starting at different values of $\langle\lambda\rangle$, in Model 1. For initial values $\langle\lambda\rangle\gtrsim 0.8$, the number of selected vacua stops shrinking. This indicates that at such high values, selection effects are negligible. Therefore, the details of the initial conditions are irrelevant as long as large values of $\lambda$ are preferred, as explained in the text.
• Figure 3: The red, wiggly curves show the probability that the $i$-th flux is $n$, $\tilde{p}_i(n)$, in the penultimate vacua of $N=7000$ decay chains starting from $\lambda\gtrsim 0.8$ in Model 1, as a function of $i$. For comparison, the blue, smooth curves show the probabilities that would have been obtained without cosmological selection, just from restricting to vacua with small cosmological constant. The differences are immediately apparent and quite drastic. For example, no fluxes greater than 4 survive the selection process; without selection, there would be many such fluxes. The fluxes associated with small charges (small $i$) are anomalously low after selection.
• Figure 4: Specific examples of probability distributions $\tilde{p}_i(n)$, plotted against $n$ for 6 of the 250 fluxes in Model 1. The cosmological dynamics drives most fluxes into a narrower range (red/light shaded bars) than the distribution obtained from landscape statistics alone (blue/dark bars).
• Figure 5: Constant action surfaces for $\lambda=0.8$ (top-left), $\lambda=0.4$ (top-right), $\lambda=0.2$ (bottom-left), and $\lambda=0.1$ (bottom-right) in the $i$-$|n_i|$ plane. (Recall that the charges $q_i$ are ordered so as to increase monotonically with $i$.) The action $B$ grows towards the bottom right with a line spacing of $1$ in all four plots, corresponding to greater suppression of the decay.