Spontaneous Creation of Inflationary Universes and the Cosmic Landscape

TL;DR

The paper proposes SOUP, a principle in string theory that modifies the Hartle-Hawking wavefunction to include decoherence from environment modes, yielding Ψ ∼ ${\cal P} \exp({\cal F})$ with ${\cal F} = -S_E - {\cal D}$ and leading decoherence term ${\cal D} \sim c V_9 / l_s^9$. By evaluating tunneling probabilities to a range of string vacua (including S^{10} and KKLT/KKLMMT inflationary scenarios), the authors find that inflationary universes are statistically favored over direct transitions to today’s small cosmological constant or decompactified higher-dimensional spaces. Decoherence from perturbative gravity/matter modes suppresses problematic vacua and stabilizes extra dimensions during inflation, enabling a preferred inflationary road toward our universe. The framework suggests testable implications, such as the nature of cosmic strings, and offers a path to select a vacuum without privileging anthropic reasoning, while highlighting the need for refined modeling of the decoherence term and broader sampling of vacua.

Abstract

We study some gravitational instanton solutions that offer a natural realization of the spontaneous creation of inflationary universes in the brane world context in string theory. Decoherence due to couplings of higher (perturbative) modes of the metric as well as matter fields modifies the Hartle-Hawking wavefunction for de Sitter space. Generalizing this new wavefunction to be used in string theory, we propose a principle in string theory that hopefully will lead us to the particular vacuum we live in, thus avoiding the anthropic principle. As an illustration of this idea, we give a phenomenological analysis of the probability of quantum tunneling to various stringy vacua. We find that the preferred tunneling is to an inflationary universe (like our early universe), not to a universe with a very small cosmological constant (i.e., like today's universe) and not to a 10-dimensional uncompactified de Sitter universe. Such preferred solutions are interesting as they offer a cosmological mechanism for the stabilization of extra dimensions during the inflationary epoch.

Figures (7)

• Figure 1: Starting with nothing, quantum tunneling happens via a $S^{D}$ instanton with radius $a=1/H$ to a $D$-dimensional de Sitter universe, which then grows to $\hat{a}$ and beyond.
• Figure 2: A $S^4 \times M$ instanton tunneling to the 4-dimensional de Sitter universe with a cosmologically stable 6 spatial dimensional space $M$. Some examples are $M=S^6, S^2 \times S^2 \times S^2$, three-fold Calabi-Yau manifold with fluxes etc.
• Figure 3: ${\cal{F}}$ as a function of $\Lambda$. The semi-classical approximation breaks down (indicated by the dashed vertical line at the right) when $\Lambda$ is large.
• Figure 4: The potential $V(\sigma)$ as a function of the size $\sigma$ of the compactified dimensions. If the size of the extra dimensions grows substantially in the early universe, the universe will end up with 10 uncompactified dimensions. So cosmological stabilization may be needed in addition to dynamical moduli stabilization.
• Figure 5: The 4 paths for $T=0$ to $T= (\pi/2 - i u)/H$ discussed in the text, from left to right : $w=0$, $0<w<\pi/2H$, $w=\pi/2H$ and $w>\pi/2H$. Actually, there are infinitely many paths reachable simply by analytic continuation. Here $\cosh u = {\hat{a}} H$.