Observational Consequences of a Landscape

TL;DR

The paper investigates observational consequences of the landscape paradigm, arguing our universe likely originated from a Coleman-De Luccia tunnelling event that yields an open FRW geometry with negative curvature. By combining an anthropic bound on curvature (analogous to Weinberg's bound) with landscape-statistics arguments for inflationary parameters, the authors show the number of e-folds $N$ is unlikely to be far above the minimal required to form structure, with a quantified tendency toward $N$ near the observational lower bound ($\sim 62$). They derive a bound relating curvature, cosmological parameters, and primordial perturbations, and estimate a probability distribution $P(N) \propto 1/N^4$ that favors modest inflation while still allowing $N$ in the 62–64 range to have potentially observable consequences. If $N$ is close to this bound, one expects measurable signatures such as residual spatial curvature and possible distortions in the CMB at the lowest multipoles, offering a possible empirical window into the landscape framework.

Abstract

In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the "overshoot" problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.

Figures (4)

• Figure 1: A highly unusual potential which is a typical example of the ones we will consider.
• Figure 2: A conformal diagram showing the bubble nucleation. The background space, labelled "False vacuum," is the initial de Sitter minimum.
• Figure 3: Cosmological perturbations at decoupling as a function of comoving scale. $L_c$ is the critical length below which structure has collapsed or will collapse in our universe, assuming dark energy is a cosmological constant.
• Figure 4: Contour lines for the bound, eq. \ref{['boundtoday']}. Each point on the diagram corresponds to a different value of $\Omega_{matter} =\Omega_{total} - \Omega_{\Lambda}$; $(\delta \rho / \rho)_{dc}$ has been set to $3 \times 10^{-3}$, which corresponds to a scale of 1 Mpc. The white triangle corresponds to unphysical universes where $\Omega_{matter} <0$. In the black area the bound is violated and structure cannot form. The disk in the upper-right is our universe.