Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces

Abstract

We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum of the potential the usual semiclassical bubble nucleation rate, Γ = A e −B , increases rapidly as function of the number of fields in the theory. As a consequence, the fraction of vacua with tunneling rates low enough to maintain metastability appears to fall exponentially as a function of the moduli space dimension. We discuss possible implications for the landscape of string theory. Notably, if our results prove applicable to string theory, the landscape of metastable vacua may not contain sufficient diversity to offer a natural explanation of dark energy.

Kink Collisions in Curved Field Space

“…Moreover, string theory offers the possibility of an enormous landscape of local minima, making it important to determine if tunneling events and bubble collisions are essential cosmological processes. These considerations have inspired numerous authors to study transitions between collections of metastable vacua, with results of possible importance to key outstanding issues, such as the cosmological constant problem and the search for experimental signatures of a multiverse [6][7][8][9][10][11][12][13][14][15].…”

Certification and the potential energy landscape

“…We anticipate that the certification method presented in this paper will turn out to be a standard tool to verify the numerical SPs obtained from various numerical methods. Another possible application is to make rigorous statements about SPs random potential surfaces, such as the ones studied in statistical physics and cosmology, as well as in pure mathematics [20,21].…”

“…More specifically, even if a numerical approximation is heuristically validated, it could turn out to be a nonsolution at higher precision, or Newton iterations may have unpredictable behavior, such as attracting cycles and chaos, when applied to points that are not in a basin of attraction [4][5][6][7][8] of some solution. We note that if the given system is a set of polynomial equations, then one can use numerical polynomial homotopy continuation [9][10][11][12][13][14][15][16][17][18][19][20][21][22] to compute all the isolated solutions (see e.g. [23][24][25] for some related approaches).…”

Structural analysis of high-dimensional basins of attraction

“…Yet, the importance of such computations is apparent: the volume of the basin of attraction for the extrema of a generic energy landscape, be that of biological molecules [6], an artificial neural network [7][8][9], a dynamical system [10,11], or even of a "string theory landscape" (where the minima corresponds to different de Sitter vacua [12,13]), is essential for understanding the systems' behavior.…”