The Distribution of Vacua in Random Landscape Potentials

Understand

Landscape cosmology posits the existence of a convoluted, multidimensional, scalar potential -- the "landscape" -- with vast numbers of metastable minima.

• Random matrices and random functions in many dimensions provide toy models of the landscape, allowing the exploration of conceptual issues associated with these scenarios.
• We compute the relative number and slopes of minima as a function of the vacuum energy $\Lambda$ in an $N$-dimensional Gaussian random potential, quantifying the associated probability density, $p(\Lambda)$.
• After normalisations $p(\Lambda)$ depends only on the dimensionality $N$ and a single free parameter $\gamma$, which is related to the power spectrum of the random function.