"Our universe at criticality: folding funnels and percolation"

A striking fact about our universe is that it seems poised near a phase transition. The Higgs metastability, cosmological constant and weak hierarchy problems can all be understood as problems of near criticality. A natural arena for the statistical physics of universes is the vast energy landscape of string theory, in conjunction with the cosmological mechanism of eternal inflation for instantiating in space-time the myriad metastable states of the energy landscape. As an inhabitant of such a multiverse, how should we reason probabilistically about the expected physical properties of our own universe? In this talk, by applying careful Bayesian reasoning I will present a well-defined probability distribution for occupying different vacua. Remarkably, these probabilities favor vacua whose surrounding landscape topography is that of a deep valley or funnel, akin to folding funnels of naturally-occurring proteins. Furthermore, by casting the problem in the language of network theory, I will argue that we likely inhabit a region of the energy landscape that is poised near the directed percolation phase transition. As usual, the predictive power of criticality lies in scale invariant observables, characterized by critical exponents that are insensitive to the details of the system. As an example, I will show that the probability distribution for the cosmological constant is a power-law, with a specific critical exponent, which favors small, positive vacuum energy. Tantalizingly, this hints at a deep connection between non-equilibrium critical phenomena on the landscape and the near-criticality of our universe.