Spacetime condensation in (2+1)-dimensional CDT from a Hořava–Lifshitz minisuperspace model

Abstract

A spacetime condensation phenomenon underlies the emergence of a macroscopic Universe in causal dynamical triangulations, where the time extension of the condensate is strictly smaller than the total time. It has been known for some time that the volumes of spatial slices in the bulk of the macroscopic Universe follow a time evolution which resembles that of a sphere, and their effective dynamics is well described by a minisuperspace reduction of the general relativistic action. More recently, it has been suggested that the same minusuperspace model can also provide an understanding of the condensation phenomenon itself, thus explaining the presence of an extended droplet of spacetime connected to a stalk of minimal spatial extension. We show here that a minisuperspace model based on the general relativistic action fails in that respect for the (2+1)-dimensional case, while a successful condensation is obtained from a minisuperspace model of Hořava–Lifshitz gravity.