Particle theory

Abstract:

In this article, we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated, and their relationship with the structure of the underlying random geometry is explored. Modifications due to interactions with matter fields are also briefly discussed. The approach to the subject is that of classical statistical mechanics, and most of the tools come from probability and graph theory.

Abstract:

An axion-like-particle (ALP) in the post-inflationary scenario with domain wall number N > 1 can be dark matter if the residual ℤN symmetry has a small explicit breaking. Although we cannot determine the full dynamics of the system reliably, we provide evidence that such an ALP can account for the observed dark matter abundance while having a relatively small decay constant and consequently a possibly large coupling to photons. In particular, we determine the number of domain walls per Hubble patch around the time when they form using numerical simulations and combine this with analytic expectations about the subsequent dynamics. We show that the strongest constraint on the decay constant is likely to come from the dark matter ALPs being produced with large isocurvature fluctuations at small spatial scales. We also comment on the uncertainties on the dark matter small-scale structure that might form from these overdensities, in particular pointing out the importance of quantum pressure in the N = 1 case.