Week 13.06.2022 – 19.06.2022

In this talk we will introduce CosmoLattice, a modern code for simulating the non-linear dynamics of interactive scalar-gauge theories in an expanding universe. As a demonstration of its power we will solve three very different problems of early Universe cosmology: i) the generation and use of gravitational waves as a probe of particle couplings, ii) the dynamics of non-minimally coupled scalar fields in the Jordan frame, and iii) the non-linear dynamics of helical gauge field production during the last efoldings of axion-inflation

I will speak about my recent work with Zechuan Zheng where we study the SU(Nc) lattice Yang-Mills theory in the t Hooft limit Nc -> infinity, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on maximal length of wilson loops, and the positivity conditions on certain correlation matrices. We thus obtain rigorous upper and lower bounds on plaquette average at various couplings. The results are quickly improving with the increase of the cutoff L. In particular, for D=4 and L=16, the upper bound data in the most interesting weak coupling phase are not far from the Monte-Carlo results and they reproduce well the 3-loop perturbation theory. We also attempt to extract the information about the gluon condensate from this data. Our results suggest that bootstrap can provide a tangible alternative to, so far uncontested, Monte Carlo approach. I will also mention our bootstrap results for an "unsolvable" two-matrix model in the large N limit, where this method appears to be superior in efficiency over Monte Carlo.