Expansion of the universe | EPFL Graph Search

The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion; the universe does not expand "into" anything and does not require space to exist "outside" it. To any observer in the universe, it appears that all but the nearest galaxies (which are bound by gravity) recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation only applies with respect to local reference frames and does not limit the recession rates of cosmologically distant objects. Cosmic expansion is a key feature of Big Bang cosmology. It can be modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric, where it corresponds to an increase in the scale of the spatial part of the universe's spacetime metric (which governs the size and geometry of spacetime). Within this framework, stationary objects separate over ti

Aspects of Gauge Theories Vacua

Adrien Florio

This thesis is concerned with gauge theories, their complicated vacuum and resulting effects. After an introduction to the subject, it is divided into four parts. Firstly, we treat the problem of chiral charge dynamics at finite temperature. Quantum field theory predicts a possibility for massless fermions to be transferred into electromagnetic fields with non-zero helicity and vice-versa. This phenomenon has applications ranging from cosmology to heavy-ions physics. We present a numerical investigation from first principles of the resulting complex dynamics and find a qualitative agreement with previous studies based on hydrodynamical approaches but measure rates that differ by up to an order of magnitude. We interpret this effect as contributions coming from small scales not previously taken into account. Secondly, we present a study of open-boundary conditions in lattice QCD at finite temperature. They were designed to ease up the problem of "topological freezing", which plagues numerical simulations close to the continuum limit. In particular, we determine the length of the "boundary zone" for two different temperatures. We also use the boundary effects to extract screening masses. Thirdly, we move on to present a compendium of lattice techniques, including some new algorithms, to perform real-time classical simulations of bosonic matter, Abelian and non-Abelian gauge fields in an expanding universe. We also briefly introduce CosmoLattice, a numerical software designed to perform such simulations, which are particularly interesting to study the reheating phase of our universe. Finally, we study yet another technique to probe non-perturbative sectors of field theories. Namely, we show that one can reconstruct the Schwinger pair production rate, which is the rate of production of particles due to the presence of a strong electric field, using only a few terms of the weak magnetic field expansion. This surprising result is obtained by using techniques coming from the field of resurgence and the analysis of asymptotic expansions. We conclude this work by presenting some general outlooks, sharing aspects of all these different yet related topics.

EPFL2020

The art of simulating the early universe. Part I. Integration techniques and canonical cases

Adrien Florio, Daniel Garcia Figueroa, Francisco Torrenti, Wessel Valkenburg

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.

2021