Towards lattice simulations of scalar holographic cosmological models
Lee, Joseph Kin Lok
Over the past decades, inflation has been the leading paradigm for describing the initial conditions of Big Bang cosmology. It provides an account of our spatially flat universe, and gives excellent agreement with the approximately Gaussian and nearly scale-invariant spectrum of the cosmic microwave background (CMB), as revealed by observations. However, shortcomings of inflation, including questions regarding the initial singularity and a want for a UV complete theory, motivate alternative descriptions of the very early Universe, such as via a holographic approach. In the holographic framework, cosmological observables are described by correlation functions of dual three-dimensional quantum field theories. The CMB power spectrum is related to the correlation function of the energy-momentum tensor (EMT) of the dual theory. In the high multipole region of the CMB, the perturbative holographic prediction has been shown to be competitive with the prediction from inflation and the Lambda-Cold Dark Matter (ΛCDM) model, the ‘standard model’ of Big Bang cosmology. In contrast, for the low multipole region, the dual theory becomes nonperturbative, and perturbative calculations can no longer be relied upon. As part of the LatCos collaboration, we aim to use lattice field theory to nonperturbatively compute the EMT correlation function of the dual quantum field theory. In particular, we focus on the simplest version of the holographic dual theories, which is the class of three-dimensional theories with massless scalar field in the adjoint of SU(N) and a φ4 interaction. A feature of this class of theories is superrenormalisability, where they suffer from severe infrared (IR) divergences in perturbation theory. A study via finite-size scaling was performed to establish the nonperturbative IR finiteness of these theories, as well as to obtain the critical mass in order to approach the massless limit in our result. In this thesis I study the renormalisation of the EMT operator and correlation function on the lattice. The EMT is the collection of Noether currents related to spacetime symmetries, and is a conserved quantity in the continuum. On the lattice, continuous translational symmetry is broken into a discrete subgroup, and the EMT has to be renormalised. Here we utilise the Wilson flow to perform nonperturbative renormalisation of the EMT operator. Using this result, we then introduce a position-space window filtering method to eliminate contact terms and to calculate the full renormalised EMT correlation function on the lattice. These milestones allow us to make a prediction of the CMB power spectrum across a wide range of multipoles, which can be tested against measurements from Planck, and constitute the first steps toward testing the viability of the holographic framework as a description of the very early Universe.