Towards lattice simulations of scalar holographic cosmological models
View/ Open
Date
10/01/2023Author
Lee, Joseph Kin Lok
Metadata
Abstract
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.