The Cosmological Constant and Discrete Space-Times

TL;DR

This thesis investigates the impact of a time-dependent cosmological constant on universe expansion and explores vacuum energy in discrete extra dimensions, offering new insights into cosmological constant contributions and quantum field zero-point energies.

Contribution

It introduces a novel analysis of a dynamic cosmological constant's effects and proposes a method to determine quantum zero-point energies in discrete extra-dimensional models.

Findings

Identification of future singularities in models with evolving cosmological constants

Calculation of Casimir energy density in discrete extra dimensions

Establishment of a lower bound on the size of discrete gravitational dimensions

Abstract

In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations of scaling laws motivated by renormalisation group running and different choices for the interpretation of the renormalisation scale. Apart from well known solutions like de Sitter final states we also observe the appearance of future singularities. As the second topic we explore vacuum energy in the context of discrete extra dimensions, and we calculate the Casimir energy density as a contribution to the cosmological constant. The results are applied in a deconstruction scenario, where we propose a method to determine the zero-point energy of quantum fields in four dimensions. In a related way we find a lower bound on the size of a discrete gravitational extra dimension, and finally we discuss the graviton and fermion mass spectra in a scenario, where the extra dimensions form a discrete curved disk.