Cosmic Acceleration from topological considerations III: Lie group

TL;DR

This paper explores the idea that the universe's accelerated expansion could be explained by its topology, modeled as a principal fiber bundle with a Lie group fiber, offering an alternative to dark energy.

Contribution

It introduces a novel topological model of the universe using Lie groups as fibers in a principal fiber bundle to explain cosmic acceleration.

Findings

Accelerated expansion occurs for certain Lie group topologies.

The evolution of density parameters differs from the ΛCDM model.

Different topologies may better match observational data.

Abstract

Recent observations on the large-scale structure of the universe indicate that the cosmological constant cannot be the definitive answer to the nature of dark energy. Therefore, it is a good time to propose alternatives to understand the late-accelerated expansion of the universe. In this work we study the possibility that the acceleration of space-time is due to the topology of the universe. We assume that the topology of the universe is a principal fiber bundle whose base space is our 4-dimensional spacetime and the fiber is an $N$-dimensional Lie group that evolves with time. For the base space we consider a homogeneous and isotropic spacetime, we find that the base space is currently accelerating for $1 < N$ compact semi-simple Lie groups whose scale-factors are equal and for $1 < N$ non-Abelian Lie groups whose scale-factors are different and as long as its structure constants satisfy some conditions. However when we study the evolution of the density parameters these differ from the evolution within the $\Lambda$CDM model, this led us to think in the possibility of use a different group as fiber in order to obtain the right evolution of the density parameters. We conclude that it is possible that the accelerated expansion of the universe is due to consider a different topology of the universe as a principal fiber bundle.