Dynamical systems in scalar-tensor cosmology

Abstract

The value of the Hubble constant, H0, as predicted using Cosmic Microwave Background (CMB) data under the ΛCDM model stands at a 5σ tension with that obtained from measurements of Cepheid variables. Efforts to find a solution to this Hubble tension focus significantly on modifications of ΛCDM prior to the emission of the CMB. However, it has been claimed that only a combination of new physics in the early and late Universe, and new local physics can ultimately resolve the tension. The aim of this work is to examine whether these modifications to early- and late-time physics still approach the evolution observed in ΛCDM. Scalar fields, with dynamics governed by their potential energy, were introduced within the concordance model, and the expansion of the Universe was analysed using the framework of dynamical systems and phase portraits. Three free, self-interacting potentials were examined, with the dynamics obtained being similar throughout. While these models reproduced the expected ΛCDM evolution with a new epoch occurring before recombination in which the early-time modifications dominate the expansion, significant fine-tuning of the boundary conditions of the system was required to achieve this. In an attempt to mitigate this issue, an additional model was analysed, in which the potential energy was dampened by a tempering function, localizing the respective field to reach a maximum at a specific point in the history of the universe. While this also reproduced the previous evolution, the tempering did not resolve the fine-tuning issues of the model. Despite these problems, such modifications can reproduce the evolution of the Universe as predicted by ΛCDM, making further research in this area, possibly focusing on resolving the fine-tuning problem, a promising avenue to pursue.