Abstract
Despite the successes of the standard model of cosmology, the search for solutions to the singularity problem and problems with the cosmological constant continue. Nonsingular bouncing and emer- gent cosmologies provide an alternative scenario for the origin of the universe, perhaps without the need of a quantum gravity era. Writing a system as a set of ordinary differential equations and com- pleting a dynamical systems analysis is useful to understand the qualitative behaviour of a model, and investigate whether singularity can be avoided.In this thesis, we explore the dynamics of Friedmann-Lemaître-Robertson-Walker cosmologies which go beyond ΛCDM. First, we analyse the range of dynamical behaviour admitted by a system consisting of cold dark matter, radiation and dark energy with a quadratic equation of state that evolves between two effective cosmological constants. We find that all models are nonsingular for any initial condition, provided that dark matter and radiation are produced after the bounce, for example in a period of reheating. We then consider parameter values for the dark energy component, such that non-singular models emerge between Planck and inflationary scales, and at late-times approach a low energy effective cosmological constant consistent with observations. However, we find that the class of models left does not allow for an early- and late-time accelerated expansion, connected by a decelerating period where large-scale structure could form.
We also complete a dynamical systems analysis of the original emergent universe scenario, to understand whether emergence can come from a non-singular state replacing the typical singularity of General Relativity, for any initial condition. We find that only a subset of initial conditions leads to emergence, either from a static Einstein state, as in the original emergent model, or from a de Sitter state.
Finally, we study the dynamics when a dark energy with a quadratic equation of state interacts with cold dark matter. We find there are parameter ranges for this system such that trajectories always expand from a high energy non-singular de Sitter state for any initial condition. For flat and negative curvature models this de Sitter state is represented by a fixed point, the asymptotic past from which the universe emerges. We find a subset of positive curvature models that during contraction get arbitrarily close to the de Sitter state, thus having a quasi-de Sitter bounce, then emerge from the bounce and expand, evolving toward spatial flatness. We find a subclass of models in which all trajectories have at least one decelerated matter dominated phase, and accelerate at late-times as they evolve towards an effective low energy cosmological constant. We also find that the dark energy can evolve over large energy scales, therefore this model could help to alleviate the cosmological constant problem.
| Date of Award | 7 Aug 2025 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Marco Bruni (Supervisor), David Wands (Supervisor) & Johannes Noller (Supervisor) |