String compactifications and early universe cosmology

This PhD project explores the interplay between string compactification mechanisms and early universe cosmology, with a particular focus on the phenomenon of kination and its impact on string moduli dynamics. The nature of the universe between inflation and nucleosynthesis is unknown. The goal of this project is to study this epoch and explore how the dynamics of moduli fields-arising from the compactification of extra spatial dimensions-can naturally lead to a period in the early universe where kinetic energy dominates over potential energy, a phase commonly referred to as kination, and observational signatures that result from this.

Research Context: String theory posits the existence of extra spatial dimensions, the shape and size of which are determined by moduli fields. These fields, which include the dilaton, volume modulus, and complex structure moduli, are crucial as they encode information about the geometry of the compactified dimensions and ultimately influence the four-dimensional effective field theory. Approaches such as flux compactifications, non-perturbative effects (like gaugino condensation and instanton contributions), and perturbative correction can stabilise moduli under certain conditions. However, these methods often leave open questions regarding the dynamics of these fields in the very early universe, particularly during cosmological epochs where their evolution can have significant observational consequences.

Research Objectives:1. Model Building and Compactification Schemes-Develop and analyse models of string compactifications that incorporate realistic stabilization mechanisms for moduli fields.This involves exploring various scenarios including flux compactifications, the inclusion of non-perturbative corrections, and loop-level effects to generate stable potentials for the moduli. The project will systematically classify these models according to their ability to yield controlled moduli dynamics in the early universe. 2. Dynamical Analysis of Strong Moduli-Investigate the time evolution of moduli fields in the context of early universe cosmology. 3. Kination and Cosmological Implications-Explore the phenomenological consequences of a kination phase driven by moduli evolution.

Methodology: The research methodology combines advanced analytical techniques with state-of-the-art numerical simulations. Initially, theoretical models will be developed using effective field theory approaches to describe the low-energy dynamics of moduli fields derived from string compactifications. This will be followed by a detailed dynamical systems analysis to characterize fixed points, attractor solutions, and transition phases, particularly the onset of kination. Numerical simulations will be used to explore the non-linear regime where perturbations grow large.
Expected Contributions and Impact: This PhD project is expected to provide significant contributions to our understanding of both string theory and early universe cosmology. By bridging the gap between abstract string compactification models and observable cosmological phenomena, the research aims to: i)Demonstrate that a kination phase can naturally arise from string moduli evolution and delineate its implications for cosmic evolution ii)Offer potential observational signatures-such as distinctive gravitational wave spectra or altered relic densities-that could provide indirect evidence for a string theory-driven kination epoch in cosmological data.

Overall, this project aims to determine how the microphysics of extra dimensions may leave an observable imprint on the evolution of the early universe.
This project falls within he STFC particle physics research area.