Abstract
The NobelPrizewinning detection of gravitational waves (GWs) in 2015 opened up a brand new window into observational cosmology, paving the way for the use of GWs to search directly for signatures of new physics. Moreover, recent computational developments in numerical relativity (NR) allow us to investigate Einstein’s equations in regimes where the gravitational force is strong – a very promising area to test and search for physics beyond the standard model of cosmology. In this thesis we will focus in the use of numerical relativity to investigate the strongfield regime of the early universe.We will start by studying inflation, the current paradigmatic theory of the Big Bang that assumes a period of accelerated expansion to explain why the current universe is homogeneous and isotropic at the largest cosmological scales. The prevalent mechanism is to use a scalar field that is assumed to homogeneously rolldown a modeldependent potential, extracting the energy that drives the accelerated expansion. However, if such a process can only begin in cases where the universe is already smooth, it becomes, to some extent, redundant. In this thesis we will derive and test a simple analytical criterion to predict if inflation can begin from inhomogeneous initial conditions. We will show that convex and concave potentials that vary on superPlanckian scales are significantly more robust than those that vary on subPlanckian scales.
Then, we will pioneer the use of gravitational waves to detect cosmic strings, relics that are expected to have been formed after a phase transition in the early universe, and one of the key targets of the current LIGO/Virgo/KAGRA (LVK) detector searches. We will present the first fully general relativistic dynamical simulations of abelian Higgs circular cosmic strings loops that collapse and can either (i) unwind and disperse or (ii) form a black hole. To maximise the discovery potential of such events – often obscured by background noise in the detectors – we will construct their timedomain gravitationalwave strain waveform, which features a lowfrequency infall followed by a characteristic merger and ringdown, with a large contribution of GW memory.
Lastly, we will simulate the formation of primordial black holes (PBHs) from sub and superhorizon perturbations in a matter dominated universe with numerical relativity. We will discuss the two primary mechanisms of formation that depend on the initial perturbation mass and its geometry – via direct collapse of the initial overdensity and via postcollapse accretion of the ambient dark matter. In both cases, we will confirm that the process occurs around a Hubble time, and the initial mass of the black hole is MBH ∼ 10−2H−1M2 Pl. We will also discuss how post formation, the PBH undergoes rapid mass growth beyond the selfsimilar limit M ∝ H−1, showing that most its final mass is accreted from the ambient dark matter.
Date of Award  1 May 2022 

Original language  English 
Awarding Institution 

Supervisor  Eugene Lim (Supervisor) & Diego Blas (Supervisor) 