Abstract
In the quest for relativistic effects in large-scale structures, we use numerical relativity simulations to describe the spacetime evolution during nonlinear structure formation. We explore how structures decouple from the expanding universe to collapse, finding criteria from the Top-Hat model to be robust estimators. Additionally, we characterise spacetime with gravito-electromagnetism, describing filaments as carrying a gravitational current, and the Petrov classification, invariantly identifying the generation of gravitational waves during this collapse.A new Einstein Toolkit thorn ICPertFLRW was developed to generate the initial conditions. These are fully nonlinear based directly on the gauge invariant comoving curvature perturbation Rc, commonly used to model early-universe fluctuations. Assigning a simple 3-dimensional sinu-soidal structure to Rc, we have a lattice of quasi-spherical over-densities representing idealised dark matter halos connected through filaments and surrounded by voids. This is implemented in the synchronous-comoving gauge, using a pressureless perfect fluid (dust) description of cold dark matter, set at an initial redshift z ≈ 300 and then fully evolved with Einstein Toolkit.
With the simulation results, we look into whether the Top-Hat spherical and homogeneous col-lapse model provides a good description of the collapse of over-densities. We find that the Top-Hat is an excellent approximation for the evolution of peaks, where we observe that the shear is negligible and collapse occurs when the linear density contrast reaches the predicted critical value δ(1) = 1.69. Additionally, we characterise the turn-around boundary and show how its evolution depends on the initial distribution of matter, finding that it grows fastest in denser directions.
While relativistic cosmology can be formulated covariantly, one concern with numerical relativity simulations is gauge variance; although observables should be gauge-invariant, simulations do not necessarily focus on their computations. To address this issue, we consider invariants built from the Weyl tensor, notably the electric and magnetic parts and the Weyl scalars (gauge-invariant at first-order in cosmology), and invariants used for the Petrov classification. We then developed the EBWeyl post-processing code, which has been thoroughly tested on five analytic metrics and can be applied to any numerical spacetime in any gauge.
In the simulation data, we look at the distribution of the electric and magnetic parts of the Weyl tensor, finding that they are stronger along and around the filaments respectively. We find that the spacetime is of Petrov type I everywhere, so we introduce a method to dynamically classify different regions at different times of the simulation box in leading order Petrov types. Along the filaments, the leading order Petrov type is D, while the centre of the over-density remains conformally flat, type O, in line with the Top-Hat model. The surrounding region demonstrates a sort of peeling-off in action, with the spacetime transitioning between different Petrov types as non-linearities grow, with the production of gravitational waves.
| Date of Award | 30 Nov 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Marco Bruni (Supervisor), Kazuya Koyama (Supervisor) & Helvi Witek (Supervisor) |