(Quantum Cosmology) Non-Linear General Relativity for Stochastic Inflation

Abstract for professionals

My PhD project will advance the early universe theory of inflation, which explains the origin of galaxies and large-scale structure in the Universe, by developing stochastic methods with nonlinear evolution to make quantitative statistical predictions from inflationary models. Non-Gaussian signatures are inherently present in primordial fluctuations due to the non-linearities produced by both general relativity and the fact that the inflaton potential responsible for driving inflation may be interacting.
The goal of this project is to analytically and numerically model nonlinear inflationary dynamics in order to make bispectrum and higher-order correlator predictions which encompass a much broader range of inflationary scenarios, including those with multiple fields. This is an important discriminant between competing inflation models that can be used to distinguish them observationally.
An important element of the project will be to exploit the new GRChombo numerical relativity pipeline to model these nonlinear effects using full 3D general relativistic simulations, comparing the results with perturbative analytic expectations from effective field theory. In the last years, consequent insights have been made by the DAMTP cosmology group lead by Dr. Paul Shellard, now able to constrain a wide range of these models by using innovative separable techniques to extract and reconstruct the bispectrum (three-point correlator) from Planck satellite maps of the cosmic microwave background (CMB). Direct confrontation with new observational data sets, from both CMB experiments (Simons Observatory) and galaxy surveys (SDSS, DES etc), will guide and constrain the understanding of inflation in fundamental physics.
Stochastic nonlinear methods have other wide-ranging applications, including the creation of primordial black holes and the generation of gravitational waves in the early universe.

Abstract for newcomers

I work on the cosmology of the early universe. This means finding the best mathematical description of the first few seconds of the universe, considering it as a dynamic system, and testing the predictions of this model against real astrophysical data. In particular, I will predict the distribution in space of the different types of energy and matter at any time using a promising theory called Stochastic Inflation. Inflation refers to the first instants of the universe which allowed an exponential growth of its size – and since then, the universe kept expanding. Stochastic refers to the mathematical description of the early universe’s quantum fluctuations; random fluctuations of energy in the initial vacuum propagated in time and produced an inhomogeneous universe; e.g. today super cluster of galaxies against empty millions of light years.
There is a time at which those perturbations are big enough to be accounted for with the rival theory of quantum physics: the General Relativity of Albert Einstein, which describes gravity between massive objects (e.g.; solar system; you and the Earth). We can make predictions about the future of these growing quantum perturbations from an Inflation model by using a numerical simulation of gravity. By doing so, I hope to support the growing link between these two theories (Quantum Physics and General Relativity). This requires ambitious simulation software, and so I am a member of the GRChombo collaboration which develops such code.

(Quantum Cosmology) Slow-roll oscillating non-Gaussianities from singular kinetic pre-inflationary universe

Abstract for professionals

Modern inflation theory is based on Mukhanov-Sasaki equations which give a perturbative framework to propagate initial quantum fluctuations as sources of the Cosmic Microwave Background (CMB) anisotropies encountered at the recombination epoch. Following previous work on initial conditions for the power spectrum, this work extends the kinetic pre-inflation model to the derivation of the primordial bispectrum, related to 3-point correlations. We derive here the main perturbations contributing to the bispectrum thanks to the In-In formalism for different initial conditions of a simple constant slow-roll and single-field inflation. In addition to an oscillating locally-shaped bispectrum, it is found that the dependence on the time and nature of the transition between pre-inflation and inflation is strong. As a main result, UV and IR divergences are encountered for the non-Gaussianities, showed to be independent of the choice of the vacuum and so treated within the assumption of an old transition time compared to the experimental cutoff.

Abstract for newcomers

This work studied a particular model of initial conditions for the universe, i.e. of a type of inflationary universe. While most models don't incorporate any origin and focus on the inflation process itself, this model combine both aspects by providing an initial singularity at the start and then propagates the subsequent universe into a "kinetic" era before transitioning to the usual models with a stable inflation of the apparent size of the universe. As this is quite a peculiar formulation, usual mathematical tools to compute post-inflation observable quantities need some careful study. This is what we did to compute the correlation between each 3 points of the sky at the time of the Hot Big-Bang following Inflation.

(Cosmology) Optimal combination of the spatial correlation function and galaxy cluster counts

Abstract

To understand the story of the universe, physicists have identified cosmological observables : the CMB, supernovae but also galaxy clusters hosting most of the matter in the universe. From these last ones, many direct and indirect observables can be reconstructed including galaxy clusters counts and space correlations. Between these two, correlations are expected and encourage the exploration of a unification of two distinct formalisms - at least in the refinement of cosmological parameters.

(Quantum Cristallography) N-Representable one-electron reduced density matrices reconstruction at non-zero temperatures

Abstract

This article retraces different methods that have been explored to account for the atomic thermal motion in the reconstruction of one-electron reduced density matrices from experimental X-ray structure factors (XSF) and directional Compton profiles (DCP). Attention has been paid to propose the simplest possible model, which obeys the necessary N-representability conditions, while accurately reproducing all available experimental data. The deconvolution of thermal effects makes it possible to obtain an experimental static density matrix, which can directly be compared with theoretical 1-RDM (reduced density matrix). It is found that above a 1% statistical noise level, the role played by Compton scattering data becomes negligible and no accurate 1-RDM is reachable. Since no thermal 1-RDM is available as a reference, the quality of an experimentally derived temperature-dependent matrix is difficult to assess. However, the accuracy of the obtained static 1-RDM, through the performance of the refined observables, is strong evidence that the Semi-Definite Programming method is robust and well adapted to the reconstruction of an experimental dynamical 1-RDM.

(Game Theory) Nash equilibirum in network games

Abstract

In this work, I studied games called 'Shapley Network Design' which model the passage from A to B with a fixed number of paths and travellers. I derived the general Nash equilibrium for quadratic costs and compared it to the optimal equilibrium obtained thanks to a genetic algorithm.