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In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are…
The applicability of the highly idealized secondary infall model to `realistic' initial conditions is investigated. The collapse of proto-halos seeded by $3\sigma$ density perturbations to an Einstein--de Sitter universe is studied here for…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…
We perform numerical evolutions of cosmological scenarios using a standard general relativistic code in spherical symmetry. We concentrate on two different situations: initial matter distributions that are homogeneous and isotropic, and…
We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background,…
We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor…
We present a novel approach to generate higher-order initial conditions (ICs) for cosmological simulations that take into account the distinct evolution of baryons and dark matter. We focus on the numerical implementation and the validation…
Constraining cosmological parameters from large-scale structure observations requires precise and accurate tools to compute its properties. While perturbation theory (PT) approaches can serve this purpose, exploration of large parameter…
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii)…
Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of…
We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential…
Reconstructing the initial conditions of the universe is a key problem in cosmology. Methods based on simulating the forward evolution of the universe have provided a way to infer initial conditions consistent with present-day observations.…
We present a new recipe for relativistic quantum simulation using the first quantisation approach, under periodic (PBC) and Dirichlet (DBC) boundary conditions. The wavefunction is discretised across a finite grid represented by system…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
To understand the universe and to interpret the cosmological parameters governing its evolution it is necessary to contrast the data from galaxy surveys with simulation. Typically it entails using computationally expensive N -body…
In this paper we introduce a new public Einstein-Boltzmann solver, \texttt{MGCLASS II}, built as a modification to the publicly available \texttt{CLASS} code, that allows to obtain cosmological observables for Modified Gravity theories. It…