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We show how to exploit symmetry assumptions to determine the dynamical equations for the particular geometry that underpins given matter field equations. The procedure builds on the gravitational closure equations for matter models without…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
Chameleon scalar fields can screen their associated fifth forces from detection by changing their mass with the local density. These models are an archetypal example of a screening mechanism, and have become an important target for both…
We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link…
We investigate the cosmological dynamics of a class of supersymmetric chameleon models coupled to cold dark matter fermions. Supergravity corrections ensure that these models are efficiently screened in all astrophysical objects of…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that…
Initial conditions for cosmological N-body simulations are usually calculated by rescaling the present day linear power spectrum obtained from an Einstein-Boltzmann solver to the initial time employing the scale-independent matter growth…
Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…
We show how standard Newtonian N-body simulations can be interpreted in terms of the weak-field limit of general relativity by employing the recently developed Newtonian motion gauge. Our framework allows the inclusion of radiation…
We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…
We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level…
Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…
Multiple modifications of general relativity (GR) have been proposed in the literature in order to understand the nature of the accelerated expansion of the Universe. However, thus far all the predictions of GR have been confirmed with…
In this work we study the cosmological simulations as a tool to understand the formation of large-scale structure of the universe, for this, we show the equivalence of Newtonian cosmology with Poisson gauge and we study the solution of the…
Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. To study the coupling between a Klein-Gordon equation and…
One of the main objectives of stage IV galaxy surveys is to constrain gravity on cosmological scales. To this end, it is crucial to make accurate theoretical predictions in the nonlinear regime of structure formation in order to maximise…
We study the lattice Green's function (LGF) of the screened Poisson equation on a two-dimensional rectangular lattice. This LGF arises in numerical analysis, random walks, solid-state physics, and other fields. Its defining characteristic…
Chameleon gravity is a scalar-tensor theory that includes a non-minimal coupling between the scalar field and the matter fields and yet mimics general relativity in the Solar System. The scalar degree of freedom is hidden in high-density…