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In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or…
This paper is concerned with theories of gravity that contain a scalar coupled both conformally and disformally to matter through the metric. By systematically deriving the non-relativistic limit, it is shown that no new non-linear…
We offer predictions of symmetron modified gravity in the neighborhood of realistic dark matter halos. The predictions for the fifth force are obtained by solving the nonlinear symmetron equation of motion in the spherical NFW…
In this paper we present a novel fast method to solve Poisson equation in an arbitrary two dimensional region with Neumann boundary condition. The basic idea is to solve the original Poisson problem by a two-step procedure: the first one…
The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…
A possible gluon-condensate-induced modified-gravity model with f(R) \propto |R|^{1/2} has been suggested previously. Here, a simplified version is presented using the constant flat-spacetime equilibrium value of the QCD gluon condensate…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
Current constraints on f(R) gravity from the large-scale structure are at the verge of penetrating into a region where the modified forces become nonlinearly suppressed. For a consistent treatment of observables at these scales, we study…
As an entry for the 2012 Gordon-Bell performance prize, we report performance results of astrophysical N-body simulations of one trillion particles performed on the full system of K computer. This is the first gravitational trillion-body…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
Different efficient and accurate numerical methods have recently been proposed and analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter $\varepsilon\in (0,1]$, which is inversely proportional to the speed…
Nonlinear scalar-tensor theories of gravity have been considered as candidates for dark matter and dark energy. Often, they possess screening mechanisms, which allow the fifth force mediated by the additional scalar degree(s) of freedom to…
We generalise the SuperEasy linear response method, originally developed to describe massive neutrinos in cosmological $N$-body simulations, to any hot dark matter (HDM) species with arbitrary momentum distributions. The method uses…
Modified gravity models require a screening mechanism to be able to evade the stringent constraints from local gravity experiments and, at the same time, give rise to observable astrophysical and cosmological signatures. Such screened…
Modifications of gravity have been considered to model the primordial inflation and the late-time cosmic acceleration. Provided that modified gravity models do not suffer from theoretical instabilities, they must be confronted with…
Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique…