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f(R) gravity is one of the simplest generalizations of general relativity, which may explain the accelerated cosmic expansion without introducing a cosmological constant. Transformed into the Einstein frame, a new scalar degree of freedom…
We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(N lg N) computational complexity through an embedded metric-query, allowing hierarchical application of…
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method.…
We model the chameleon effect on cosmological statistics for the modified gravity f(R) model of cosmic acceleration. The chameleon effect, required to make the model compatible with local tests of gravity, reduces force enhancement as a…
We present asevolution, a cosmological N-body code developed based on gevolution, which consistently solves for the (a)symmetron scalar field and metric potentials within the weak-field approximation. In asevolution, the scalar field is…
We present a simple physically motivated picture for the mildly non-linear regime of structure formation, which captures the effects of the bulk flows. We apply this picture to develop a method to significantly reduce the sample variance in…
A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to…
Special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating N-body systems in astrophysics are presented, explained and compared…
We summarize the present state of research on the darkon fuid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional…
Infrared modifications of General Relativity (GR) can be revealed by comparing the mass of galaxy clusters estimated from weak lensing to that from infall kinematics. We measure the 2D galaxy velocity distribution in the cluster infall…
We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the…
In this work we demonstrate a surprising way of exploitation of the mosaic--skeleton approximations for efficient numerical solving of aggregation equations with many applied kinetic kernels. The complexity of the evaluation of the…
The Layzer-Irvine equation describes energy conservation for a pressure less fluid interacting though quasi-Newtonian gravity in an expanding Universe. We here derive a Layzer-Irvine equation for scalar field theories where the scalar field…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of a modulated plane wave. In this regime, the solution exhibits rapid oscillations in both time and space,…
We present a new test of the modified gravity endowed with the Vainshtein mechanism with the density profile of a galaxy cluster halo observed through gravitational lensing. A scalar degree of freedom in the galileon modified gravity is…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…
Accurate predictions for the non-linear matter power spectrum are needed to confront theory with observations in current and near future weak lensing and galaxy clustering surveys. We propose a computationally cheap method to create an…
We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the {\tt ECOSMOG} code. Our simulations include the Vainshtein screening…
Studying the dynamical, nonlinear regime of modified theories of gravity remains a theoretical challenge that limits our ability to test general relativity. Here we consider two generally applicable, but approximate methods for treating…