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Accounting for large-scale structure in our universe will require not only reasonably accurate mathematical models of its cosmogony, topology and cosmology, but also a more deeper understanding of our fundamental physical concepts of space,…
In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions…
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation…
The new frontier of cosmology will be led by three-dimensional surveys of the large-scale structure of the Universe. Based on its all-sky surveys and redshift depth, the SKA is destined to revolutionize cosmology, in combination with future…
We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer…
Modeling galaxy formation in a cosmological context presents one of the greatest challenges in astrophysics today, due to the vast range of scales and numerous physical processes involved. Here we review the current status of models that…
Measuring the sum of the three active neutrino masses, $M_\nu$, is one of the most important challenges in modern cosmology. Massive neutrinos imprint characteristic signatures on several cosmological observables in particular on the…
We present a new method for simulating cosmologies that contain massive particles with thermal free streaming motion, such as massive neutrinos or warm/hot dark matter. This method combines particle and fluid descriptions of the thermal…
The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure…
In this paper we describe the set of ``New Worlds Simulations'', three very large cosmology simulations, Qo'noS, Vulcan, and Ferenginar, that were carried out on the Summit supercomputer with the Hardware/Hybrid Cosmology Code, HACC. The…
The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing pressure, which is justified only for…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…
Theoretical models for structure formation with Gaussian initial fluctuations have been worked out in considerable detail and compared with observations on various scales. It is on nonlinear scales $\lsim 10 \ h^{-1}\ {\rm Mpc}$ that the…
A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations…
With the beginning of the XXIst century, a physical model of our Universe, usually called the Standard Cosmological Model (SCM), is reaching an important level of consolidation, based on accurate astrophysical data and also on theoretical…
Accelerating expansion of the Universe is a great challenge for both physics and cosmology. In light of lacking the convincing theoretical explanation, an effective description of this phenomenon in terms of cosmic equation of state turns…
We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial Fourier mode amplitudes are fixed to the…
Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary…
A new varying-$c$ cosmological model constructed using two additional assumptions, which was introduced in our previous work, is briefly reviewed and the dynamic equation of the model is derived distinctly from a semi-Newtonian approach.…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…