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The Theory of General Relativity (GR) is very well-tested on local Solar System scales, but tests on the largest cosmological scales have been limited by the volume and precision of existing galaxy surveys. This situation is expected to change in the coming decade with the advent of several new spectroscopic redshift surveys like desi and Euclid. In this project, we test the nature of gravity on these scales by using cosmological simulations to construct mock galaxy catalogs that mimic surveys as closely as possible. In particular, we focus on ΛCDM and three variants of the f(R) model of modified gravity: F6, F5, F4, each of which enhance the strength of gravity relative to GR with increasing intensity. Because of the inherent nonlinearity of the f(R) model, we use large-scale numerical simulations that self-consistently evolve dark matter particles according to these modified equations of motion. In computing the two-point 3D real-space correlation function of the resulting dark matter halos, we find that due to differences in the intensity of the enhancement of gravity, dark matter halos in F4 are significantly less clustered than GR, F6 is slightly less clustered, and F5 is slightly more clustered. We transform each of these halo catalogues using the Halo Occupation Distribution model, which determines the likelihood of a halo having a certain number of galaxies based upon its mass. Finally, we trim these galaxy catalogues even further by applying survey realism, ensuring that the galaxy distribution in the two cosmologies is identical to the observer., Astro 99

Previous studies have used n-body simulations to model the Hyades open cluster in an attempt to determine the initial conditions of the progenitor globular cluster at the time of its formation. In this thesis, we perform new simulation of the evolution of the Hyades using up-to-date information of its stream members using GAIA data release 2 (GAIA DR2) data. Our simulations were performed in a gravitational background potential with a co-evolving halo potential based in cosmological simulations and a static disk potential, using NBODY6++ code to compute the interactions between stars in the cluster and the gravitational background. This study produced several simulations of stellar streams with similar morphology to the observed Hyades cluster. We have performed a large grid of simulations that span a reasonable amount of the parameter space that may described the initial conditions of the Hyades star cluster, comparing final-day mass profile and morphology of the simulated streams with those of the observed stream to conclude that the Hyades’ progenitor cluster likely had an initial mass of between 1400–1600 M⊙ and an initial half-mass radius of between 4–6 pc. We found the initial position and velocity vectors of the cluster that would have resulted in its current-day position and velocity for all simulations in the parameter space, and we observed the effects of varying the mass and half-mass radius of the initial cluster on the final-day mass profile and morphology. We also performed additional tests to observe the impact of the external dark matter halo in the evolution of the star cluster., Astro 98, {"references":["Bose, S., Ginsburg, I., & Loeb, A. (2018). Dating the Tidal Disruption of Globular Clusters with GAIA Data on Their Stellar Streams. The Astrophysical Journal Letters, 859(1), 6.","Bose, S., Hellwing, W. A., Frenk, C. S., Jenkins, A., Lovell, M. R., Helly, J. C., & Li, B. (2015). The Copernicus Complexio: statistical properties of warm dark matter haloes. Monthly Notices of the Royal Astronomical Society, 455(1), 318-333.","Ernst, Just, Berczik, & Olczak. (2013). Simulations of the Hyades. ArXiv.org, 536, 29.","Hellwing, W. A., Frenk, C. S., Cautun, M., Bose, S., Helly, J., Jenkins, A., ... & Cytowski, M. (2016). The Copernicus Complexio: a high-resolution view of the small-scale Universe. Monthly Notices of the Royal Astronomical Society, 457(4), 3492-3509.","King, I. R. (1966). The structure of star clusters. III. Some simple dynamical models. The Astronomical Journal, 71, 64.","Khalisi E., Wang L., & Spurzem, R. (2019). NBODY6++; Manual for the Computer Code. Version 4.1. Updated August 13, 2019.","Küpper, A., Maschberger, T., Kroupa, P., & Baumgardt, H. (2011). Mass segregation and fractal substructure in young massive clusters – I. The McLuster code and method calibration. Monthly Notices of the Royal Astronomical Society, 417(3), 2300-2317.","Miyamoto, M., & Nagai, R. (1975). Three-dimensional models for the distribution of mass in galaxies. Publications of the Astronomical Society of Japan, 27, 533-543.","Meingast, S., & Alves, J. (2018). Extended stellar systems in the Solar neighborhood - I. The tidal tails of the Hyades. ArXiv.org, 621, ArXiv.org, Dec 14, 2018.","Perryman, M., Brown, A., Lebreton, Y., Gomez, A., Turon, C., Strobel, G., . . . Crifo, F. (1998). The Hyades: Distance, structure, dynamics, and age. Astronomy and Astrophysics, Astronomy and Astrophysics.","Smith, R., Flynn, C., Candlish, G. N., Fellhauer, M., & Gibson, B. K. (2015). Simple and accurate modelling of the gravitational potential produced by thick and thin exponential discs. Monthly Notices of the Royal Astronomical Society, 448(3), 2934-2940."]}

We use the IllustrisTNG (TNG) simulations to explore the galaxy-halo connection as inferred from state-of-the-art cosmological, magnetohydrodynamical simulations. With the high mass resolution and large volume achieved by combining the 100 Mpc (TNG100) and 300 Mpc (TNG300) volumes, we establish the mean occupancy of central and satellite galaxies and their dependence on the properties of the dark matter haloes hosting them. We derive best-fitting HOD parameters from TNG100 and TNG300 for target galaxy number densities of $\bar{n}_g = 0.032\,h^3$Mpc$^{-3}$ and $\bar{n}_g = 0.016\,h^3$Mpc$^{-3}$, respectively, corresponding to a minimum galaxy stellar mass of $M_\star\sim1.9\times10^9\,{\rm M}_\odot$ and $M_\star\sim3.5\times10^9\,{\rm M}_\odot$, respectively, in hosts more massive than $10^{11}\,{\rm M}_\odot$. Consistent with previous work, we find that haloes located in dense environments, with low concentrations, later formation times, and high angular momenta are richest in their satellite population. At low mass, highly-concentrated haloes and those located in overdense regions are more likely to contain a central galaxy. The degree of environmental dependence is sensitive to the definition adopted for the physical boundary of the host halo. We examine the extent to which correlations between galaxy occupancy and halo properties are independent and demonstrate that HODs predicted by halo mass and present-day concentration capture the qualitative dependence on the remaining halo properties. At fixed halo mass, concentration is a strong predictor of the stellar mass of the central galaxy, which may play a defining role in the fate of the satellite population. The radial distribution of satellite galaxies, which exhibits a universal form across a wide range of host halo mass, is described accurately by the best-fit NFW density profile of their host haloes., Comment: 20 pages, 13 figures, 1 table, comments welcome

Self-consistent ${\it N}$-body simulations of modified gravity models are a key ingredient to obtain rigorous constraints on deviations from General Relativity using large-scale structure observations. This paper provides the first detailed comparison of the results of different ${\it N}$-body codes for the $f(R)$, DGP, and Symmetron models, starting from the same initial conditions. We find that the fractional deviation of the matter power spectrum from $\Lambda$CDM agrees to better than $1\%$ up to $k \sim 5-10~h/{\rm Mpc}$ between the different codes. These codes are thus able to meet the stringent accuracy requirements of upcoming observational surveys. All codes are also in good agreement in their results for the velocity divergence power spectrum, halo abundances and halo profiles. We also test the quasi-static limit, which is employed in most modified gravity ${\it N}$-body codes, for the Symmetron model for which the most significant non-static effects among the models considered are expected. We conclude that this limit is a very good approximation for all of the observables considered here., Comment: 31 pages, 16 figures. Version to appear in MNRAS