Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this paper, we show how the framework of numerical relativity can be used for studying cosmological models. The author is working to develop a large-scale simulation of the dynamical processes in the early universe. These take into account interactions of dark matter, scalar perturbations, gravitational waves, magnetic fields, and turbulent plasma. The code described in this report is a GRMHD code based on the Cactus framework and is structured to utilize one of several different differencing methods chosen at run-time. It is being developed and tested on the University of Houston’s Maxwell cluster. 1. Introduction Our knowledge of how the universe evolved comes primarily from observations of large structures such as stars, galaxies, clusters, and super-clusters of galaxies as well as from observations of the cosmic microwave background (CMB) radiation. Based on these observations, the standard model of cosmology was developed during the mid to late twentieth century. Some elements of this model include the existence of primordial metric perturbations, magnetic fields, and an early universe filled with nearly homogenous and isotropic plasma [1]. The perturbed Friedmann-Robertson-Walker (FRW) metric, which describes the spacetime curvature of the early universe, takes the following form: Here is the scale factor and , , , and are the scalar, vector, and tensor perturbation terms. Many cosmological models relate density fluctuations and variations in the CMB to perturbations in the FRW metric at the time of recombination. These perturbations start off small and grow as a power-law with time as the competing forces of universal expansion and gravitational attraction affect their growth [1]. Work by Kodama and Sasaki [2], Sachs and Wolfe [3], and Mukhanov et al. [1] all showed analytically how metric perturbations could cause density perturbations in a hydrodynamic fluid. Recently, beyond the standard model cosmological theories, [4] has suggested that primordial fluids and fields are potential sources of observable gravitational waves. This realization opens up exciting new possibilities, making primordial gravitational radiation an important source of information about the early universe. Taken together, this leads to the idea that there was a dynamical interaction between matter, electromagnetic, and gravitational fields in the early universe that affected the evolution of our universe. Signatures of these interactions
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