This work identifies the initial conditions of general relativistic magnetohydrodynamic (GRMHD) simulations of both the electroweak and quantum chromodynamic phase transitions. Each phase transition has a well known vacuum expectation value associated with it, which will be the starting point for each calculation. Energy, temperature, scale factor, Hubble parameter, time, thermal degrees of freedom, dark matter density, regular matter density and radiation density are the nine parameters that will be found for each phase transition. Some of the parameters are needed to calculate others, and some of the parameters are direct inputs required by our computer code. In addition, the magnitude of velocity variations as well as density and temperature perturbations is found using numerical simulations. The data generated by these inputs combined with the evolution equations can be analyzed to determine if the simulation conforms to the Friedmann-Robertson-Walker (FRW) model and whether or not the hypothesized values are accurate.

We present the results of General Relativistic Magnetohydrodynamic simulations utilizing initial conditions from both the Electroweak and Quantum Chromodynamic (QCD) phase transitions in order to determine if seed magnetic fields may be generated via the Biermann Battery Mechanism of Magnetogenesis. These simulations occur in a simulated early universe between 10(-11) s and 10(3) s after the Big Bang. We find that magnetic fields greater than 10(-20) G may be generated on the Mpc scale. This is believed to be strong enough to generate the large intergalactic magnetic fields seen today. Further work is needed to understand how these fields may have impacted the large-scale structures we currently observe.

We present the results of Relativistic Magnetohydrodynamic simulations utilizing initial conditions from both the Electroweak and quantum chromodynamics phase transitions to see if seed magnetic fields may be generated via the Biermann battery mechanism of magnetogensis. These simulations occur in a simulated early universe between 10 −11 s and 10 –3 s after the Big Bang. We find that magnetic fields on the order of 10 −19 G are generated on small scales and magnetic fields of 10 −25 G are generated on the Mpc scale. Further work is needed to understand how these fields may have impacted the large‐scale structures we observe today.

We describe a technique for using simulated tensor perturbations in order to place upper limits on the intensity of magnetic fields in the early universe. As an example, we apply this technique to the beginning of primordial nucleosynthesis. We determined that any magnetic seed fields that existed before that time were still in the process of being amplified. In the future, we plan to apply this technique to a wider range of initial magnetic fields and cosmological epochs.

The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence using numerical simulations. Many researchers simply assume that relativistic turbulence has the same invariants and obeys the same dynamics as non-relativistic systems. Our results show that this assumption may be incorrect.

This work is a follow-up to the paper, Numerical Relativity as a Tool for Studying the Early Universe. In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an averaging process as opposed to conventional methods of gravitational wave extraction using a complex Weyl scalar. We calculate the normalized energy density, strain and degree of polarization of gravitational waves produced by a simulated turbulent plasma similar to what was believed to have existed shortly after the electroweak scale. This calculation is completed using two numerical codes, one which utilizes full General Relativity calculations based on modified BSSN equations while the other utilizes a linearized approximation of General Relativity. Our results show that the spectrum of gravitational waves calculated from the nonlinear code using an averaging process are nearly indistinguishable from those calculated from the linear code. This result validates the use of the averaging process for gravitational wave extraction of cosmological systems.

Physics Department, University of Houston Clear Lake, Houston, Texas 77058E-mail: garrison@uhcl.eduAbstract. This work is a follow-up to the paper, "Numerical Relativity as a Toolfor Studying the Early Universe". In this article, we present the rst results of directnumerical simulations of primordial plasma turbulence as it applies to the generation ofgravitational waves. We calculate the normalized energy density, strain and degree ofpolarization of gravitational waves produced by a simulated turbulent plasma similar towhat was believed to have existed at the electroweak scale, 246 GeV. This calculationis completed using two numerical codes, one which utilizes full General Relativitycalculations based on modi ed BSSN equations while the other utilizes a linearizedapproximation of General Relativity. Our results show that there is a signi cantdi erence between the spectrum of gravitational waves calculated using a nonlinearcode as opposed to that calculated with a linear approximation. This implies thatsimulations that do not take into account nonlinear e ects may not give accurateresults.

In this paper, we study the dynamics of the Chern-Simons Inflation Model proposed by Alexander, Marciano and Spergel. According to this model, inflation begins when a fermion current interacts with a turbulent gauge field in a space larger than some critical size. This mechanism appears to work by driving energy from the initial random spectrum into a narrow band of frequencies, similar to the inverse energy cascade seen in MHD turbulence. In this work we focus on the dynamics of the interaction using phase diagrams and a thorough analysis of the evolution equations. We show that in this model inflation is caused by an over-damped harmonic oscillator driving waves in the gauge field at their resonance frequency.

Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, 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 a 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.

We present results of numerical simulations of the Chern-Simons inflation model proposed by Alexander, Marciano, and Spergel. According to this model, inflation begins with a fermion condensate interacting with a gauge field. Crucial to the success of this mechanism is the assumption that the Chern-Simons interaction would drive energy from the initial random spectrum into a narrow band of frequencies at superhorizon scales. In this work, we numerically confirm this expectation. These gauge fields and currents, when combined with the Friedmann equations, were broken into a system of hyperbolic equations and numerically simulated. It was found in our simulation that, by including the effects of the chiral anomaly for the axial vector current, inflation can end satisfactorily after approximately 60 e-folds.

In this talk I discuss an often over-looked aspect of most cosmological models, dynamical interactions caused by gravitational waves. I begin by reviewing our current state of cosmological knowledge and gravitational waves. Then, I review work done to understand the nature of primordial magnetic fields. Finally, I combine the ideas of gravitational wave theory and plasma turbulence to develop a new theory of cosmic structure formation. Eventually, this work could help to explain the distribution of mass-energy in the observable universe as well as the anisotropies in the Cosmic Microwave Background without a heavy dependence on dark matter. This work seeks to explain how the dense, hot, turbulent plasma of protons, neutrons, electrons and neutrinos cooled in the presence of gravitational waves to form into structures and develop a statistical mechanics to describe this dynamical system.

As Cosmologists struggle to understand the evolution of our universe, an often over-looked element is the affect of gravitational radiation on the primordial plasma field. This appears to be due to the inaccurate approximation of the primordial plasma field as a simple hydrodynamic fluid, therefore neglecting the full dynamics of the magneto-fluid. In this paper, we show how gravitational waves may have had a significant impact on the evolution of our universe. While more work is needed, the author hopes to eventually develop a large-scale simulation of structure formation in the early universe, which takes the interactions of scalar perturbations, gravitational waves, magnetic fields and a dynamic plasma field into account.

Some theories suggest that gravitational waves created in the early universe may be observable with future gravitational wave interferometers. As a result, identifying the characteristics of these gravitational waves and their corresponding power spectrums at different epochs has become an important area of study. The general solutions to these equations can become quite complex, making the task of obtaining analytical results a difficult one without simplifying assumptions. Using numerical techniques, a general solution to the birefringent gravitational wave equation is explored. This form of the gravitational wave equation is partly composed of a mode function that resembles the Coulomb wave equation from quantum mechanics, which has been explored computationally in the past. An attempt is then made to numerically solve these equations and the corresponding power spectrum for the present universe. Current/planned observatories such as LISA and Advanced LIGO can test these results.