Relativistic Effects in Cosmological Simulations

In this PhD thesis I present the implementation of a method to study the evolution of the large scale structure in a weak-field approximation of General Relativity. Our starting point is the assumption that we can reproduce the classical evolution of the universe with an N-body code in which small scales---below 1 Mpc---interactions are particle-to-particle in the Newtonian limit, while in the large scales these interaction are mediated through the relativistic gravitational field in the weak-field approximation. We have implemented this idea by first redesigning Gevolution code from a monolithic application into a relativistic Particle-Mesh (PM) library libgevolution. Then we have modified Gadget4, a Newtonian TreePM code, adding libgevolution as a plug-in replacement to its original Newtonian PM. This project goes by the name of GrGadget. The advantage of a combined Tree+PM approach with respect to a pure PM method lies in the fact that we can simulate huge cubic boxes, with a length of the order of the 2 Gpc/h, representing a portion of the visible universe and still be able to resolve structures where dark matter halos hosting galaxies are formed on scales below 100 kpc/h using reasonable computational resources. Furthermore one can scale the size of the box without necessarily needing to increase the memory requirements or sacrifying the small scale resolution. Running GrGadget we have also realized that failing to resolve the non-linear structures, for example in the case of a pure PM code, would underestimate the amplitude of the highest Fourier modes of the relativistic fields by more that a 30% factor.

In this PhD thesis I present the implementation of a method to study the evolution of the large scale structure in a weak-field approximation of General Relativity. Our starting point is the assumption that we can reproduce the classical evolution of the universe with an N-body code in which small scales---below 1 Mpc---interactions are particle-to-particle in the Newtonian limit, while in the large scales these interaction are mediated through the relativistic gravitational field in the weak-field approximation. We have implemented this idea by first redesigning Gevolution code from a monolithic application into a relativistic Particle-Mesh (PM) library libgevolution. Then we have modified Gadget4, a Newtonian TreePM code, adding libgevolution as a plug-in replacement to its original Newtonian PM. This project goes by the name of GrGadget. The advantage of a combined Tree+PM approach with respect to a pure PM method lies in the fact that we can simulate huge cubic boxes, with a length of the order of the 2 Gpc/h, representing a portion of the visible universe and still be able to resolve structures where dark matter halos hosting galaxies are formed on scales below 100 kpc/h using reasonable computational resources. Furthermore one can scale the size of the box without necessarily needing to increase the memory requirements or sacrifying the small scale resolution. Running GrGadget we have also realized that failing to resolve the non-linear structures, for example in the case of a pure PM code, would underestimate the amplitude of the highest Fourier modes of the relativistic fields by more that a 30% factor.