Abstract:
The universe is initially highly homogeneous but then develops large inhomogeneities through gravitational dynamics. This is due to the classical dynamics of the particles, which tend to fall into the minimum of the potential. Particles that are in underdense regions are attracted to neighboring overdense regions, so that initially overdense regions become denser and denser, and underdense ones become emptier and emptier. This process creates large clumps of matter connected by filaments and separated by large voids. This inhomogeneous distribution of matter in the Universe is known as the cosmic web. The gravitational evolution of the inhomogeneities can be studied by using N-body simulations, a dynamical model of the Universe made up of a large number of particles which can be solved numerically on a computer. Some (many) of these particles end up in high-density regions called halos.
In the initial conditions we refer to protohalos as the regions that will collapse and form halos. This thesis aims to find the initial characteristics of the regions that contain particles that will end in high density regions called halos. The protohalos are the progenitors of halos, in the sense that they are the regions occupied by halo particles in the initial conditions. These regions will collapse and shrink to form halos.
There is a density field in the protohalo region which generates a potential because all the particles in the field attract the other particles and all these particles that attract each other develop a potential energy field and we have to look at the minimum of the potential energy region because this is where the particles will pile up and form a high density region. the physically relevant quantity for the formation of a protohalo is the energy of the protohalo region because dynamically the energy is the quantity that determines the evolution time of a system.
Among the available data in the output of an N-body simulation are the initial positions and velocities of the particles that belong to the protohalos. It is known that the position of the center of mass of the protohalo is well described by minima of the energy field (Marcello Musso and
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Ravi K. Sheth, 2021). And the next step will be about determining whether their shape is also described by the energy field. The aim of this thesis is to test numerically whether this hypothesis is correct, constructing the energy of the protohalo regions from the initial positions and velocities of their particles.
