Determinación numérica del espectro de fluctuaciones escalares de paredes de dominio

Abstract

The present work aimed to calculate the scalar fluctuations on a 4-dimensional static domain wall embedded in a 5-dimensional space-time in coordinates according to begin with, the double wall solution to the Scalar Field Einstein system and the perturbations of the gravitational stage are taken as a starting point, the excitations of the metric were separated into tensor, vector and scalar modes, the latter determined by a pair of equations Schrödinger type whose eigenfunctions share the same eigenvalue except for the zero mode. These equations were solved by separating the tensor, vector and scalar modes, to finally arrive at two Schrödinger-type solutions for the scalar modes that act on the domain wall, finding scalar states located in 4 dimensions. Those equations are solved thereby of the numerical method called half increment using Mathematica software, both equations thanks to a change of variable can be treated as one, and these solutions that can give us more information about the problem treated, giving us a very strong indication about the concordance of our universe, with the one proposed by the present work, however, we must take into account the restrictions used, being one of them the fact that when breaking the symmetry of the double wall, it is when it can actually observe the phenomenon of the localization of scalar fluctuations.