Determinación numérica de la localización de campos de materia sobre una pared de dominio con expansión De-Sitter

Abstract

The purpose of this work was to locate fields of matter on a 4-dimensional dynamic domain wall (dS4) contained in a 5-dimensional space-time, for which, it was started from the resolution of the Coupled Einstein-Scalar Field System, to obtain the equation of motion of the scalar field. The fermions were then coupled to the domain wall using a Yukawa term, to later find the eigenvalue equation that describes the fluctuations of the fermionic fields in those wall. For the resolution of the aforementioned equation, two scenarios were taken into account, a symmetric and an asymmetric wall, likewise, the left and right part, present due to the chirality of the fermionic fields, was analyzed. The resolution was carried out through the use of numerical methods, specifically, the half-increment method, which was developed thanks to the Mathematica software tools, obtaining as a result two located states for the left part and one for the right part. (both from the symmetric and asymmetric part), where it was observed that the state found in the right potential corresponds approximately to the value of the second state found in the left potential, which provides a positive result because it is known that the Potentials are supersymmetric partners.