A general method for transforming non-physical configurations in BPS states

TL;DR

This paper introduces a method to transform non-physical BPS configurations into physically meaningful states across various scalar field models, with applications in cosmology and condensed matter.

Contribution

The authors develop a novel procedure to convert non-physical BPS solutions into valid states, expanding the applicability of BPS methods in different physical contexts.

Findings

Identified non-physical BPS configurations in a complex scalar field model.

Proposed a transformation procedure to recover physical BPS states.

Applied the method to cosmological models with compatible parameters.

Abstract

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model.In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named non-physical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.