Gravitational-Scalar Instability of a Cosmological Model Based on a Two-Component System of Degenerate Scalarly Charged Fermions with asymmetric Higgs Interaction. II. WKB-Aapproximation

TL;DR

This paper investigates the evolution of short-wavelength gravitational-scalar perturbations in a cosmological model with degenerate scalarly charged fermions, revealing the emergence of unstable modes through analytical and numerical methods.

Contribution

It introduces a WKB-approximation approach and a computational program to analyze perturbations, highlighting the instability of certain short-wavelength modes in the model.

Findings

Unstable short-wavelength perturbation modes are identified.

A numerical model for perturbation evolution is developed.

A connection between perturbation evolution and eigenvalue problems is established.

Abstract

Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the problem of eigenvectors and eigenvalues of a linear operator. By means of an applied mathematical package, a program for calculating the amplitudes of perturbations of the cosmological model was created. It is shown that unstable short-wavelength perturbation modes arise in such a system. A numerical model for the evolution of gravitational-scalar perturbations of the cosmological model has been constructed and analyzed.