Compact self-gravitating solutions of quartic (K) fields in brane cosmology

TL;DR

This paper investigates the existence and stability of compacton domain walls in brane cosmology models with non-standard kinetic (K) fields coupled to gravity, revealing conditions for their stability and the influence of gravitational parameters.

Contribution

It provides a detailed analytical and numerical analysis of compacton domain walls in K field theories with gravity, including stability conditions and parameter correlations.

Findings

Existence of compacton domain walls depends on gravitational and cosmological constant parameters.

Linear perturbations are confined within the compacton domain wall, behaving normally despite non-standard kinetics.

Stability requires specific correlations between gravitational constant and bulk cosmological constant.

Abstract

Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. Firstly, K field theories allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Secondly, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Thirdly, when gravity is taken into account, location of gravity in the sense of Randall--Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant, which is thoroughly analyzed.