A general thick brane supported by a scalar field

TL;DR

This paper investigates thick brane models supported by scalar fields in 5D gravity, revealing conditions for their structure, asymptotic behavior, and the relation to the Randall-Sundrum model, including the existence of solution families.

Contribution

It establishes the conditions under which scalar field supported thick branes have AdS asymptotics and connects their thin brane limit to the RS2 model, introducing a family of solutions with varying potentials.

Findings

Thick branes always have AdS asymptotics far from the brane.

Existence of solutions requires the potential to change sign and satisfy a fine-tuning condition.

A family of solutions with different potentials can be generated due to scale invariance.

Abstract

A thick Z_2-symmetric domain wall supported by a scalar field with an arbitrary potential V(\phi) in 5D general relativity is considered as a candidate brane world. We show that, under the global regularity requirement, such a configuration (i) has always an AdS asymptotic far from the brane, (ii) is only possible if V(\phi) has an alternating sign and (iii) V(\phi) satisfies a certain fine-tuning type equality. The thin brane limit is well defined and conforms to the Randall-Sundrum (RS2) brane world model if the asymptotic value of V(\phi) (related to \Lambda, the effective cosmological constant) is kept thickness-independent. Universality of such a transition is demonstrated using as an example exact solutions for stepwise potentials of different shapes. Also, due to scale invariance of the Einstein-scalar equations, any given regular solution creates a one-parameter family of solutions with different potentials. In such families, a thin brane limit does not exist while the ratio \Lambda/(brane tension)^2 is thickness-independent and is in general different from its value in the RS2 model.