Self-tuning solution of the cosmological constant problem with antisymmetric tensor field

TL;DR

This paper proposes a self-tuning mechanism using an antisymmetric tensor field in a 5D warped geometry to address the cosmological constant problem, avoiding fine-tuning and allowing for de Sitter and anti-de Sitter solutions.

Contribution

It introduces a novel self-tuning solution involving a three-index antisymmetric tensor field with a $1/H^2$ term, enabling a vanishing cosmological constant without fine-tuning.

Findings

Existence of self-tuning solutions without fine-tuning.

The solution accommodates shifts in brane tension.

De Sitter solutions with horizons are possible.

Abstract

We present a self-tuning solution of the cosmological constant problem with one extra dimension which is curved with a warp factor. To separate out the extra dimension and to have a self-tuning solution, a three index antisymmetric tensor field is introduced with the $1/H^2$ term in the Lagrangian. The standard model fields are located at the $y=0$ brane. The existence \cite{kklcc} of the self-tuning solution (which results without any fine tuning among parameters in the Lagrangian) is crucial to obtain a vanishing cosmological constant in a 4D effective theory. The de Sitter and anti de Sitter space solutions are possible. The de Sitter space solutions have horizons. Restricting to the spaces which contain the $y=0$ brane, the vanishing cosmological constant is chosen in the most probable universe. For this interpretaion to be valid, the existence of the self-tuning solution is crucial in view of the phase transitions. In this paper, we show explicitly a solution in case the brane tension shifts from one to another value. We also discuss the case with the $H^2$ term which leads to one-fine-tuning solutions at most.