Time-Like Extra Dimension and Cosmological Constant in Brane Models

TL;DR

This paper explores models with time-like and space-like extra dimensions in brane-world scenarios, analyzing their configurations, solutions, and implications for the effective 4D cosmological constant.

Contribution

It constructs general brane models with mixed time-like and space-like extra dimensions and classifies solutions with zero bulk cosmological constant.

Findings

Existence of static solutions with both time-like and space-like extra dimensions.

Non-static solutions can have only space-like extra dimensions.

Explicit examples of simplest models and their implications for 4D cosmological constant.

Abstract

We discuss the general models with one time-like extra dimension and parallel 3-branes on the space-time $M^4 \times M^1$. We also construct the general brane models or networks with $n$ space-like and $m$ time-like extra dimensions and with constant bulk cosmological constant on the space-time $M^4\times (M^1)^{n+m}$, and point out that there exist two kinds of models with zero bulk cosmological constant: for static solutions, we have to introduce time-like and space-like extra dimensions, and for non-static solutions, we can obtain the models with only space-like extra dimension(s). In addition, we give two simplest models explicitly, and comment on the 4-dimensional effective cosmological constant.