Dynamical solutions in the 3-Form Field Background in the Nishino-Salam-Sezgin Model

TL;DR

This paper explores dynamical 3-form flux compactifications in a six-dimensional model, revealing limited cosmological evolution and conditions for expanding or contracting 3-space, with implications for brane-world cosmology.

Contribution

It introduces new dynamical solutions in the Nishino-Salam-Sezgin model, analyzing their cosmological implications and the behavior of internal space and 3-space evolution.

Findings

Time evolution restricted to internal azimuthal dimension

Existence of expanding and contracting 3-space solutions

Accelerating solutions with diverging scale factor

Abstract

We investigate the dynamical 3-form flux compactifications and their implications for cosmology in our brane world in the six-dimensional Nishino-Salam-Sezgin model, which is usually referred to as the Salam-Sezgin model. We take the background of the 3-form field acting on the internal space and timelike dimensions without the U(1) gauge field strength. The first class of solutions we discuss is the dynamical generalization of the static solutions obtained recently. In this class, we find that the time evolution is restricted only in the azimuthal dimension of the internal space and not in the ordinary three-dimensional one, which does not give a cosmological evolution. The second class of solutions is obtained by exchanging the roles of the radial coordinate and the time coordinate from the assumptions in the first class. At the center of the internal space, there is a conical singularity which may be interpreted as our 3-brane world, but it is difficult to realize a warped structure in the direction of the ordinary 3-space. Except for the oscillating solutions, a dynamical evolution leads to expanding or contracting ordinary 3-space, depending on the choice of time direction. Furthermore, in the expanding solutions, there are decelerating and accelerating ones: In the latter solution, the evolution is sustained for a finite proper time and the scale factor of the 3-space diverges.