Inhomogeneous tachyon decay, light-cone structure and D-brane network problem in tachyon cosmology

TL;DR

This paper studies how light-cone structures on unstable D-branes with inhomogeneous tachyon decay reveal the behavior of open strings, kink formation, and implications for a D-brane network in early universe cosmology.

Contribution

It provides a detailed analysis of light-cone structures during tachyon decay, highlighting differences between open and closed strings and their dynamics near kinks, with implications for cosmological models.

Findings

Open strings are redshifted and become non-dynamical except at kinks.

Open strings on kinks can move freely along the kink surface.

Light-cone tilting indicates open strings tend to move towards kinks.

Abstract

We investigate light-cone structure on the world-volume of an unstable D-brane with a tachyon decaying inhomogeneously by using a field theoretical description. It is shown that (i) light-cones governing open strings are narrower than those governing closed strings and will eventually collapse inward in all directions except at kinks, where the tachyon remains at the top of its potential; and that (ii) light-cones governing open strings at a kink will be narrowed only in the direction perpendicular to the kink surface. It is also shown that (iii) future-directed light-cones governing open strings near a kink are tilted towards the kink, compared with those governing closed strings. The result (i) implies that open strings except at kinks are redshifted, compared with closed strings, and will eventually cease to be dynamical. On the other hand, the result (ii) shows that open strings on a kink surface can move freely along the kink surface and are dynamical but do not feel the existence of the spatial dimension perpendicular to the kink surface. The result (iii) indicates that open strings near a kink have tendency to move towards the kink. Hence, the light-cone structure vividly illustrates how open strings behave during the dynamical formation of a kink. We also discuss about a possibility that the early universe has a network of various dimensional D-branes, black-branes and tachyon matter. A problem associated with the network and a possible solution to the problem are discussed.