Inhomogeneous tachyon condensation

TL;DR

This paper studies the dynamics of inhomogeneous tachyon condensation in effective field theories, revealing how singularities form and proposing methods to regulate infinities, with implications for understanding tachyon matter.

Contribution

It provides a detailed analysis of inhomogeneous tachyon condensation, including the emergence of caustics and singularities, and explores regularization techniques within effective field theories.

Findings

Perturbations tend to freeze during condensation.

Finite-time development of singular second derivatives at minima.

Regularization of infinities at kinks is possible, but caustics remain.

Abstract

We investigate the spacetime-dependent condensation of the tachyon in effective field theories. Previous work identified singularities in the field which appear in finite time: infinite gradients at the kinks, and (in the eikonal approximation) caustics near local minima. By performing a perturbation analysis, and with numerical simulations, we demonstrate and explain key features of the condensation process: perturbations generically freeze, and minima develop singular second derivatives in finite time (caustics). This last has previously been understood in terms of the eikonal approximation to the dynamics. We show explicitly from the field equations how this approximation emerges, and how the caustics develop, both in the DBI and BSFT effective actions. We also investigate the equation of state parameter of tachyon matter showing that it is small, but generically non-zero. The energy density tends to infinity near field minima with a charateristic profile. A proposal to regulate infinities by modifying the effective action is also studied. We find that although the infinities at the kinks are successfully regularised in the time-dependent case, caustics still present.