Exact solutions in the Dirac-Born-Infeld effective theory and the fate of tachyon

TL;DR

This paper derives exact solutions in the Dirac-Born-Infeld theory for scalar fields, revealing that late-time tachyon behavior resembles massless scalars rather than pressureless matter, challenging previous assumptions about tachyon matter.

Contribution

It provides exact solutions in the DBI effective theory and clarifies the late-time behavior of tachyon fields, showing they act as massless scalars rather than pressureless matter.

Findings

Massive and massless oscillating scalars are not pressureless for any momenta.

Late-time tachyon behaves as a massless scalar of zero modes.

Modified potentials can prevent caustic singularities near the vacuum.

Abstract

We show that the equation of motion from the Dirac-Born-Infeld effective action of a general scalar field with some specific potentials admits exact solutions after appropriate field redefinitions. Based on the exact solutions and their energy-momentum tensors, we find that massive scalars and massless scalars of oscillating modes in the DBI effective theory are not pressureless generically for any possible momenta, which implies that the pressureless "tachyon matter" forming at late time of the tachyon condensation process should not really be some massive matter. It is more likely that the tachyon field at late time behaves as a massless scalar of zero modes. At kinks, the tachyon can be viewed as a massless scalar of a translational zero mode describing a stable and static D-brane with one dimension lower. Near the vacuum, the tachyon in regions without the caustic singularities can be viewed as a massless scalar that has the same zero mode solution as a fundamental string moving with a critical velocity. We find supporting evidences to this conclusion by considering a DBI theory with modified tachyon potential, in which the development of caustics near the vacuum may be avoided.