Tachyon field theory description of (thermo)dynamics in dS space

TL;DR

This paper explores the connection between de Sitter space dynamics and tachyon field theory on unstable D-branes, revealing geometric and thermal parallels, including tachyon condensation and phase transitions to closed strings.

Contribution

It demonstrates that geodesic motion in dS space matches tachyon field theory, providing a geometric picture of tachyon condensation and linking dS thermodynamics to string phase transitions.

Findings

Geodesic motion in dS space corresponds to tachyon condensation.

Tachyon radiation temperature matches the dS temperature, both being Hagedorn.

Bulk dS phase transition to closed strings is characterized by tachyon dynamics.

Abstract

In this work, we present a few pieces of evidence in support of a possible connection of the gravitational theory in dS space to the worldvolume theory of unstable D-branes. We show that the action describing the geodesic motion of a massive particle (or point-like object) in static dS space turns out to be the same as that of the tachyon field theory for an unstable particle. The motion along the radial direction from the origin, a locally Minkowski spacetime, to the horizon, a locally Rindler space times a sphere, represents just the tachyon condensation process, therefore providing a geometric picture of tachyon condensation. We further study a scalar in global or flat dS and the tachyon fluctuations in a homogeneous tachyon background, representing either the full or half S-brane, on unstable D-branes and find that certain dynamics of the dS universe corresponds to that of the homogeneous full or half S-brane. The thermal temperature of tachyon radiation is found to agree with that felt by any timelike observer in dS space. In string theory context, this temperature is just the Hagedorn one, signaling a phase transition to closed strings. An understanding of this transition in the bulk dS space is also given.