Time and Tachyon

TL;DR

This work investigates the time-dependent dynamics of a tachyon on unstable D-branes described by a scalar Born-Infeld action with a runaway potential, showing that late-time configurations map to non-interacting dust with $u_\mu=-\partial_\mu T$ and rest density $\varepsilon(x)=|\Pi|/\sqrt{1+(\nabla T)^2}$. By coupling this tachyon action to gravity, the author recasts the Hamiltonian constraints into a form compatible with canonical quantization, enabling a many-fingered time Schrödinger equation in which the tachyon field $T$ serves as the time variable; at late times a subsector decouples from gravity, recovering the Wheeler–DeWitt equation of vacuum gravity. The analysis clarifies when and how the tachyon can play the role of intrinsic time in quantum cosmology, while also clarifying the early-time regime where $T$-dependence persists due to the potential and higher-derivative corrections. The results provide a concrete link between open-string tachyon dynamics and dust-like matter in GR, suggesting a path to defining time in quantum gravity and offering insights into the interplay between tachyon condensation and gravitational quantization.

Abstract

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born-Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of non-interacting (incoherent), non-rotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late `time' we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler - de Witt equation of quantum gravity.