Cosmological solutions of supercritical string theory

TL;DR

The paper investigates quintessence-driven FRW cosmologies arising from string theory in supercritical dimensions, showing the tree-level dilaton potential yields a cosmological equation of state $w= -\frac{D-3}{D-1}$ at the boundary between acceleration and deceleration and that the spacetime is globally conformally Minkowski. Through a worldsheet analysis, it constructs exact solutions with nonzero tachyon, notably a lightlike Liouville-type wall, and uses these to constrain the tachyon couplings to the dilaton and metric in the spacetime effective action, finding that the Einstein term must depend nontrivially on the tachyon. The authors derive a two-derivative effective action for the dilaton-tachyon-metric system, showing that to accommodate the tachyon, the function multiplying the Ricci scalar $R$ must be nonconstant, i.e. a tachyon-dependent Weyl rescaling between string and Einstein frames is required. Overall, the work provides a controlled framework for noncritical string cosmology and closed-string tachyon dynamics, with implications for stability and possible dynamical dimension changes in early- and late-time cosmology.

Abstract

We study quintessence-driven, spatially flat, expanding FRW cosmologies that arise naturally from string theory formulated in a supercritical number of spacetime dimensions. The tree-level potential of the string theory produces an equation of state at the threshold between accelerating and decelerating cosmologies, and the resulting spacetime is globally conformally equivalent to Minkowski space. We demonstrate that exact solutions exist with a condensate of the closed-string tachyon, the simplest of which is a Liouville wall moving at the speed of light. We rely on the existence of this solution to derive constraints on the couplings of the tachyon to the dilaton and metric in the string theory effective action. In particular, we show that the tachyon dependence of the Einstein term must be nontrivial.

Figures (9)

• Figure 1: Penrose diagram of the decelerating universe ($w > w_{\rm crit}$). The initial singularity is spacelike, and the future boundary is null.
• Figure 2: Penrose diagram of the accelerating ($-1 < w < w_{\rm crit}$) universe. The initial singularity is null, and the future spacelike boundary is obscured from observers by a horizon.
• Figure 3: Penrose diagram of the universe with critical equation of state ($w = w_{\rm crit}$). The initial singularity is null, as is the future boundary.
• Figure 4: Oriented propagators are drawn with a directed line between $X^ +$ and $X^ -$.
• Figure 5: All interaction vertices correspond to diagrams composed of outgoing lines.