Cosmological solutions of supercritical string theory

We study quintessence-driven, spatially flat, expanding Friedmann-Robertson-Walker 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.

Figure 1

Penrose diagram of the decelerating universe ($w>w_{\mathrm{crit}}$). The initial singularity is spacelike, and the future boundary is null.

Figure 2

Penrose diagram of the accelerating ($-1<w<w_{\mathrm{crit}}$) 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 ($w=w_{\mathrm{crit}}$). 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.

Figure 6

Generic structure of OPEs in the lightlike tachyon background.

Figure 7

A bubble of nothing, which destroys spacetime. If the exterior is flat with vanishing dilaton gradient, the bubble properly accelerates all the way to future infinity. If the exterior has a flat string-frame metric and timelike linear dilaton gradient, the spatial thickness of the diagonal line approaches ${\alpha }^{\prime }|\dot{\Phi }|$ as $t\to \infty$. Our solution corresponds to a limit that focuses on the upper left-hand corner of the diagram.

Figure 8

A plot of the position of a particle pushed by the bubble wall, as a function of time. The solution has ${\mu }^2=1$, $\beta =0.1$, $X_0^{\pm }=0$, and the trajectory corresponds to $p^{+}=3$, $H_{\perp }\equiv \frac{{\alpha }^{\prime }{p}_i^2}{2}=4$. We set ${\alpha }^{\prime }=1$.

Figure 9

A plot of the velocity of a particle accelerated by the bubble wall, as a function of time. (Numerical values are set in accordance with the trajectory depicted in Fig. 8 above.)