Two-dimensional String Cosmology Research Articles

The torus one-point diagram in two-dimensional string cosmology

We calculate numerically the torus one-point string diagram in the two-dimensional string cosmology background by decomposing the one-point functions in c = 1 and c = 25 Liouville CFT into torus one-point Virasoro conformal blocks and integrating over the fundamental domain of the torus moduli space. We find a remarkably simple result as a function of the outgoing closed string energy. This torus one-point diagram is expected to contribute to the one-point cosmological wavefunction at order gs, and to the four-point cosmological wavefunction at order {g}_s^2 through the disconnected product of the torus one-point diagram and the sphere three-point diagram.

A two-dimensional string cosmology

We study two-dimensional string theory on a time-dependent background, whose worldsheet description consists of Liouville theory at central charge c = 1 and Liouville theory at central charge c = 25, together with the conformal ghosts. We compute the tree-level three-point and four-point components of the cosmological wavefunction in string perturbation theory. The latter is evaluated numerically by decomposing the Liouville four-point correlation functions into Virasoro conformal blocks and three-point function coefficients and integrating over the moduli space of the four-punctured sphere string diagram. This computation numerically confirms a surprisingly simple conjectural result for the four-point wavefunction component whose physical interpretation remains to be clarified.

On `graceful exit' from inflationary phase in two-dimensional Liouville string cosmology

Within the context of a super-critical (Liouville) string, we discuss (target-space) two-dimensional string cosmology. A numerical analysis indicates that the identification of time with the Liouville mode results in an expanding universe with matter which exhibits an inflationary phase, and `graceful exit' from it, tending asymptotically to a flat-metric fixed point. This fixed point is characterized by a dilaton configuration which, depending on the initial conditions, either decreases linearly with the cosmic time, or is a finite constant. The rôle of matter in inducing such phenomena is emphasized. Although preliminary, this toy model seems to share all the features expected to characterize a phenomenologically acceptable cosmological string model.

Graceful exit problem and stress-energy-momentum tensors revisited in the two-dimensional string cosmology

We study the graceful exit problem and the role of the stress-energy-momentum tensors in the two-dimensional string cosmology. The one-loop quantum correction of conformal fields is incorporated in the arbitrary large N limit to ensure exact quantum solvability. The only solution which gives the bounded curvature with the asymptotic flatness is restricted to the first branch under some conditions. However, even in this case, the accelerating expansion is forever. We show that the only nonvanishing quantum stress-momentum tensor is the pressure part ( T xx ) which is of relevance to the dynamical evolution of the universe in the comoving coordinate. The quantum energy part is zero since the negative contribution of the induced conformal matters always cancels the positive quantity of the induced dilaton part in terms of the constraint equations.

Exact solutions in two-dimensional string cosmology with back reaction

We present analytic cosmological solutions in a model of two-dimensional dilaton gravity with back reaction. One of these solutions exhibits a graceful exit from the inflationary to the FRW phase and is nonsingular everywhere. A duality related second solution is found to exist only in the ``pre-big-bang'' epoch and is singular at $\tau = 0$. In either case back reaction is shown to play a crucial role in determining the specific nature of these geometries.

Singularity and exit problems in two-dimensional string cosmology

A broad class of two-dimensional loop-corrected dilaton gravity models exhibit cosmological solutions that interpolate between the string perturbative vacuum and a background with asymptotically flat metric and linearly growing dilaton. The curvature singularities of the corresponding tree-level solutions are smoothed out, but no branch-change occurs. Thus, even in the presence of a non-perturbative potential, the system is not attracted by physically interesting fixed points with constant dilaton, and the exit problem of string cosmology persists.