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

TL;DR

This paper investigates the graceful exit problem in two-dimensional string cosmology, demonstrating that quantum corrections lead to a universe with eternal acceleration and identifying the key role of pressure in the quantum stress-energy tensor.

Contribution

It provides an exact quantum solution incorporating one-loop corrections, revealing conditions for bounded curvature and the dominance of pressure in the quantum stress-energy tensor.

Findings

Bounded curvature with asymptotic flatness occurs in the first solution branch.

Quantum energy contributions cancel out, leaving pressure as the main dynamical factor.

The universe exhibits eternal acceleration under the studied conditions.

Abstract

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 equation.