ar X iv : h ep - t h / 93 06 07 0 v 1 1 6 Ju n 19 93 225 /

We apply CGHS-type dilaton gravity model to (1+1)-dimensional cosmological situations. First the behavior of a compact 1-dimensional universe (i.e. like a closed string) is classified on the assumption of homogeneity of universe. Several interesting solutions are found, which include a Misner-type universe having closed time-like curves, and an asymptotically de Sitter universe first pointed out by Yoshimura. In the second half of this talk, we discuss the modification of the classical homogeneous solutions, considering inhomogeneity of classical conformal matters and also quantum back-reaction respectively. ⋄ An expanded version of the talk presented by T. Mishima at Yukawa Institute of Theoretical Physics workshop ‘Quantum Gravity’ (24-27, November 1992). † On leave of absence from Institute for Nuclear study, University of Tokyo, Midori-cho, Tanashi-shi, Tokyo 188, Japan ∗ e-mail address: [email protected]