2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148248We study the cosmological solutions of the two-dimensional Brans-Dicke equations considering a gas of $c=1$ strings in $S^{1}\times \mbox{\bf R}$ as the source of the gravitational field. We also study the implications of the $R$-duality invariance on the solutions. To this purpose we conjecture that, as it happens for massless fields in finite boxes, the free energy of a gas of massless string excitations is not given by the corresponding toroidal compactification.20 pages, including 10 figures in a uuencoded file (using uufiles), LaTeX, FTUAM-93/14 (LaTeX errors corrected)High Energy Physics - Theorytext