  Cosmological solutions of the beta function equations for the background
fields of the closed bosonic string are investigated at the one-loop level.
Following recent work of Kostelecky and Perry, it is assumed that the spatial
sections of the space-time are conformally flat. Working in the sigma-model
frame, the non-trivial tachyon potential is utilized to determine solutions
with sufficient inflation to solve the smoothness and flatness problems. The
graceful exit and density perturbation constraints can also be successfully
implemented.
