GOWDY COSMOLOGY AND 2-DIMENSIONAL GRAVITY

We obtain the Gowdy cosmology by compactifying (3 + 1)-dimensional general relativity on a two-torus T2. We fix the conformal gauge in the resulting effective (1 + 1)-dimensional theory and show that it is equivalent to a nonlinear sigma model with a background minisuperspace metric and a background minisuperspace dilaton field. We generalize the Gowdy model by introducing a nonzero cosmological constant and nonzero theta angle and show that it is equivalent to a nonlinear sigma model with a background minisuperspace tachyon field and a background minisuperspace antisymmetric tensor field, respectively. The minisuperspace backgrounds do not lead to vanishing beta functions; in some cases, however, it is possible to shift the minisuperspace dilaton field to obtain vanishing beta functions in a manner similar to that of the Liouville model.