M-theory resolution of four-dimensional cosmological singularities via U-duality

We consider cosmological solutions of string and M-theory compactified to f our dimensions by giving a general prescription to construct four-dimension al modular cosmologies with two commuting Killing vectors from vacuum solut ions. By lifting these solutions to higher dimensions we analyze the existe nce of cosmological singularities and find that, in the case of non-closed Friedmann-Robertson-Walker universes, curvature singularities are removed f rom the higher-dimensional model when only one of the extra dimensions is t ime-varying. By studying the moduli space of compactifications of M-theory resulting in homogeneous cosmologies in four dimensions we show that U-dual ity transformations map singular cosmologies into non-singular ones. (C) 20 00 Elsevier Science B.V. All rights reserved.