Cosmologies with Two-Dimensional Inhomogeneity

We present a new generating algorithm to construct exact non static solutions of the Einstein eld equations with two-dimensional inhomogeneity. In nite dimensional families of G1 inhomogeneous solutions with a self interacting scalar eld, or alternatively with perfect uid, can be constructed using this algorithm. Some families of solutions and the applications of the algorithm are discussed. Recently there has been a considerable interest in scalar eld cosmologies. This interest is related to the studies of in ationary models where the scalar eld (in aton) acts as the main driving force for in ation. On the other hand, one of the most important issues related to the in ationary scenario is how sensitive are the in ationary models to the change in the initial conditions [1]. The dependence of the in ationary scenario on the initial conditions is usually studied either numerically or perturbatively, under some simplifying assumptions, or analytically, within the framework of exact solutions using cosmological models with a high degree of symmetry. Until now, it was only possible to study exact scalar eld cosmological models with one dimensional inhomogeneity [2]. The main purpose of this letter is to make a step further in the study of exact inhomogeneous cosmologies by presenting a new generating algorithm to obtain solutions with a single isometry. The algorithm allows one to obtain spacetimes with homogeneity broken in two directions from already known ones with one dimensional inhomogeneity. One starts with a vacuum orthogonal G2 cosmology which is well studied and some general solutions for certain topologies are known (for a recent review see Ref. [3].) Then, by using a known algorithm the solution is transformed into a massless scalar eld G2 cosmology. The second step involves a conformal transformation which breaks the G2 symmetry leaving one with the solution with the G1 symmetry but with a self interacting scalar eld with a Liouville type of potential. Our algorithm generalizes a recently proposed solution generating technique developed by Fonarev [4], which is only valid for static metrics. To this end we consider a vacuum G2 cosmology with the following line element ds = e( dt + dz) +G(t; z) edx + e dy : (1) If pv; Gv and fv represent a vacuum solution of the Einstein eld equations then, by using a simpli ed version of the Charach-Malin [5] algorithm the following solution p = B pv + C logGv f = fv + E pv + F logGv (2) = Apv +D logGv