New nondiagonal singularity-free cosmological perfect-fluid solution.

We present a new non-diagonal G2 inhomogeneous perfect-fluid solution with barotropic equation of state p = ρ and positive density everywhere. It satisfies the global hyperbolicity condition and has no curvature singularity anywhere. This solution is very simple in form and has two arbitrary constants. PACS Numbers: 04.20-Jb; 04.20-Cv; 98.80-Dr. The study of exact inhomogeneous cosmological models is mainly motivated by the fact that our Universe is not strictly spatially homogeneous. It was extensively believed until very recently that all the cosmological models (homogeneous or not) had to originate in a big-bang singularity whenever they satisfied an energy condition for the matter contents and the model contained matter everywhere. This belief was greatly reinforced by the powerful singularity theorems [1]. However, in a remarkable letter published by J.M.M. Senovilla in 1990 [2], a new perfect-fluid inhomogeneous cosmological solution without big-bang singularity and without any other curvature singularity was presented. The matter contents of that solution satisfied a realistic equation of state for radiation dominated era p = ρ/3 with density (and therefore pressure) positive everywhere. In a subsequent paper [3] this solution was shown to be geodesically complete and satisfying causality conditions such as global hyperbolicity. It was also proven that the singularity theorems for the existence of incomplete geodesics could not be applied in that case because they need some boundary or initial conditions, such as the existence of a causally trapped set, which did not hold in that case. In consequence, the existence ∗Also at Laboratori de F́ısica Matemàtica, IEC, Barcelona.