New families of singularity-free cosmological models

During the previous decade the interest for singularity-free cosmological models was supported by the publication of the first known geodesically complete perfect fluid cosmology [1]. Until then such possibility had been overlooked due to the restrictive conditions imposed by singularity theorems [2], [3]. These theorems required physically reasonable restrictions such as energy, causality and generic conditions, but they also imposed the existence of certain trapped sets, such as compact achronal sets without edge or closed trapped surfaces, which were not so obvious. Namely this latter condition is the one which has been used to avoid the formation of singularities. More details about geodesic completeness of the Senovilla spacetime may be found in [4]. Since 1990, the number of new cosmological models which were singularity-free did not increase very much, most of them within the framework of G2 orthogonally transitive spacetimes [5]. But in 2002 a family of stiff fluid cosmologies depending on two almost arbitrary functions was shown to be geodesically complete [6]. It is so far the largest family of singularity-free perfect fluid cosmologies. It was obtained requiring that the velocity of the fluid should be orthogonal to the gradient of the transitivity surface element at every point of the spacetime. In this talk we show that this restriction may be removed and thereby the family of singularity-free cosmologies is enlarged. In the next section we show the Einstein equations for G2 orthogonally transitive stiff fluid spacetimes and simplify them so that the analysis of the geodesics may be carried out conveniently. In Section 3 regularity theorems [7] are used to derive conditions on the spacetimes to be geodesically complete.