Abstract
I first focus on how to best describe the space of cosmological space–times and what its essential properties are and some comments on the dynamical behavior revealed by studies that will be described in more detail by John Wainwright. I will then relate this both to observations and to anthropic issues (i.e. the possible existence of observers). This space includes some viable singularity free solutions which will be briefly described, thus posing the issue of the tension between very special initial conditions and the existence of initial singularities. I will conclude with remarks on the issue of realized infinities in this context and the concept of multiverses.
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