JB:"It is regularly stated by cosmologists that there is "nothing outside the universe". What is "nothing"."
The nothing in your quote means that there is nothing else besides our universe. Or in other words that there is no "outside" for our universe, only the "inside".
JB:"A four-dimensional Euclidean space-time will have these properties because the time axis is perpendicular to the space axes. This implies that any differential within three-dimensional space with respect to time will have to be zero."
Nah, it ain't working that way. First of all, the spacetime is not euclidean, is lorentzian, so time is pseudo-orthogonal on the space, so to speak.
Second of all, the time derivative in a foliation is not vanishing, unless you really don't know mathematical analysis. The difference being that you do not calculate d/dt[a(t_fixed)] but d/dt[a(t)]|t=t_fixed.
Maybe our universe is flying apart to unbend space-time towards a state of zero entropy; as it had been before creation?
