When there's no matter around, when you have nothing but the vacuum energy, there's no right or wrong way to slice it. Some ways of slicing desiter spase make it look like it's expanding. Other ways of slicing disiter space make it look as if it is stationary. So in our current universe we're exactly into sitter space - which will eventually empty out more and more. In deciter space, at any one moment, the uniform, the density, is more or less uniform.

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