Expanding Universe in Milne Coordinates

If we have a particle (X,Y,Z,T) = (a(T),a(T),a(T),T) in comoving coordinates, in Milne coordinates this is:

t=T cosh( a(T)*sqrt(3) )
x=T/sqrt(3) * sinh( sqrt(3)*a(T) )

which gives a parametric equation in T. We can plot these curves. e.g. for linear expansion we have the lines a(T) = v.T for various constants v.

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