Milne universe: Ωk=1; a=H₀·t; H=H₀/a=1/t; rH=c·t;

Metric: ds²=c²·dT²-dx²=(c²-H²r²)·dt²+H·r·dt·dr-dr²;

Transformation: ř=r/rH; v=c·tanh[dr/dt/c];

dx=(dr-dt·r/t)·cosh[ř]+c·dt·sinh[ř];

dT=dt·cosh[ř]+(dr·t-dt·r)·sinh[ř]/c/t;

x=c·t·sinh[ř];

T=t·cosh[ř];

dr=[c·(dx·T-dT·x)+(c²·dT·T-dx·x)]·arccoth[c·T/x]/√[(c·T)²-x²];

dt=(c²·dT·T-dx·x)/c²/√[T²-x²/c²];

r=R·a=c·t·arctanh[v]=√[(c·T)²-x²]·arctanh[x/T/c];

t=T·√[1-v²/c²]=√[T²-(x/c)²];