Milne universe (disguised Minkowski): Ωk=1, a=H₀·t, H=H₀/a=1/t, rH=c·t

Colors: World lines, Hubble radius, Light cone, Constant t, Constant T

Transformation: T=t·cosh[r/c/t], x=c·t·sinh[r/c/t], vₓ=c·tanh[dr/dt/c]

r=R·a=c·t·arctanh[vₓ]=√[(c·t)²-x²]·arctanh[x/c/t], t=T/γ=√[T²-(x/c)²];

Proper (r), Comoving (R), Minkowski (x). Plot range: t|η|T|r|R|x=0..70

Static | Crunch | Rip | Radiation | Matter | Milne | Hyper | Λk | ΛCDM

   r(t)

↑ r(t) / ↓ R(t)

   R(t)

↑ R(t) / ↓ R(η)

   R(η)

↑ R(η) / ↓ x(T)

   x(T)

↑ a=1 / ↓ a=3

   r(t)

↑ r(t) / ↓ R(t)

   R(t)

↑ R(t) / ↓ R(η)

   R(η)

↑ R(η) / ↓ x(T)

   x(T)

↑ R(η) / ↓ f(t)

   f(t)

Static | Crunch | Rip | Radiation | Matter | Milne | Hyper | Λk | ΛCDM

Main |  Code | Info | a, ȧ, ä, ã, â, H, Ḣ, Ḧ, rH, rE, rP, rL, Σr, Ω