Milne universe, Minkowskian Big Bang: Ωk=1; a=H0·t; H=H0/a=1/t; rH=c·t

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

Coordinates: Proper r(t) | Comoving R(t) | Conformal R(η) | Radar x(T)

Transformation: x=c·t·sinh[ř]; T=t·cosh[ř]; v=c·tanh[dr/dt/c]; ř=r/t/c

r=c·t·arctanh[v]=√[c²T²-x²]·arctanh[x/T/c]; t=T·√[1-v²/c²]=√[T²-x²/c²]

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