Horizons of a closed and dark energy dominated universe: ΩΛ=2, Ωk=1-ΩΛ

Colorcode: Antipode, Horizon, Hubbleradius, Particlehorizon, Lightcone

H=H₀·√[ΩΛ+(1-ΩΛ)/a²]=tanh[H₀·t·√ΩΛ]·H₀·√ΩΛ, a=√[1-1/ΩΛ]·cosh[H₀·t·√ΩΛ]

This model begins at scalefactor a=√[1-1/ΩΛ] with H=0, ä=H₀²·√[ΩΛ²-ΩΛ]

Coordinates: r(t), r(a), R(t), R(a), R(η): proper, comoving, conformal

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

   r(t)

↑ r(t) / ↓ r(a)

   r(a)

↑ r(a) / ↓ R(t)

   R(t)

↑ R(t) / ↓ R(a)

   R(a)

↑ R(a) / ↓ R(η)

   R(η)

↙ R(t) / ↓ R(a) \ ↘ R(η)

   φ(Я)

↑ Spacetime / ↓ Functions

   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