Evolution of the cosmic horizons in a closed & static universe (H=Ḣ=0)

H0=67.15, Ωr=0.3, Ωm=1.1, ΩΛ=0.0073, Ωk=1-Ωr-Ωm: a_max=4.334 @ t=440.1

When ȧ=ä=0 is met, the universe gets to an unstable static equilibrium

rK=c/H0/√[-Ωk/a²], Max separation: rM=πrK, Loop: 2rM, Volume: V=2π²rK³

Colors: Hubble radius, 1/2 circumference, Particle horizon, Light cone

Gray dashed curves: worldlines of objects comoving with the Hubbleflow

Proper (r) & comoving (R) distances, Plotrange: r|R|t|η=[0…80]&[0…800]

Static | Crunch | Rip | Radiation | Matter | Milne | Hyperbolic | ΛCDM

   r(t)

↑ r(t) / ↓ R(t)

   R(t)

↑ R(t) / ↓ R(η)

   R(η)

↑ a=1 / ↓ dʲa/dtʲ=0

   r(t)

↑ r(t) / ↓ R(t)

   R(t)

↑ R(t) / ↓ R(η)

   R(η)

[Main]¦[Code]     Index: a, ȧ, ä, ã, â, H, Ḣ, Ḧ, rH, rE, rP, rL, Σr, Ω