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Summary

Description
Deutsch: Comoving worldlines (gray dashed), Lightcone RL (orange), Hubbleradius RH (blue), Particlehorizon RP (green), Event horizon RE (purple), Antipode RM (pink) in a closed inflationary universe (ΩΛ=2, Ωk=-1). Coordinates: comoving distances R by conformal time η=RP/c (x=R, y=η). This model begins with a nonzero scale factor of a=√(1-1/ΩΛ) where H=0, ä=H0²√(ΩΛ²-ΩΛ). The horizontal purple line is at t=∞, η=22.8708 Gyr (we set H0=67.15 km/s/Mpc at a=1).
Date
Source Own work, relativity.yukterez.net/o/closedlambda.html
Author Simon Tyran, Vienna (Yukterez)
Other versions
big crunch universe (Ωr=2, Ωk=-1) proper
big crunch universe (Ωr=2, Ωk=-1) comoving
big crunch universe (Ωr=2, Ωk=-1) conformal
big crunch universe (Ωr=2, Ωk=-1) polar
big crunch universe (Ωm=2, Ωk=-1) proper
big crunch universe (Ωm=2, Ωk=-1) comoving
big crunch universe (Ωm=2, Ωk=-1) conformal
big crunch universe (Ωm=2, Ωk=-1) polar
closed inflationary universe (ΩΛ=2, Ωk=-1) proper
closed inflationary universe (ΩΛ=2, Ωk=-1) comoving
closed inflationary universe (ΩΛ=2, Ωk=-1) conformal
closed inflationary universe (ΩΛ=2, Ωk=-1) polar
flat universe (Ωr=1) proper
flat universe (Ωr=1) comoving
flat universe (Ωr=1) conformal
flat universe (Ωm=1) proper
flat universe (Ωm=1) comoving
flat universe (Ωm=1) conformal
hyperbolic universe (Ωk>0, ΩΛ=0) proper
hyperbolic universe (Ωk>0, ΩΛ=0) comoving
hyperbolic universe (Ωk>0, ΩΛ=0) conformal
big rip universe (Ωr+Ωm+ΩΛ=1) proper
big rip universe (Ωr+Ωm+ΩΛ=1) comoving
big rip universe (Ωr+Ωm+ΩΛ=1) conformal
flat universe (Ωr+Ωm+ΩΛ=1) proper
flat universe (Ωr+Ωm+ΩΛ=1) comoving
flat universe (Ωr+Ωm+ΩΛ=1) conformal
milne model (Ωk=1) proper
milne model (Ωk=1) comoving
milne model (Ωk=1) conformal
milne model (Ωk=1) minkowski

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Captions

Spacetime diagram of a closed inflationary universe, conformal time

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25 January 2025

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Date/TimeThumbnailDimensionsUserComment
current21:53, 27 January 2025Thumbnail for version as of 21:53, 27 January 20253,840 × 1,712 (107 KB)Yukterez1 digit was off
13:50, 26 January 2025Thumbnail for version as of 13:50, 26 January 20253,840 × 1,712 (107 KB)Yukterezincreased the numerical precision to the max
01:10, 26 January 2025Thumbnail for version as of 01:10, 26 January 20253,840 × 1,712 (107 KB)Yukterezmaking the initial scale factor as close as numerically possible to a0=√(1-1/ΩΛ)
23:00, 25 January 2025Thumbnail for version as of 23:00, 25 January 20253,840 × 1,712 (104 KB)YukterezUploaded own work with UploadWizard

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