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Summary

Description
English: R(t), R(a) & R(η) diagrams as polar φ(я) projections. Comoving worldlines (gray dashed), Lightcone RL (orange), Hubbleradius RH (blue), Particlehorizon RP (green) and Antipode RM (purple) in a closed universe (Ωr=2, Ωk=-1). Coordinates: comoving distances R by cosmic time t (φ=R, я=t,a,η). The Lightcone origin is at the turning point at Scalefactor a=√2 and t=√2/H0 when the Hubbleparameter H=0 and the universe is between expansion and contraction. The Big Bang is at the center of the diagram.
Date
Source Own work, relativity.yukterez.net/o/bigcrunch.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 diagrams of a closed radiation dominated big crunch universe, polar projections

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26 January 2025

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Date/TimeThumbnailDimensionsUserComment
current23:01, 31 January 2025Thumbnail for version as of 23:01, 31 January 20255,860 × 1,960 (401 KB)Yukterezincrease border to avoid cropping at resize
22:30, 31 January 2025Thumbnail for version as of 22:30, 31 January 20255,760 × 1,920 (419 KB)YukterezUploaded own work with UploadWizard

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