File:Hyperbolic.universe.proper.coordinates.png

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    Summary

    Description
    English: Comoving worldlines (gray dashed), Lightcone rL (orange), Hubbleradius rH (blue) & Particlehorizon rP (green) in a hyperbolic universe. Initial parameters at a=1: Ωr=0.000092136, Ωm=0.315, ΩΛ=0, H0=67.15 km/Mpc/s (Ωr includes photons and neutrinos). Those are the same parameters as in our current ΛCDM model, but with Ωk instead of ΩΛ. Coordinates: proper distances r by cosmic time t (x=r, y=t). The lightcone origin is at t=13.842 Gyr. The big bang is at the bottom of the vertical t axis.
    Date
    Source Own work, relativity.yukterez.net/o/hyperbolic.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
    phantom energy (w=-2/3) proper
    phantom energy (w=-2/3) comoving
    phantom energy (w=-2/3) conformal
    big rip universe (w=-4/3) proper
    big rip universe (w=-4/3) comoving
    big rip universe (w=-4/3) 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

    Licensing

    I, the copyright holder of this work, hereby publish it under the following license:
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    Captions

    Spacetime diagram of a hyperbolic universe, proper coordinates

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    3 January 2025

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    Date/TimeThumbnailDimensionsUserComment
    current12:08, 5 January 2025Thumbnail for version as of 12:08, 5 January 20253,840 × 2,096 (315 KB)wikimediacommons>Yukterezpixel cosmetics

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