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.
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Captions
Spacetime diagram of a hyperbolic universe, proper coordinates