1. z = 0: The present in cosmic time measured from the ideal cosmic time zero of Big Bang cosmology: i.e., the Big-Bang singularity which was at lookback time equal to the age of the observable universe = 13.797(23) Gyr (Planck 2018).

2. z = 10,000: Which is a bit earlier than radiation-to-matter-dominance transition epoch (cosmic time ∼ 47,000 years, cosmic redshift z=3600) (see Wikipedia: Chronology of the universe: Matter domination; Wikipedia: Scale factor (cosmology): Matter-dominated era; Wikipedia: Age of the universe = 13.797(23) Gyr (Planck 2018)).

3. z = ∞: The ideal cosmic time zero, the time of the Big-Bang singularity which was at lookback time equal to the age of the observable universe = 13.797(23) Gyr (Planck 2018). In fact, virtually all cosmologists do NOT believe the Big-Bang singularity is real. The real observable universe probably tracks into Big Bang cosmology no earlier (and probably somewhat later) than the Planck epoch, 10**(-43) s after the ideal cosmic time zero.

On a log-log plot, the main divisions axes are in powers of 10 rather than in equal amounts.
1. Logarithmic plots are useful for plotting quantities that vary by orders of magnitude---we need them all the time in astronomy.
2. By the by, in the jargon of logarithmic plots, a dex is a factor of 10.
3. On the log-log plots in the Image 1 and Image 2, the large tick marks are separated by factors of 10 (i.e., 1 dex). The small tick marks in each dex are at factors of 2, 5, and 8.

      z = (λ_observed-λ_rest)/λ_rest ,

where λ_observed is the observed wavelength and λ_rest is the wavelength in the rest frame of emission. Note z is dimensionless number (i.e., it has no units).

Cosmological redshift is itself the most easily obtained high accuracy/precision direct-observable cosmic distance measure.

Thus, it the most basic direct-observable cosmic distance measure and astronomers customarily use it in preference to all others which harder to obtain and usually much less accurate/precise or are model-dependent which means NOT direct NOR indirect observables.

The upshot is that cosmological redshift is the natural independent variable for plots displaying the other cosmic distance measures as dependent variables which is why it is used for that purpose in Image 1 and Image 2.

A giga-light-year is the distance light travels in a gigayear moving at the vacuum light speed relative to an inertial frame of reference.

The vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns is exactly 1 Gly/Gyr.

They are calculated for the Λ-CDM model (AKA concordance model) which is fitted to observations.

The Λ-CDM model currently fits all observations within uncertainty and is considered the most trustworthy cosmological model currently available.

Further improved observations may require it to be revised or abandoned, but for now it the best we have.

But even if the Λ-CDM model is revised or abandoned, it still fits the observable universe so well, the cosmic distance measures it predicts must still be correct to good accuracy/precision.

1. LOS comoving = physical distance: Physical distance is just ordinary distance which is what can be measured with a ruler at one instant in time. However, we CANNOT do that for cosmologically remote astronomical objects, except asymptotically as z → 0. So physical distance is a model-dependent result NOT an observable, except asymptotically as z → 0.

2. Lookback time is the time since a light signal started out toward us from cosmological redshift z. It is the light travel time is also model-dependent result NOT an observable, except asymptotically as z → 0 where it just physical distance r divided by vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns