General Caption: Image 1: A diagram of the observable universe. Image 2: A cartoon observable universe embedded in a much larger surrounding outer universe.

Images:

1. Image 1 Caption: A diagram of the observable universe with particle horizon (the defined boundary of the observable universe) at the comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value). The cosmological value just given and those below are according to the Λ-CDM model which is the favored cosmological model circa 2021, but perhaps NOT forever.
   1. The Milky Way is at the center and observable universe comoving diameter ∼ 28.5 Gpc.

   2. We see that Aristotle (384--322 BCE) was half right: the observable universe is a sphere centered on us. It must be since it is that part of the universe from which a light signal could have reached us since the Big Bang which was time ago of the age of the observable universe = 13.797(23) Gyr (Planck 2018) (see Planck 2018: Age of the observable universe = 13.797(23) Gyr).

   3. The particle horizon is the FARTHEST point which a light signal (and therefore any signal) could have reached us since the Big Bang had the observable universe been transparent all the time. It was actually opaque until the recombination era t = 377,770(3200) y after the Big Bang (which includes decoupling) when the hydrogen ions (H**(+) and electrons recombined and made the observable universe transparent to the primordial cosmic background radiation (CBR) which evolved into the cosmic microwave background (CMB) of cosmic time the present.

   4. Assuming the cosmological principle that the observable universe is homogeneous and isotropic in average properties on a large enough scale, we infer that the observable universe everywhere looks like the very nearby contemporary/local universe on average at cosmic time the present.

      However, the farther you look out, the further back in cosmic time you look because of the finite vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s. So we see the observable universe as it looked further in the past, the farther out we look. Astronomers have this great advantage over historians: we can literally see the past.

   5. The diagram gives an artist's impression of the large scale structure of the observable universe whose actual realization in reality is often called the cosmic web.

   

2. Image 2 Caption: A cartoon of the observable universe (characterized by the Hubble length = L_H = c/H_0 = 4.2827 Gpc/h_70 = 13.968 Gly/h_70) embedded in a much larger surrounding universe.
   1. The Hubble length is a characteristic size for the class of cosmological models called the Friedmann-Lemaitre models. In the past, the Hubble length was taken as a good estimate of the size scale of the observable universe since there was no well established model to provide a definitely good value. But now the Λ-CDM model gives a precise comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value), and so the Hubble length is less important as an estimate of the size scale of the observable universe than it was.

   2. As noted above, we have the formula Hubble length = L_H = c/H_0 = 4.2827 Gpc/h_70 = 13.968 Gly/h_70, where H_0 is the Hubble constant. The Hubble length is a bit less than a third of the comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value) (i.e., the radius of particle horizon).

      For all larger astronomical distance scales, see astronomical_distances_larger.html.

      Since Hubble constant value changes a bit with every new measurement, it is convenient to write H_length in terms of the reduced Hubble constant h_70 = H_0/(70 (km/s)/Mpc) as we have done above.

      The favored Hubble constant value circa 2018 is 67.74(46) (see Wikipedia: Λ-CDM model parameters). Revisions by a few percent are possible.

   3. Beyond the particle horizon (i.e., the edge of the observable universe):

      There is no reason to believe the particle horizon defines the boundary of the whole universe---we don't have to follow Aristotle (384--322 BCE) anymore.

      So the observable universe is very probably embedded in a much larger universe which is much the same as the observable universe for a long way. This probability is because the observable universe shows no signs of a boundary and has homogeneity and isotropy: i.e., it obeys the cosmological principle.

      However, well beyond the particle horizon according to the multiverse paradigm, there could be boundary between our pocket universe and a false-vacuum background universe with other pocket universes.

Images:

1. Credit/Permission: © Andrew Colvin (AKA User:Azcolvin429), 2010 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:Observable Universe with Measurements 01.png.
   
2. Credit/Permission: © David Jeffery, 2004 / Own work.
   Image link: Itself.