▲ 28 r/askastronomy
Objects near the edge of the observable universe are not fading from our view
There is a very common misconception that objects close to the edge of the observable universe are currently fading from our view due to cosmological redshift, when in fact is generally true that objects near the edge of the observable universe having decreasing redshift. This confusion is understandable as the evolution of cosmological redshift can be counterintuitive. I thought I'd create this post as I saw some of these misconceptions repeated in comments on a recent post in this sub.
The plots below have been done for the standard ΛCDM cosmological model, but what is said is qualitively true for an expanding universe where the radii of the observable universe and cosmological event horizon are finite.
The evolution of the redshift of the cosmic microwave background (CMB)
The CMB is emitted from the surface of last scattering, which is essentially the furthest object we can see in the universe. The surface of last scattering is close to, but not at, the edge of the observable universe as the edge of the observable universe is defined by the speed of light, rather than what we can actually see.
If we look at the evolution of the redshift of the CMB over time, we see it increases with time. However this graph does NOT represent the redshift of a a single object . Instead it shows the redshift of series of "surfaces of last scattering", with each surface being progressively further away than the last.
Evolution of the redshift of the CMB
Notes: the redshift of CMB as a function of time is given by a(t)/a(t_RC) -1 , where a(t) is the scale factor and t_RC is the time of recombination when the CMB was emitted.
The evolution of redshift of objects comoving with expansion
If we instead look at how the redshift of a single object that is moving away from us with the expansion of the universe, we see that at the point in time it enters our observable universe the redshift is infinite, but very quickly drops down to a minimum. The accelerating expansion then causes its redshift to climb asymptotically back to infinity as t goes to infinity.
Notes: the evolution of redshift of a comoving object can be found numerically from the evolution of our light cone's comoving radius. The amount of galaxies that are entering the observable universe decreases with time and galaxies with χ>63 Glyrs will never enter the observable universe.
The evolution of apparent magnitude of objects comoving with expansion
Redshift is not the full picture though of how bright an object appears to us, so we should also look the evolution of apparent magnitude. Apparent magnitude is a logarithmic measure of brightness, and the higher the value the less bright an object appears. It is affected by various factors, but below I have only included the cosmological factors, which are redshift and angular distance.
As redshift tends to be the dominant factor, again the graphs follow the pattern of a sharp decrease in apparent magnitude from infinity as the object enters the observable universe, before a climb back up to infinity as t goes to infinity.
Notes: the apparent magnitude as a function of time can be found numerically from the evolution comoving radius of our light cone and the evolution of redshift. The numbers in the graph are rather arbitrary as they depend on the absolute magnitude (which I've set as the same for all objects), but the shape of the graph is not.
Other factors affecting the visibility of objects
There are other factors that affect how bright an object appears. For example the absolute magnitude of objects tends to evolve over time, though for the furthest objects this evolution will be slowed by cosmic time dilation. Of course too galaxies only become visible in new regions entering the observable universe a long time after they have entered the observable universe. There is also extinction from dust, etc which I have not considered.
Whilst the above is mostly theoretical there are proposals to measure the evolution of redshift of objects and some preliminary measurements have even been done to this end:
u/OverJohn — 23 days ago
▲ 3 r/astrophysics
That galaxies beyond the Hubble sphere have superluminal recession velocity tends to a source of much confusion. On an introductory level it is usually explained by the expansion of space, but this also often gives the false impression that space is similar to a physical material that can be stretched. I wanted to try to make a simple visual explanation to show superluminal recession velocities are due to mundane reasons.
The easiest way to understand why recession velocities can be superluminal is to first look at expansion in flat spacetime. This allows us to compare the familiar inertial velocities of special relativity, which cannot exceed c, with superluminal recession velocities. Below is a Minkowski diagram showing a trajectory in inertial coordinates:
The average coordinate speed of the red trajectory is the spatial distance along the green dotted line divided by the amount of time passed along the blue dotted line. If we shorten the trajectory so the start and finish are closer in time, in the limit we get the instantaneous coordinate speed. For inertial coordinates, the average and instantaneous coordinate speed cannot exceed c for physical objects.
If we draw a Minkowski diagram of the same trajectory, but switch the coordinate grid to expanding coordinates we get:
Minkowski diagram of expanding coordinate grid
Again, the average coordinate speed of the red trajectory is simply the spatial distance along the green dotted curve divided by the amount of time passed along the blue dotted line, and we can get the instantaneous coordinate speed as before. Note to get the times and the distances you need to use the spacetime metric and not simply measure the lengths of the curves on the diagram. As we are using different rulers and clocks to define the distance travelled and time passed, we find our coordinate speed can exceed c for physical objects.
The recession velocity of a galaxy is simply the coordinate velocity in expanding coordinates, and we can see that even in special relativity (i.e. flat spacetime) expanding coordinate velocities may exceed c. So superluminal recession velocities are really not very remarkable.
Of course in cosmology gravity is important, so the spacetime of our cosmological models is not flat. However expanding coordinates in curved cosmological spacetimes are just a generalization of expanding coordinates in flat spacetime, and the basic reason superluminal recession velocities occur is the same. I.e. it is down to choice of clocks and rulers that are used to define coordinates.
To get an idea of the similarity between expanding coordinates in flat spacetime and the expanding coordinates of our favoured cosmological model, below is proper distance-cosmological time plot of locally inertial coordinate lines (extended as far as possible) in the standard LCDM model and a similar plot of inertial coordinate lines in flat spacetime.
u/OverJohn — 2 months ago