Cosmological Horizons

See Cosmological Horizons - further reading for a list of books related to this subject
In cosmology the idea of a horizon is fairly common. General relativity tells us that there are regions of the universe from which we cannot receive information, and the boundary of such a region is called a horizon. On Earth we have a similar situation, where objects further than a certain distance are below the horizon. Thus we can see a ship gradually appearing over the horizon.
A recent paper covering this area in detail is Expanding Confusion: common misconceptions of cosmological horizons
Unfortunately this leads to the analogy of a galaxy appearing from behind a cosmological horizon, and my claim is that this never happens. But I would like to start by clarifying what is and especially what isn't a cosmological horizon.

Two non-horizons

Horizons II: Art Print
Firstly, the thing that actually limits our view of the universe is the cosmic microwave background radiation. Although this is seen in terms of radiation filling the universe, it originated when the matter in the universe was a plasma, and hence opaque. Thus we can imagine that we are seeing a sort of fog, and we can see things closer/later than the fog because it had cleared by then, but anything further/earlier than this surface is invisible. However, this is not considered a horizon, because it does not exclude all information, just the sort we can detect at present. For instance, if we had neutrino telescopes then we would be able to see back to a much earlier stage of the universe.

The second thing to note is that light has a finite speed, and so when we observe distant parts of the universe, we are observing them when they were considerably younger than we are now. We are not seeing them 'now' (indeed 'now' isn't really defined ). This may seem to be labouring the obvious, but you have to be careful not to deduce that if we can't see a galaxy when it of the same age as us, then it must be behind some sort of horizon.


See also Stretchy Space? for more discussion of how to interpret superluminal velocities
Probably the biggest myth in this area is saying that since current cosmological models say that some galaxies will have speeds greater than light, then such galaxies must have infinite redshift, effectively putting them beyond a horizon. This is not true. In fact, with the current model, anything with a redshift greater than about 1.4 will be travelling away faster than light, and such objects are certainly seen. You can explain this in terms of space stretching if you like, but I would see it in terms of the coordinate system chosen by cosmologists not being particularly suitable for describing the velocities of distant objects.

What is going on here can best be seen by considering the Milne universe, which is a description of a universe without gravity but using the framework of General relativity. Here one can look at things in terms of GR or in the familiar terms of Special Relativity. However, the coordinate systems are different for the two cases. In the SR coordinates everything is travelling slower than light as we know it must. But anything with a redshift greater than a certain value will be travelling faster than light in the GR coordinates.

Particle Horizons

A type of horizon which is fairly certain to exist is what is known as a particle horizon. This tells you how much of the universe you can have received information from at a given time. Note that graphs showing particle horizons are generally confusing, as they often show a background of the other parts of the universe evolving with time, implying that at a certain stage of their evolution they cross the particle horizon. This is not the case - whatever enters our past light cone has just experienced the big bang.

The other thing to note is that for particle horizons to occur the rate of expansion of the universe (the derivative of the scale factor with time) must be infinite at time zero. This is the case in all models of the actual universe, according to GR (Although you might not think so, looking at graphs of the expansion of the universe against time). However, in the Milne universe, where the rate is constant, there are no particle horizons.

Goodbye Cruel World

Much of the current experimental work in cosmology is looking at the possibility of a non-zero cosmological constant, which implies that the expansion of the universe is accelerating. In this case galaxies can cease to have contact with us. A galaxy which does this has crossed the cosmological event horizon. All we would see is an increasingly redshifted and time-dilated version of events in the galaxy, never quite reaching the time of crossing the horizon.

In special relativity there is a similar effect, which says that if you have a head start and can accelerate constantly then you can stay ahead of a light beam, despite the fact that you will never actually reach the speed of light. This means that you would never receive any information from Earth after a certain time. Unlike the cosmological case the situation is not symmetric, so Earth could still receive signals from you.

On a clear day you can see forever...

What about black hole event horizons? You may be interested in Black Holes - do they exist?
So you see that in no case do galaxies appear in a fully formed state like a ship from over the horizon. Furthermore, if the cosmological constant is actually zero (I realise current experiments indicate that it isn't, but who knows?) then all events in the universe will eventually be within our view. Are we inventing limits where none exist?