# Universe Questions

I just read an article that says that the Hubble telescope has “seen” a galaxy about 13.2 billion light years away. The Hubble is obviously seeing it as it looked that far back (about 600 million years after the Big Bang).

Do we have a way of knowing how far it is from us currently? What I mean is that, presumably, that galaxy could have been moving in a completely different direction than us, and could now be much further away, or even much closer (although I suspect that we would already be able to see it if it were significantly closer).

Also, am I correct in assuming that we would never be able to see at least 1/2 the universe? I ask this because, assuming that the Big Bang was a 3-D “explosion”, half of the matter and energy would have veered in a direction opposite to ours and thus its light would never be able to reach us.

Finally, years ago I went to the Hayden Planearium and Neil Degrasse Tyson made the following comment: “No matter where we are in the universe, we are always in the middle”. I had a hard time trying to understand this, so I hope someone here can explain.

Not sure. What I wonder is where in the universe the Big Bang occurred. Is it supposed to have occurred in the exact center of the universe and matter has expanded equally in all direction since the beginning of time?

No, Tyson got it right, as you expect. Stuff did not explode in space. Space (really spacetime) expanded in all directions. The implication of that is that there cannot be a center. (And Einstein agrees: a center would be a preferred reference frame and that’s verboten.)

When we look outward from Earth we see the same thing everywhere, in every direction, all the way back to those earliest galaxies. Go to any place in the universe, you see the same thing everywhere, in every direction.

How far is that? Best estimates today is that the diameter of observable universe is 46.5 bly, so those those 13.2 bly galaxies are somewhere around 45 bly away.

In an expanding Universe there are several different definitions of distance. I assume when they say the galaxy is 13.2 blys away they are talking about “light travel distance”. Light travel distance, as the name suggests is how far the light has actually traveled to reach us and it is often used by astrophysicists when speaking about distance as measurement of light travel distance is often independent of exactly details of cosmological expansion (and the exact details of cosmological expansion depend on the cosmological model employed).

Proper distance is another measure of distance used and (pedagogically) it could be described as the distance we would have to travel to get to the galaxy if expansion suddenly stopped now (of course expansion can’t suddenly stop, so you have to be a little careful of thinking of this as the actual distance to an object). Knowing the proper distance requires knowledge of the history of cosmological expansion. An object that is 13.2 blys away in light travel distance would be 30 blys away currently in proper distance, using the LCDM cosmological model.

Obviously, as the Universe is expanding, the proper distance to the galaxy when the light we now see from itwas emitted would’ve been much less. For a galaxy 13.2 blys away (light travel distance), the proper distance would’ve been at a very rough guess about 1 or 2 blys when the light was emitted.

As NdG says, we can assume that we are at the centre of expansion, at least in as far as the recession velocity of galaxies depends only on their distance to us and not on their direction. This doesn’t mean we are in a special spot in the Universe as this equally true everywhere. This may seem paradoxical, but we are dealing with curved spacetime, so if you like this is a result of the curvature of spacetime, even though cosmological space is flat.

The galaxy you’re talking about is 13.4 billion light years away, so we’re seeing it as it was 400,000 years after the Big Bang:

http://www.newsweek.com/hubble-farthest-galaxy-photo-video-433802

Huh, to put it mildly. “LCDM”?

I just put that in there to emphasize that when observing a distant galaxy, assigning a proper distance depends on theoretical cosmological model used. LCDM stands for “Lambda cold dark matter”. The “Lambda” signifies that the model has dark energy in the form of a cosmological constant and “cold dark matter” signifies that the model has dark matter with relatively little kinetic energy. The LCDM model has a number of parameters whose values are taken from observation. The bog-standard version is actually fairly simple and doesn’t take into account a number of things, including inflation, but it still manages to fit observation fairly nicely.

The universe could in on the surface of a “hypersphere” (or torus, etc). It is like the 2D surface of a sphere… it has no edge or center.

Shape of the universe
“Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat, but the data are also consistent with other possible shapes”

If the universe is infinite and flat I’m not sure about what you can say about whether you’re near the edge or center… BTW if we were on a hypersphere all galaxies could be expanding apart from each other at a finite speed but if the universe was infinite and flat, galaxies further away from the center would tend towards an infinite speed…

They in fact do move at ever-increasing velocities away from us, so that we will never see any more of their light as they are apparently receding faster than C. This will never reach infinite speeds, of course, but that doesn’t matter.

That we can’t see galaxies receding faster than c is one of my bugbears, to explain:

The Hubble sphere is the sphere around us where galaxies are receding from us at c and it depends only on the current value of the Hubble parameter. The particle horizon is the hard limit on the current distance to the furthermost galaxies we could possibly see (i.e. it is the sphere that defines the observable Universe) and it depends on the entire past evolution of the Hubble parameter as compared to the length scale of the Universe.

Clearly the Hubble sphere and the particle horizon depend on the Hubble parameter in rather different ways and so do not necessarily coincide. An easier way to see this is that, if the Universe suddenly stopped expanding today, then the Hubble sphere would cease to exist as galaxies would no longer be receding from us, but there would still be a size limit to the observable Universe as it would still take more time for light to reach us for galaxies outside the current observable Universe.

Now finding the general condition for the Hubble sphere and particle horizon to always be at the same place gives an equation that is beyond me to solve, but in a flat single-parameter radiation-dominated Universe they do indeed coincide. However in the LCDM model and indeed any model that is based remotely on realistic physical parameters the Hubble sphere lies inside the particle horizon. Or in other words we can observe (and in fact have observed) some galaxies that are currently receding from us faster than c. The very furthest galaxies that have actually been observed (e.g. the one mentioned in the OP) are receding from us at speed in excess of 2c according to the LCDM model.

Another point often raised though is that the furthest galaxies we see, may be currently receding from us at speeds in excess of c, but where receding at slower speeds when the light we currently see from them was emitted. This brings me to something called the cosmological event horizon. The cosmological event horizon is the limit of events that are happening at the current time that we will be able to see from our position in space in the future. The current distance to the cosmological event horizon depends on the entire future evolution of the Hubble parameter as compared to the length scale of the Universe.

Again the Hubble sphere and the cosmological event horizon depend on the Hubble parameter in rather different ways and so do not necessarily coincide. An easier way to see this is that if expansion were to cease at some point in the future then light from current events will always be able to reach us so there would be no cosmological event horizon, but there would still be at the current time a Hubble sphere due to current expansion.

The Hubble sphere and the cosmological event horizon coincide in de Sitter spacetime, which is empty space with a positive cosmological constant. In the LCDM model the Hubble sphere lies inside the cosmological event horizon and so we will in future be able to observe (some) galaxies that are currently receding from us at speeds in excess of c. As the Universe is currently dominated by dark energy, and if we assume that the dark energy is a cosmological constant, then its future evolution will be similar to de Sitter spacetime and so the cosmological horizon is only a little further than the Hubble sphere. However this was not the case in the past and according to the LCDM model the very furthest galaxies we have currently observed (e.g. again the one mentioned in the OP) were receding from us at speeds in the region of 8c (!) when the light we currently see from them was emitted.

I was thinking that I heard that nothing can move faster than the speed of light… but perhaps the expansion of space itself can…

Indeed it can. It might be more useful to think about light speed as the fastest information can travel.

At what speed is the original singularity receding from us?

Isn’t the “original singularity”, well…everything, including us?

The BB singularity doesn’t have a spatial location (and if we had to give it one we would say it covered the whole of space), so it doesn’t make sense to talk if its recession velocity. That said, if there were light rays arriving at us from the boundary of the observable Universe they would’ve been emitted at the time of the singularity. Galaxies on the particle horizon (i.e. the boundary of the observable Universe) are receding from us at a rate slightly in excess of 3c (again using the LCDM model). The boundary of the observable itself is not only expanding due to the expansion of the Universe, but also expanding at c due to its lightlike nature. This means that new galaxies are always entering the observable Universe and the boundary of the observable Universe is currently expanding at a rate a little in excess of 4c.