# Will acceleration rate of expansion of space become faster than speed of light?

From watching cosmology lectures, it seems that the space between galaxies is expanding at an accelerating rate, my question is since it is the space that is (acceleratingly expanding), the special relativity does not apply in this case? in other words since it is not anything that is accelerating with relative distance, would at some point galaxies that are far enough from each other separate faster than speed of light?

Please note, I am not asking if the galaxies would move faster than speed of light, but whether the rate of expansion of space be faster than speed of light so in effect each galaxy would be as if it is behind an event horizon where even light can not escape?

If yes, is there a name for such an event horizon that is cause by expanding space outside rather than the conventional black hole event horizon caused by stretching of space within the event horizon?

How would one be able to differentiate between a black hole even horizon and a galactic even horizon caused by accelerating expansion of space outside? (not sure if the concepts of inside and outside are still meaningful in such cases)

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Yes indeed, in the circumstances you describe a horizon does form, and it's called a cosmological event horizon. Googling for this term will lots of articles on the subject, though for once Wikipedia has let me down and does not have a good article on the subject. However each galaxy wouldn't be behind it's own horizon as groups of galaxies tend to be gravitationally bound together. For example the Milky Way would stay bound to Andromeda and a dozen or so smaller galaxies.

Your question suggests you're think of this horizon as a sort of shell that would stop outsiders looking in on the galaxy behind the horizon, but it's really the other way round. The cosmological event horizon is like a shell that stops us looking out. In this respect it's the opposite of a black hole that stops us looking in.

A quick footnote: I had another Google and found http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf, which seems interesting reading on the subject.

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According to the Lineweaver-Davis paper you linked to, the event horizon is not the distance at which the Universe recedes faster than light. This distance is called the Hubble Sphere and is inside the event horizon, which recedes faster than light. None of these comprise the limit of how far we can see, this is the particle horizon which has much larger recession velocity. –  Thriveth Jun 9 '13 at 13:19
Curious about your comment John, we usually think of white holes as 'thermodynamic reversed black-holes', but how do GR describe reversed-orientation black holes like our cosmological event horizon? aren't those a kind of black hole reversal? is possible that we wrongly confuse white holes with this membrane-inverted black holes? –  lurscher Jun 9 '13 at 19:26

Actually, any uniform expansion of the Universe, no matter how small, will at large enough distances make the galaxies there - which are locally at rest - recede from us faster than the speed of light. No matter how slow the expansion is, as long as it is uniform everywhere in space!

This is not in violation of any laws of physics; Special Relativity forbids it, but special relativity relies on a Minkowski spacetime geometry which is only a valid approximation locally (kind of like the flat earth approximation is only valid locally). You can think of it like raisins in a rising dough - the expansion of the dough can make two far-away raisins recede from each other at superluminal speed, but nothing can travel from one raisin to another faster than light.

It is important to note that the distance where the Universe recedes from us at light speed is not a horizon. We can see much further than that. This is because the expansion of the Universe is (or rather, has been) slowing down, which means the Hubble sphere is moving outwards. Photons emitted from a region of, say, $2c$, will locally move at $1c$ towards us, which is still receding from us by $1c$. This will bring it into regions that are receding even slower from us, etc., until it gets inside the Hubble Sphere where it will start moving towards us. Therefore, many of the galaxies we see today are moving away from us faster than light - and always have been!

But there is a horizon - or rather, there are two: the particle horizon and the event horizon. The particle horizon is the distance from which light emitted at $t=0$ can have reached us by now. This will continue to grow forever, and is currently around 46 billion light years away. But the particle horizon is being increasingly redshifted, making up a time dilation effect which means that while there is no limit to how far we will be able to see, there is a time limit to how much we can see. At the particle horizon, we can basically only see what happened at $t=0$, Big Bang itself, which in practice means the Cosmic Microwave Background that was emitted around 380.000 years later.

The time dilation also means there is a limit to where light that is emitted at a certain time, e.g. now, will ever be able to reach us. This limit is called the event horizon, and that one is moving away from us in absolute distance, but getting nearer to us in so called co-moving distance. This means in practice that the horizon is moving outwards slower than the expansion of the Universe, so galaxies near it will "escape" it. What this means isn't that we cannot see these galaxies anymore, but that their history as we see it will slow down and eventually stall as their redshift approaches infinity - comparable to when something falls into a Black Hole. The event horizon would be the same as the Hubble Sphere in Special Relativity, but in General Relativity which governs our Universe, it is not. The event horizon is also (very!) different from our particle horizon.

To sum it up:

• Any uniform expansion will make all of the Universe beyond some distance recede from us faster than light.
• Receding faster than light does not mean it is not observable, the Hubble sphere is not a horizon.
• Galaxies situated between our event horizon and our Hubbls sphere are, and always have been, receding from us faster than light; yet we are fully able to observe them (and do it routinely). As expansion of the Hubble sphere asymptotically catches up with the event horizon, the size of this region approaches zero.
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The above answer is, credit where credit due, heavily inspired by this paper by Tamara Davis and Charles Lineweaver. –  Thriveth Jun 9 '13 at 14:18