Did the expansion rate of the universe exceed lightspeed?

No, that's just nonsense It did and it still does - but this is misleading. Percy has already explained this, but i will repeat:Space itself is expanding - there is no actual motion. You can tell this because you are experiencing no acceleration as the Universe expands: everything appears to be moving away from you and you seem to be at the centre of the expansion. But if you chat with someone in the one of the galaxies that is moving away, they will tell you that they also are not accelerating, and it is they, not you, that are at the centre of the expansion! So even though this galaxy is moving away at ever increasing speed, it is not actually moving! The intervening space is simply expanding. It is quite possible that the amount of expansion increases the relative distance between two galaxies faster than a light ray can close that distance. This is where the expansion can be said to be greater than the speed of light, in a bastardisation of terminology. There are galaxies that we can see today (as they were billions if years ago) that we can never travel to, no matter if we travelled at the speed of light. They are forever lost to us.

Certainly Actually, it was - so fast that fast doesn't even begin to capture it! Yep, and in ten of those 10^-34 seconds, ~five billion Planck times, the points would be separated by one thousand Planck lengths, so around 60m/s. And in thirty of those 10^34 seconds, 15 billion Planck times, the points would be separated by 1 billion Planck lengths, still well below the speed of light.But in 100 doublings, which is fifty billion Planck times, the points would now be separated by 2^100 = 10^30 Planck lengths!!! So a mere 10^19 times fast than the speed of light Never undersetimate the power of exponentiation...Edited by cavediver, : No reason given.

Sure. There are going to be pairs of galaxies for which causal communication is possible, and pairs for which it is impossible. In our accelerating FLRW space-time, the former evolve into the latter. But you can have exactly the same scenario in flat space-time and SR. If I start accelerating away from you, there will come a time after which I am out of causal contact with you. I will be asymptoting to a particular null ray radiating from your world line, and no null rays emiited after that asymptote will intersect my trajectory. I will always be 'below' them (on a classic space-time diagram). We need a sketch pad add-in... Percy???

I disagree - I think the scanarios I have discussed with Percy and Chiroptera provide such meaningful comparisons. I admit, you have to choose your scenario carefully, and you cannot make any blanket statement regarding the two phenomena.

Yes, very true. Which is why I was objecting to your absolutist "no meaningful way"

Of course How is it not meaningful? Unless you are thinking of a statement such as "during the inflationary epoch, space-time expanded much faster than the speed of light", which I agree that although true, is rather misleading, because as you state, you can (typically) always find a length scale at which space is expanding "faster than light".The point is:1) two objects can have a perceived recession "velocity" caused by the expansion of space that is less than c.2) this "velocity" can exceed c (though of course not be directly perceived) for two sufficiently separated objects.3) This in no-way contradicts the usual limits of the speed of light nor any part of Special Relativity.No part of 1), 2), and 3) is meaningless.

No. They are entirely different concepts with very little relation The only 'limit' is an *observational* limit on the speed of another object. If you were to accelerate towards another star, you would find that there is actually no limit to how quickly you can get there. If you could survive the acceleration, you could cross the Galaxy in a day. If you came back a few days later, you would have spent less than a week on a trip of over 100,000 light years. But because you cannot be *observed* to travel faster than the speed of light, by necessity, the earth and its inhabitants will have aged about 100,000 years - i.e. the time it would take to make that journey at the speed of light.

No, this just another observational effect. It is not why there is a 'limit'. I appreciate that this is the way it is often explained, but that doesn't make it correct!Let's try the longer version, as the short version seems to have created confusion all round As an object with rest-mass, you have a 4-dimensional velocity vector with fixed length (which we will call length c). When you are at rest, your vector points purely in the time direction. We sometimes loosely say that you are always travelling at the speed of light into the future. What you think of as velocity is actually a rotation of this vector, such that it now points a little into space (in your direction of travel) but still predominantly into the time direction. Thus you do not notice the difference in time, but you do start moving in space. As the 'velocity increases', the vector rotates further, until you start to notice that the component of the vector pointing in the time direction is substantially less than normal - say only half c. You are thus moving in space considerably, but only aging half as much as normal. As your vector tips towards horizontal, your time component approaches zero, while your space component approaches c. You are thus moving through space at almost the maximum possible given by your vector, but hardly aging at all. As far as you are concerned, you are traversing space with almost no passage of time - this is effectively infinite velocity. As an object with rest-mass, you cannot tip your vector perfectly horizontal (i.e. so that it points purely in a space-direction, with no component in the time direction), but you can approach as close as you like. A particle with zero rest-mass always has its vector pointing in a purely space direction.You can now see the limit. It is simply that your 4-velocity vector always has fixed length, and the most it can ever be rotated is such that it (almost) points totally in the space-direction. Stationary observers watching you are still moving through time as normal, so you do not appear to have the near infinite velocity you are experiencing. They will see your vector as tipped 45 degrees, equal amounts in time and space. This is what we usually call 'the speed of light'.What does 'inifinite' velocity look like? Well, as mentioned, you can never see an object move faster than the speed of light. So as you approach a star, travelling light years in days, what gives? Well, the 'observed' distance actually contracts, so that as soon as you reach your relativistic velocity, you already appear to have crossed most of the distance! Thus the star nevers appears to be approaching at more than c!

No, he's not - as explained in my last post. Yes, it is confusing, but if you are asking: then you are into something much deeper than simple time dilation. My reply was an attempt at a very short version of my above post.

Sure - coming up with a p-R metric on a given topolgy is not that difficult. Making it a solution of GR is the hard part! The closed FRW space-time is topologically a 4-sphere, but you still get the two singularities. In FRW space-time, then the perpetually expanding solutions are spatially infinite. However, you can compactify them using non-trivial spatial topology. Your elliptic paraboloid is essentially de-Sitter space, which is geometrically finite but expands for ever. The de-Sitter source is the cosmological constant, and the FLRW extension of FRW gives the same possibility, where we can be closed, yet expand for ever - by virtue of the CC dominating over the mass content.

Careful - although a test particle will not be accelerated in any direction (obvious from simple consideration of symmetry), there is certainly curvature. In a space of uniform density, the actual concept of 'gravity' is not applicable, and one should stick to thinking in terms of curvature.

Sorry, will have to leave this for now as I must work. But this is more difficult to understand. Nothing Yes.Edited by cavediver, : No reason given.

The point is - what does this mean? If travelling at the speed of light means you reach any destination in zero time, then what can 'faster' possibly mean? Whatever it is, it is something that cannot be described as a speed or velocity.

Yes, although we believe this is also true today at the largest scales of the Universe. Galaxies and clusters just make up localised bumps in the otherwise smooth curvature. These bumps were originally just the size of quantum fluctuations, but have been inflated and expanded into the current large-scale structure!

Love it