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## inflation

inflation was a period of faster than light expansion of the universe if so ,how then do we know that when peering out into the cosmos we are not looking at past versions of our own galaxy at different times?

2. In order to see a past version of our galaxy you need two conditions to meet:

1. A closed Universe. I think inflation has been suggested for the open Universe scene.

2. A slower than light expansion (for the whole universe extension). With a c expansion rate you see just one instance of the universe, so you don&#180;t get to see a second instance of our galaxy. Between c and c/2 you see a partial second instance of the universe. At c/2 you see exactly two instances. Between c/2 and c/3 you see a partial third instance. And so on...

3. I am revising my previous calculations.

My idea is that in a closed universe the size of which coincides with the size of the observable universe you see exactly one instance of the universe. My previous calculation assumed that if the observable universe was twice as big as the actual size you would get two instances and so on.

But I failed to consider that the youngest instance would be half the size of the older one. So if the observable universe was twice the size of the actual universe you would get infinite instances of the universe (1 + 1/2 + 1/4 + 1/8 ...), at an average expansion rate of c/2.

That the expansion rate in a closed universe would be decreasing would call for further correction.

Still you need an slower than light expansion to see any aditional instances.

Don&#180;t put any dark energy into the scheme or you will go nuts.

4. Originally Posted by jimbo
inflation was a period of faster than light expansion of the universe if so ,how then do we know that when peering out into the cosmos we are not looking at past versions of our own galaxy at different times?
Scientists at the interface of topology and cosmology are actively seeking indications of just what you're asking about in order to determine the shape, the geometry, the toplogy of the universe, but it has nothing to do with inflation or faster than light expansion. I recently read astrophysicist Janna Levin's remarkable book How the Universe Got Its Spots, which tells of current research into this question, among other things, and I highly recommend it.

Here are a few blurbs from Circles in the Sky, Detecting the shape of the universe By Ivars Peterson:

The surface of a ball is an example of a two-dimensional manifold.... Earth's surface is a two-dimensional manifold because it looks essentially flat until one gets far enough away to see that it curves into a sphere.... Another way to think about the topology of a two-dimensional manifold is in terms of gluing together the sides of a rubbery rectangle.... Thurston and Weeks were key figures in the development of a comprehensive catalog of closed three-dimensional manifolds, most of which appear to have a hyperbolic geometric structure. These weird shapes can be understood in terms of three-dimensional polyhedrons whose faces are glued together to create finite, multiply connected spaces.... The cosmological consequences are startling. If such a topology described the universe, what astronomers might think is a distant galaxy could actually be the Milky Way -- seen at a much younger age because the light has taken billions of years to travel around the universe.

5. As the OP is about inflation, and not weird topologies that could indeed yield multiple images of each galaxy (and there's no evidence of that yet), the answer is that inflation would have occurred so early in the age of the universe that there was not even normal matter, let alone galaxies. So in a sense we do see our own region of the universe no matter how far we look (that's the explanation for the CMB looking virtually identical in all directions), but it's not "our galaxy". Our galaxy formed long after the inflation was over.

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Originally Posted by jimbo
inflation was a period of faster than light expansion of the universe if so ,how then do we know that when peering out into the cosmos we are not looking at past versions of our own galaxy at different times?
The idea that inflation involves "faster that light expansion" is a common misnomer.

The expansion of the universe is not a velocity; so you can't compare it with the speed of light. The units are actually inverse time; but it is often given as "km/sec/MPsec".

The present rate of expansion is about 71 km/sec/MPsec (give or take a percent or two). This means that galaxies that are now 1 MegaParsec away are receding at 71 km/sec. Galaxies that are 10 MegaParsecs away are receding at 710 km/sec. Galaxies that are now 4225 MegaParsecs away are receding at 300000 km/sec; which is the speed of light. Galaxies 10000 MegaParsecs away are receding at more than twice the speed of light.

This is not a violation of relativity; because it is not a velocity of objects in space. It is rather the rate at which the space between objects is increasing. That is, in every second, every MegaParsec of space expands by a further 71 kilometers.

Over time, this expansion rate changes. For example; suppose a galaxy at a distance of 100 MegaParsecs is now receding at 7100 km/sec. If you wait about 13.7 billion years, that velocity will have added another 10 MegaParsecs of distance… the galaxy is now 200 MegaParsecs away. But it that galaxy is still receding at 7100 km/sec; then the expansion rate has dropped to 35.5 km/sec pre MegaParsec.

Curiously, this means that a galaxy that is receding faster than the speed of light can still be visible. Even though photons leaving that galaxy are moving through space at 300000 km/sec, the space between us and the photons is expanding even faster, and so the distance to "approaching" photons actually increases. However, there's a catch. The photon moves into regions with smaller and smaller cosmological recession velocities. Eventually, it "catches up" with expansion; being in regions where the recession velocity is equal to the approaching velocity through space. After that, the photon starts to approach us again, and eventually reaches observers on Earth to let us see the galaxy that is receding faster than light.

Here is a diagram, from Ned Wright's cosmology tutorial page, that shows the path of such a photon. The time axis is vertical, and the red lines are photons "approaching" the center line in an expanding space. Initially, the photons are carried away from the center; but in time they catch up and overtake the expansion, and eventually reach the center.

omega0.gif

So; what about inflation? Inflation is a case in which the expansion rate remains constant over time, rather than reducing. If you think about it, this means that a receding galaxy will have exponentially increasing recession velocity. As the distance between us and the galaxy increases, the recession velocity increases also, as it is proportional to the separation distance. And in this case, galaxies receding faster than the speed of light would not be visible, as a photon cannot catch up with the expansion. But this is not really a case of expansion being faster than the speed of light; it is rather about how the expansion develops over time.

Strongly recommended reference: Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe, by T. Davis and C. Lineweaver (Pub. of the Astronom. Soc. of Australia, 2004, 21, pp 97-109; also at astro-ph/0310808). This paper lists three common misconceptions.
• Misconception 1. Recession velocities cannot exceed the speed of light. In fact, there is no speed limit on cosmological recession velocities.
• Misconception 2. Inflation causes superluminal expansion, but conventional expansion does not. In fact, any expansion rate will involve superluminal recession velocities for sufficiently distant objects.
• Misconception 3. We cannot see galaxies with recession velocities greater than the speed of light. In fact, we routinely see distant objects that are now and always have been receding faster than the speed of light.

Also very good is Ned Wright's cosmology tutorial. The attached diagram in this post comes from part 2 of the tutorial.

Cheers -- Sylas

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Is there concensus about what existed at the smallest interval of time after the BB as well as the length of the smallest interval of time?