Inflation & Its Effects on Universe's Expansion

[Fabio Sachs]

I have two questions related to inflation, and wonder if there is an answer to any of them:

1- If there was inflation occurring faster than light at any time, so that the universe's radius is larger than aprox. 14 billion light years, then shouldn´t we be seeing some galaxies more than once, in diferente moments of their life time?

2- If space is something with such a real existence that it can be bent, warped, and it even has its own amount of energy no matter how empty it is, then does not inflation, or even todays accelerated expansion, mean that more "plank sized units" of space are being created out of nothing, thus breaking the consevation laws of the Universe? Or maybe there is something being transformed into space?

 

[Chalnoth]

Inflation isn't a speed, so saying it's "faster than light" is literally nonsense. One might as well say, "The length of this rod is faster than light." It makes zero sense. I realize that a number of scientists have used this language, but it is flagrantly incorrect.

The second point is that galaxies only ever formed long after inflation ended. Inflation was a period of extremely rapid expansion in the very early universe. The inflation that led to the entire observable universe need only have lasted a tiny fraction of a second. The galaxies formed much later when the expansion was much slower, and the expansion hasn't changed so dramatically since.

Finally, energy isn't conserved in an expanding universe. Conservation of energy arises as a consequence of symmetry in time. The expansion breaks that symmetry (the past is different from the future because things are closer together in the past and further apart in the future). For a more detailed discussion on energy conservation in General Relativity, see here:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

 

[Fabio Sachs]

Thanks for such a clear and fast response!
I know I have poorly frased my first question as you have very apropriately pointed out. Maybe I should have put it as Inflation having occurred at such a pace that the distance between any two things grew by (way) more than 300 000 km every second. What I hadn´t realized was that there were no galaxies formed by then!
Is the inflationary period visible for us or is it within the invisible early instants?

As for the second question, your answer seemed to me as meaning that : There is conservation except when there isn't!
I'll take a look at the link you posted and try to grasp the concept a little better...
Once again, thank you!

 

[Chalnoth]

Thanks for such a clear and fast response!
I know I have poorly frased my first question as you have very apropriately pointed out. Maybe I should have put it as Inflation having occurred at such a pace that the distance between any two things grew by (way) more than 300 000 km every second. What I hadn´t realized was that there were no galaxies formed by then!

The thing is, the recession velocity depends upon distance. The recession velocity of most of the galaxies in the visible universe is greater than c and always has been. We can see these objects because the rate of expansion has been slowing down.

Is the inflationary period visible for us or is it within the invisible early instants?

Certainly not with visible light. Prior to the emission of the CMB, which occurred a few hundred thousand years after inflation ended, our universe was opaque. The emission of the CMB is the earliest we can see with visible light.

Now, it might be possible to see the imprint of gravitational waves from the inflationary period imprinted on the CMB, but so far those haven't been detected (BICEP2 thought they detected them, but it turned out to be foreground contamination).

As for the second question, your answer seemed to me as meaning that : There is conservation except when there isn't!

Conservation laws are a result of symmetries. This is demonstrated by Noether's theorem*. You get conservation of momentum for any system that has certain properties that don't change from place to place. You get conservation of angular momentum for any system that, when rotated, looks the same in a certain mathematical sense. And you get conservation of energy when a system doesn't change over time in a particular mathematical sense.

General Relativity throws a great big wrench into all of this because it throws out the entire notion of absolute space and time. Without absolute space and time, what you mean by the words, "doesn't change from place to place" or "over time" becomes ambiguous. It is easy, for example, to write down equations that look like an expanding universe, but in actuality just represent flat space-time where there is nothing measurable that can be called "expansion".

Instead, General Relativity follows other symmetries that enforce the conservation of the stress-energy tensor. This higher-order object contains energy density, pressure, twisting forces, and momentum. The whole thing is conserved together in a very particular way, and in certain physical scenarios this forces energy to not be conserved. It also doesn't make sense to say that the energy goes into pressure or whatnot: all of the terms in the stress energy tensor can go down together just fine (the way it's conserved is specific, but a little weird and counter-intuitive).

* Fun fact: Emmy Noether is one of the few women who have theorems with their names on them. Sexism has been endemic in the sciences for a long, long time...

 

[Fabio Sachs]

Indeed women have had to struggle harder in the sciences, as well as in other fields. That is by no means helped by the convention of crediting articles with the last names only! Had you not said otherwise and I would have, in involuntary but automatic sexism, imagined a Mr, instead of a Ms. Noether..!