The Role of Inflation in the Expansion of the Universe

[N3Wparadigm]

Quick question from a newbie, was the inflation of the universe faster than the speed of light ?

Having heard about the proposed speed of inflation (on TV) it seemed to be faster than the speed of light, surely never possible, so how fast was this inflation of the universe ?

"in a millionth, of a millionth, of a millionth, of a millionth, of a millionth, of a millionth of a second, it went from smaller than the size of an atom to bigger than a galaxy"

 

[Mark M]

Quick question from a newbie, was the inflation of the universe faster than the speed of light ?

Having heard about the proposed speed of inflation (on TV) it seemed to be faster than the speed of light, surely never possible, so how fast was this inflation of the universe ?

"in a millionth, of a millionth, of a millionth, of a millionth, of a millionth, of a millionth of a second, it went from smaller than the size of an atom to bigger than a galaxy"

Welcome to the forum!

Yes it was, and so is the expansion today. Make sure you understand the universe does not have a boundary, it is either infinite, or it wraps back around on itself in all directions. When the universe expands, it expands from every point. The distance between everything doubles. The analogy of the universe going from the size of an atom to that of a galaxy is very misleading, that isn't how expansion is measured.

Remember, special relativity replaces a limit on how fast objects can move through spacetime. Space itself, however, does not have a 'speed limit' in the sense that there is no limit to the rate of expansion, the Hubble Constant.

 

[phinds]

Quick question from a newbie, was the inflation of the universe faster than the speed of light ?

Having heard about the proposed speed of inflation (on TV) it seemed to be faster than the speed of light, surely never possible, so how fast was this inflation of the universe ?

"in a millionth, of a millionth, of a millionth, of a millionth, of a millionth, of a millionth of a second, it went from smaller than the size of an atom to bigger than a galaxy"

You are very likely putting three different things together here.

First, there is what is normally called the "inflationary period" of the early universe, which happened in a very early and VERY tiny fraction of a second, during which time the universe changed size by a factor of something like 10E80, and then inflation stopped and the expansion settle down to a more sedate pace. This expansion is the second thing of the three I refereed to.

Then several billion years ago, the expansion (which until about 10 years ago was thought to be slowing down) started accelerating. It is this acceleration that has caused the distances between widely separated systems to increase at greater than light speed.

SO ... we have

1) Inflation
2) expansion
3) accelerated expansion

During none of these did anything move "in" space at FTL speeds, distances just got bigger.

 

[orp0piru]

According to Wikipedia, inflation started at 10^-36 s and ended at 10^-32 s.
During this time the radius doubled 90 times, making the volume grow by a factor of 10^78.

The start size was about 10^-20 times the size of a proton,
so in the end (after 0.999*10^-32 s) the size of the universe was about 10cm,
about the size of a tennis ball.

Since speed = distance/time,
the speed of expansion was 0.1m/(.999*10^-32 s)
about 1.001*10^31 m/s
Which when compared to the modest speed of light, 3*10^8 m/s
is MONSTROUS, about 3.3*10^22 times the speed of light.

 

[Mark M]

According to Wikipedia, inflation started at 10^-36 s and ended at 10^-32 s.
During this time the radius doubled 90 times, making the volume grow by a factor of 10^78.

The start size was about 10^-20 times the size of a proton,
so in the end (after 0.999*10^-32 s) the size of the universe was about 10cm,
about the size of a tennis ball.

Since speed = distance/time,
the speed of expansion was 0.1m/(.999*10^-32 s)
about 1.001*10^31 m/s
Which when compared to the modest speed of light, 3*10^8 m/s
is MONSTROUS, about 3.3*10^22 times the speed of light.

There is no reason to state the size of the universe at any time. If it is finite, then it doubles back on itself, and we don't know how large it would be. It may also be infinite.

 

[Flustered]

Nothing inside the universe travels faster than light, but the universe it self can travel at any speed it pleases.

 

[orp0piru]

I just did a conservative version from this lecture... in which they claim that the expansion was a few meters. I toned it down based on the stuff I read in wikipedia.

http://www.youtube.com/watch?v=e_4bMIqmV9U#t=20m25s

 

[bapowell]

According to Wikipedia, inflation started at 10^-36 s and ended at 10^-32 s.
During this time the radius doubled 90 times, making the volume grow by a factor of 10^78.

The start size was about 10^-20 times the size of a proton,
so in the end (after 0.999*10^-32 s) the size of the universe was about 10cm,
about the size of a tennis ball.

Since speed = distance/time,
the speed of expansion was 0.1m/(.999*10^-32 s)
about 1.001*10^31 m/s
Which when compared to the modest speed of light, 3*10^8 m/s
is MONSTROUS, about 3.3*10^22 times the speed of light.

It is not correct to speak of the "speed of expansion." Instead, cosmologists speak of "expansion rate." For a given expansion rate, determined by the Hubble parameter, H, one can determine the recession velocity of a distant object via Hubble's law, v=Hr, where r is the distance to the object. So, it's incorrect to equate the expansion rate of the universe to the rate of change of distance (of the radius of the universe no less) over time.

Also, the radius of the observable universe did not increase substantially at all during inflation -- where are you finding this information? The radius of the observable universe is determined by the Hubble scale, $H^{-1}$: during quasi-de sitter expansion the Hubble parameter is very close to constant, meaning that the observable universe didn't really grow all that much over the course of inflation. That's not to say that the initial inflating patch didn't grow substantially -- it did, increasing in scale by a factor of at least $\sim 10^{25}$.

Also, to the OP as well, it is a misconception to say that inflation is characterized by "faster than light expansion" or similar. Even for non-inflationary spacetimes objects with separations on the order of the Hubble distance will have superluminal recession velocities. The important difference between inflation and non-inflation is that, in non-inflationary spacetimes, the Hubble distance is increasing faster than the expansion, so that galaxies that were once moving apart with superluminal recession velocity no longer do so in the future. During inflation, the critical difference is that the Hubble distance is increasing at a slower rate than the (inflating) spacetime, so that objects that are receding superluminally will do so forever (as long as inflation lasts, that is.) This is equivalent to there existing an event horizon during inflation.

 

[orp0piru]

Also, the radius of the observable universe did not increase substantially at all during inflation -- where are you finding this information?

http://en.wikipedia.org/wiki/Inflationary_epoch
"expansion increased the linear dimensions of the early universe by a factor of at least 10^26"

Since (10^26)^3 = 10^78, the factor of volume growth, it sounds a lot like an expanding ball, to me anyway.

Also, Andrew Lange mentions an "expansion" to a "few meters" in this lecture, how is this not an expanding ball?

http://www.youtube.com/watch?v=e_4bMIqmV9U#t=20m25s

 

[N3Wparadigm]

So is it correct to say that during this inflationary period, I could choose a point in space, a selected point (A) and it moved away from another selected point (B) faster than the speed of light ? Or rather the distance between them expanded faster than the speed of light.

I don't have the education to comprehend what you're saying.

 

[phinds]

So is it correct to say that during this inflationary period, I could choose a point in space, a selected point (A) and it moved away from another selected point (B) faster than the speed of light ? Or rather the distance between them expanded faster than the speed of light.

yes, that is correct

 

[bapowell]

So is it correct to say that during this inflationary period... Or rather the distance between them expanded faster than the speed of light.

Yes, except that again, this has nothing to do with inflation. In any expanding spacetime, there is always a separation (the Hubble distance) at which this is true.

 

[bapowell]

http://en.wikipedia.org/wiki/Inflationary_epoch
"expansion increased the linear dimensions of the early universe by a factor of at least 10^26"

Since (10^26)^3 = 10^78, the factor of volume growth, it sounds a lot like an expanding ball, to me anyway.

Also, Andrew Lange mentions an "expansion" to a "few meters" in this lecture, how is this not an expanding ball?

http://www.youtube.com/watch?v=e_4bMIqmV9U#t=20m25s

No, indeed space is expanding. But the expansion factor of space and the radius of the observable universe are two different things! Perhaps when you spoke of radius of the universe you meant the scale factor (this identification is fine for closed universes), but not in general.

 

[orp0piru]

point (A) and it moved away from another selected point (B) faster than the speed of light ?

Yes. If it were not so, the observable universe's size would be a "mere" 2 x 13.7 billion light years, when actually it is 2 x 46 billion ly. The speed can be verified by measuring the red shift from the objects at the edge of the observable universe.
For more info see http://en.wikipedia.org/wiki/Size_of_Universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws

 

[N3Wparadigm]

So from the POV of point (A), point (B) moved away from it faster than the speed of light (or vice versa) -

So point (B) from the POV of point (A) has achieved the impossible and traveled faster than the speed of light?

Therefore the speed of light isn't a universal speed limit as inflation demonstrates.

?

 

[Some Slacker]

Again I think you are confusing expansion of space with moving through space.
Space has no limit to its expansion.
Anything moving through space is what has a limit.

 

[Mark M]

So from the POV of point (A), point (B) moved away from it faster than the speed of light (or vice versa) -

So point (B) from the POV of point (A) has achieved the impossible and traveled faster than the speed of light?

Therefore the speed of light isn't a universal speed limit as inflation demonstrates.

?

No. As I said in the second post, and as Flustered also stated, relativity places a limit on the velocity of objects moving through spacetime. The recession of galaxies is due to the expansion of the universe, e.g. space being created in between all of the galaxies.

It's as if I owned a river, and placed a speed limit of boats in this river at 50 mph, and kept track of their speed using the boats speedometer. A boat could be traveling down the river at 40 mph, but if the river is flowing at 30 mph, its total velocity is 70 mph. But since 30 mph is due to the flowing of the river itself, my speed limit is maintained.

Similarly, galaxies dragged along by the expansion of space faster than light do not violate special relativity.

 

[bapowell]

Therefore the speed of light isn't a universal speed limit as inflation demonstrates.

You are applying special relativity to a case where it has no business. Both observers A and B are both locally at rest -- they are at rest with respect to the expansion. It is the space itself that is doing the expanding, "carrying" observers A and B along with it. There is no violation of special relativity (which holds only locally).

(I see Mark has already just replied...)

 

[N3Wparadigm]

No. As I said in the second post, and as Flustered also stated, relativity places a limit on the velocity of objects moving through spacetime. The recession of galaxies is due to the expansion of the universe, e.g. space being created in between all of the galaxies.

It's as if I owned a river, and placed a speed limit of boats in this river at 50 mph, and kept track of their speed using the boats speedometer. A boat could be traveling down the river at 40 mph, but if the river is flowing at 30 mph, its total velocity is 70 mph. But since 30 mph is due to the flowing of the river itself, my speed limit is maintained.

Similarly, galaxies dragged along by the expansion of space faster than light do not violate special relativity.

... but if it were your goal to try and achieve 70mph in your boat to an observer on the river bank, you would use this river as a means of achieving it.

I don't understand how using the expansion of space itself is "cheating" with regard to breaking the speed of light limit, relativity still stands, if you were an observer at point (A) you would see point (B) move away at faster than light speeds, surely how this happens is irrelevant, just by very quickly placing more space between you and point (B) its the same for relativity as saying (A) is moving away from (B) the same as (B) is moving away from (A)

 

[phinds]

... but if it were your goal to try and achieve 70mph in your boat to an observer on the river bank, you would use this river as a means of achieving it.

THAT part of the anaology is why it is ONLY an analogy. You cannot "use" the expansion of the universe in the same fashion.

I don't understand how using the expansion of space itself is "cheating" with regard to breaking the speed of light limit, relativity still stands, if you were an observer at point (A) you would see point (B) move away at faster than light speeds,

yes, that it exactly what happens

surely how this happens is irrelevant

no, it is NOT irrelevant. SR places a limit on travel IN space, not travel OF space, if you see what I mean

The river analogy is a good one (but it is ONLY an analogy) in that it IS the boats speedometer that is measured, not the total speed.

 

[bapowell]

I don't understand how using the expansion of space itself is "cheating" with regard to breaking the speed of light limit, relativity still stands, if you were an observer at point (A) you would see point (B) move away at faster than light speeds, surely how this happens is irrelevant, just by very quickly placing more space between you and point (B) its the same for relativity as saying (A) is moving away from (B) the same as (B) is moving away from (A)

It's not the same, for the precise reason that special relativity applies only in static spacetime. Once you start talking about dynamics of the spacetime (like expansion) you must apply general relativity. And here you'll find that even the initial question is ill-posed, since there is no well-defined notion of relative velocity across cosmological distances in GR.