What changes the rate of inflation

[amrhima]

Main Question or Discussion Point

I was wondering, if inflation caused space to expand so rapidly, what happened to slow it down to the current rate?

 

[Landrew]

I was wondering, if inflation caused space to expand so rapidly, what happened to slow it down to the current rate?

Without being a cosmologist, my purely intuitive answer is that the speed of inflation diminishes as the size of the "exploding" sphere increases.

My crude understanding is that inflation is the creation of time and space itself, therefore space itself is constantly being created (expanded) with the expansion of the universe. This would seem to explain the apparent violation of Einstein's relativity laws, whereby some objects appear to be traveling faster than light. It also seems to explain why the more distant the object, the faster it appears to be traveling away from us.

I welcome any real cosmologists to set me straight if I'm out of bounds.

 

[bapowell]

My crude understanding is that inflation is the creation of time and space itself, therefore space itself is constantly being created (expanded) with the expansion of the universe.

This is almost correct, Landrew. The key to getting inflationary expansion is maintaining a nearly constant energy density of a negative pressure fluid. In the simplest examples, this energy density is constant: as the universe expands, more fluid is 'created'. Inflation is not related to the creation of space or time, although it does tell space and time how to behave. The space is already there -- inflation just causes it to expand, or stretch.

This would seem to explain the apparent violation of Einstein's relativity laws, whereby some objects appear to be traveling faster than light. It also seems to explain why the more distant the object, the faster it appears to be traveling away from us.

This is all true, but it's true of any expanding spacetime, not just inflating spacetimes. Hubble's law, which relates the recession velocity of an object a distance r away from an observer, $$v = Hr$$, holds (approximately) in any expanding spacetime. You can see that there's a special distance (r = c/H) at which distant objects have superluminal recession velocities.

I was wondering, if inflation caused space to expand so rapidly, what happened to slow it down to the current rate?

Good question! If the energy density driving inflation remains constant, then indeed nothing slows the expansion -- the universe goes on inflating eternally. However, in realistic models of inflation, this energy density is not, afterall, constant. The energy density decays, and in doing so, the rate of expansion decreases. In fact, the transition from inflationary to non-inflationary expansion is very important, since it coincides with the reheating of the universe -- much of the energy associated with inflation gets converted into matter and radiation, replacing all the radiation and matter that the inflationary expansion dilutes.

 

[Landrew]

This is all true, but it's true of any expanding spacetime, not just inflating spacetimes. Hubble's law, which relates the recession velocity of an object a distance r away from an observer, $$v = Hr$$, holds (approximately) in any expanding spacetime. You can see that there's a special distance (r = c/H) at which distant objects have superluminal recession velocities.

Due to my own misunderstanding of physics no doubt, but I've always thought there was a problem with Einstein's speed limit on the speed of light. If someone drives away from you at 3/4 the speed of light, his headlights on, the light should be going 1.75 times the speed of light, except to you, who can't see it, but in real terms, isn't that a superluminal light speed?

 

[bapowell]

Due to my own misunderstanding of physics no doubt, but I've always thought there was a problem with Einstein's speed limit on the speed of light. If someone drives away from you at 3/4 the speed of light, his headlights on, the light should be going 1.75 times the speed of light, except to you, who can't see it, but in real terms, isn't that a superluminal light speed?

Einstein postulated that the speed of light was the same for every observer, regardless of their state of (non-accelerated) motion. That is, two observers moving relative to each other at a constant velocity both agree that the speed of light is c= 3x10^8 m/s. Your raise an important point -- shouldn't light also be subject to the additive nature of velocities? The answer is no! Light doesn't seem to care much whether its source is moving or not -- it always travels at the same speed.

I'm not sure I've addressed your question, because I'm confused about why you've set things up so that the car is driving away from the observer. However, if you place another observer in front of the car, as per the above discussion, they will measure the speed of the oncoming light to be 3x10^8 m/s, just as the driver does.

 

[amrhima]

Due to my own misunderstanding of physics no doubt, but I've always thought there was a problem with Einstein's speed limit on the speed of light. If someone drives away from you at 3/4 the speed of light, his headlights on, the light should be going 1.75 times the speed of light, except to you, who can't see it, but in real terms, isn't that a superluminal light speed?

You assumed that (V₁ +V₂)=V₁+V₂ but in special relativity combining two velocities is different and it is in fact (V₁+V₂)= V₁+V₂/(1+V₁V₂/C²)
This gives C always when C is one of the two velocities since V+C/(1+VC/C)=C and so that means that no matter how fast you go C (the speed of light) will always be C, and no matter how energy you add V will never exceed C

I believe the hubble expansion law does mean that there might be some galaxies moving away with speed greater than the speed of light, but not through space, rather with space (i.e. as space expands)

 

[marcus]

I was wondering, if inflation caused space to expand so rapidly, what happened to slow it down to the current rate?

Actually you put your finger on a nagging problem with inflation scenarios!

It is called the "graceful exit" problem.

Almost all the scenario junkies have to do something artificial by hand to get inflation to stop.

They postulate that the "inflaton" field does a "slow roll" down a potential hill. They postulate that the "inflaton" decays. And nobody has ever seen an inflaton. Plus no theory predicts the existence of an inflaton field.

So the inflaton is a purely MADE UP thing which persists for just the right length of time to get 60 e-folds of expansion. And then for some reason runs out of steam and quits. And then DECAYS producing all the wonderful matter and energy which we know and love.

"60 e-folds" of expansion is jargon for expansion by a factor of e⁶⁰. You know the number e? The base of the natural logarithms? e⁶⁰ is deemed to be the right amount of expansion for an inflation scenario so that it solves the flatness and horizon problems.

So if anybody tells you that the "GRACEFUL EXIT PROBLEM IS SOLVED" be skeptical.

However there is now a new idea on the table being studied and discussed by a Nobel laureate named Steven Weinberg, which explains inflation without having to invent an "inflaton" field and which automatically takes care of the "graceful exit" business.
This still has to be checked out, but there is a paper on it.

http://arxiv.org/abs/0911.3165
Asymptotically Safe Inflation
Steven Weinberg
13 pages
(Submitted on 16 Nov 2009)
"Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end."

It is free for download, just click on PDF. Don't be discouraged by the mathematical parts, there are some parts in plain English. This has not been checked out and it is very new, but it solves some nagging problems in a nice natural way that doesnt involve making up a lot of stuff and putting it in by hand. Plus Weinberg is one of the giants of 20th century physics. He's old now, but he's still someone solid to count on. There's a real chance something will come of it.

 

[bapowell]

Marcus, do you have to be so negative?!?! I absolutely agree that inflation has been a difficult thing to easily incorporate into particle physics models, but there has been lots of progress. Although not personally sold, I'm impressed at how much of an exact science brane inflation has become in recent years. Plus, there's still lots of ways of getting inflation out of SUSY and SUGRA (although I agree the eta problem is difficult to get around in a tasteful manner). Also, while not necessarily leaping out of fundamental theory, chaotic inflation models naturally incorporate a graceful exit. As do so-called natural inflation models, which are based on modest extensions of the SM.

Thanks for pointing out Weinberg's paper. I just think that inflation is doing a little better than you've made it seem!

 

[Chalnoth]

Yeah, this seems to me to be a required detail of any potential inflation model, not a serious problem for inflation in general.

Basically what happens is that the field that drives inflation has to decay rather rapidly when it hits the minimum of its potential. Once the inflaton field decays, the universe is extremely hot, radiation-dominated, and spatially-flat. This causes a rapid slowdown of the expansion rate.