Inflation

[themos]

It is accepted that space-time can be allowed to expand faster than the speed of light during the Big Bang theory's inflation phase

The way I think about this is that the speed of light and the expansion of the universe are apples and oranges and can't be compared.

The speed of light is in meters per second.

The expansion is in % per second.

[JulianO]

Perhaps I wrote was a little strong; let me try to be more precise. My understanding was that, taking GR at face value, it was not possible to explain the homogeneity and isotropy of the universe. Alan Guth proposed the theory of inflation, along with a possible mechanism, to explain the thermalisation of the universe at very early timescales.

Well actually he proposed it to get rid of annoying magnetic monopoles, but it solved quite a few issues with one blow.

This theory predicts a perfect black body curve, which was what WMAP measured, thereby confirming the theory. I use the phrase "confirming the theory" in the sense that in science we never really prove things (that's for the mathematicians), but rather data either provides support for a theory, or proves it is wrong.

You are right of course that initial conditions could provide a flat universe without the need for an inflationary phase, but wouldn't Occam's razor get rid of that stunningly unlikely scenario?

I asked this question of an expert in the field (which I am definitely not!) and he said its a possibility, but would mean a very high entropy so probably unlikely, but who knows. I maintain that anything that is a staggeringly small size across such as the initial BB might well be in thermal equilibrium - but thats just applying gut feel.

I'm not familiar with the ekpyrotic model -- as I'm sure you can tell, this discussion isn't really my area of expertise

Nor mine really - but I've just had 6 hours of lectures on it!

A very readable decription of the ekpyrotic model is in Endless Universes.

Well worth a read.

I genuinely thought that the WMAP data was a strong confirmation of Guth's theory -- he even mentions it in his book! -- but perhaps I'm a little off?

Well I'm being a little pedantic - that's true. I think the power spectrum of the CMB is what supports inflation - the variation in the temperature by 1/10000, and that has definitely got from WMAP data. The black body curve is just the result of the universe being at a given temperature at last scattering, and cooling over the time since.

[smolloy]

Nor mine really - but I've just had 6 hours of lectures on it!

A very readable decription of the ekpyrotic model is in Endless Universes.

Well worth a read.

Thanks for the link! Despite being a professional physicist, I honestly love "taking my work home" -- anything to increase the breadth of my knowledge is good

The black body curve is just the result of the universe being at a given temperature at last scattering, and cooling over the time since.

Not just that, but the fact that the curve is precisely a black body (not everything giving off heat is a black body -- in fact it is very rare to see a real black body) is a consequence of inflation. That, and the fact that the CMB is the same temperature everywhere we look (aside from the small variations responsible for structure formation).

[George Jones]

Only thing I do not get is if the expansion of the universe accelerates, how can the expansion rate per megaparsec slow down?

As an example (possibly a very confusing example), consider a toy universe and galaxies A, B, C, D at three different instants of cosmological times, t = 1, t = 2, and t = 3.

At times t = 1, t = 2, and t = 3, the proper distances to galaxies A, B, C, D are given by the table:

         |   A    B    C    D
-------|-------------------
t = 1  |   1    2     3    4
t = 2  |   4    8   12   16
t = 3  |   9   18  27   36

At times t = 1, t = 2, and t = 3, the recessional speed of galaxies A, B, C, D are given by the table:

         |   A    B    C    D
-------|-------------------
t = 1  |   2    4     6    8
t = 2  |   4    8   12   16
t = 3  |   6   12  18   14

What are the values of the Hubble constant H at the three times? Since v = H d, the Hubble constant is given by H = v/d. This give that H equals 2, 1, and 2/3 at times 1, 2, and 3.

Note: 1) at each instant in time, the Hubble constant is constant, i.e., independent of the galaxy used to calculate it; 2) the Hubble constant decreases with time.

What about acceleration or deceleration of the expansion of this universe? During the time interval from t = 1 to t = 2, Galaxy A "moves" a distance Δd = 4 - 1 = 3. During the later but equal-length interval from t = 2 to t = 3, the same galaxy, Galaxy A, "moves" a greater distance, Δd = 9 - 4 = 5. This is an indication that the expansion of the universe is accelerating. The fact that this universe is accelerating is independent of which galaxy is used.

This toy model is a Freidman-Robertson-Walker universe that has its scale factor given by a(t) = t^2.

[scogyrd]

These might be daft questions but when we talk of space expanding what exactly is the space that is expanding? Does it consist of anything or is it just empty space?

And, if spave is made of something (or possibly nothing) then does that mean that the space is thinning out as it expands or is it constantly being replaced by more space to keep it at the same density? If that makes any sense.

Also, what is the difference between space expanding and objects moving apart? How can we tell the difference?

[themos]

Does it consist of anything or is it just empty space?

Empty space turns out to be quite full of stuff, if quantum theory is to be believed. You just can't make it more empty. Which is an interesting thing in itself.

And, if spave is made of something (or possibly nothing) then does that mean that the space is thinning out as it expands or is it constantly being replaced by more space to keep it at the same density? If that makes any sense

That's an interesting thought. I don't think anybody knows. All they have is some observations and a simple model for this expansion. Whether space can be said to have a "density", I am not sure.

Also, what is the difference between space expanding and objects moving apart? How can we tell the difference?

You can imagine a coordinated "moving apart" of objects everywhere. But if this was some ordinary force moving them it wouldn't be of such universal character and be the same in two completely different corners of the universe. So it makes more sense to think of it as a fundamental property of spacetime itself.

[JulianO]

Also, what is the difference between space expanding and objects moving apart? How can we tell the difference?

On small scales, space is not expanding, because the expansive force is smaller than gravity. So galaxies and solar systems are not expanding. Not would clouds of intergalactic gas expand normally, as they would either tend to stay as a cloud, or collapse if the conditions were favourable.

If we look at our local group of galaxies, they are mostly coming towards us, so the space between us is getting smaller. Its only on huge scales that things are expanding.

So billions of years down the line, observers from our galaxy will see the milky way, and few other local galaxies, and little else.

[George Jones]

Empty space turns out to be quite full of stuff, if quantum theory is to be believed. You just can't make it more empty. Which is an interesting thing in itself.

And, if spave is made of something (or possibly nothing) then does that mean that the space is thinning out as it expands or is it constantly being replaced by more space to keep it at the same density? If that makes any sense.

That's an interesting thought. I don't think anybody knows. All they have is some observations and a simple model for this expansion. Whether space can be said to have a "density", I am not sure.

I am going to expand (excuse the pun) on the comments by themos.

The cosmological constant (also called dark energy) is thought to be responsible for the acceleration of the universe, and our present standard theories cannot observationally distinguish between two possibilities: 1) the cosmological constant is a physical constant (like Newton's gravitational; 2) dark energy is an energy associated with the vacuum, which is thought to be "quite full" of quantum stuff.

If 2), then the energy density of the vacuum remains constant as space expands, because it is just more of the same vacuum. (The density of two gold bars is the same as the density of one gold bar). The total¹ energy density of the universe is the energy density of matter (via E = mc^2) plus the energy density of the vacuum. As the universe expands, matter density decreases as matter thins out (most galaxies move away from each other), so the constant energy density of the vacuum starts to dominate the energy density of of matter goes down. The transition from a matter-density dominate universe to a vacuum-density universe happen a few billion years ago

As themos has said, our present theoretical models are too simple. When we try to calculate the energy density of the vacuum, we get an answer that is many, many orders of magnitude larger than the observed value. We need better theories! To sort this, I think that we need a quantum theory of gravity with which we can do calculations.

Right now, vacuum energy density makes up about 74% of the total density of the universe. In the future, this will approach 100%.

There are some some similarities (negative pressure) between the proposed field that drove inflation field and dark energy, but the energy densities of these two things are/were vastly different.

¹In the early universe, the energy density of radiation dominated, but now it is much smaller than other densities.

[JulianO]

I am going to expand (excuse the pun) on the comments by themos.

Nice post George!

[Ptarmigan]

On small scales, space is not expanding, because the expansive force is smaller than gravity. So galaxies and solar systems are not expanding.

Help ! Do you mean that on small scales, in regions of high mass (big gravity), the expansive force is overcome by that gravity.

Or that we just see local mass (Andromeda and us) attracting eachother faster (greater than) than the expansion is pushing us apart.

ie. expansion of the space beween us is going on at the same rate as the universe is expanding just that we dont notice it cos gravity is bringing us closer faster ?

In otherwords, how do we distinguish between an expanding universe

and our rulers* becoming smaller ?

* I dont mean DavidC and GerorgeO ;-) I mean our measuring instruments.

[JulianO]

Help ! Do you mean that on small scales, in regions of high mass (big gravity), the expansive force is overcome by that gravity.

Or that we just see local mass (Andromeda and us) attracting eachother faster (greater than) than the expansion is pushing us apart.

ie. expansion of the space beween us is going on at the same rate as the universe is expanding just that we dont notice it cos gravity is bringing us closer faster ?

That is more or less the case. The dark energy force is very small, so it appears as a background force. Its sort of like if you had two cannon balls on the floor with a ruler between them. The maths says they should come together under gravity, but gravity is so weak compared to the frictional forces with the floor and the strength of the ruler that nothing happens. If you could arrange for them to be suspended freely in a vaccum in some way (e.g. remove all the other forces on them), you might see them come together slowly.

Similar with the expansive force, its very very weak, so you can completely ignore it on local and even galactic scales. However as it is a property of all space, if you get vast amounts of empty space, then it adds up to something significant (just as gravity is very weak, but you get a planets worth of mass together it adds up to something that stops you flying away).

In otherwords, how do we distinguish between an expanding universe

and our rulers* becoming smaller ?

* I dont mean DavidC and GerorgeO ;-) I mean our measuring instruments.

Well we can't if that is really happening, but because the forces are different in strength we can see the effects. We don't see the effects on rulers as there isn't enough space in a 1 meter stick to add up to any substantial expansive force (its dominated by electromagnetic interaction between atoms - although gravity theoretically should make it slightly shorter than that). There is enough space between galaxy clusters though and we can measure it there.

[themos]

then the energy density of the vacuum remains constant as space expands, because it is just more of the same vacuum

that sounds awfully like the Steady State theory, doesn't it?

[Williams]

In my view, light has mass and a finite speed in which it moves through a vaccum due to all the other stuff clutering up the late universe. It's not hard to imagine faster speeds of any particle if there was not much to interact with it early on. From what I understand, we think Gravity came along late in the game, so it was a "flying apart universe" untill Gravity showed up which is where I can imagine the original inflation idea came from in the first place.

Since our galaxy is about 13.2bn years old and we can only see a certain distance in the 370 years of looking up, it's a BIG ask to assume we would even begin to understand what happened.

Hubble discovered red shift when looking at distant galaxies and therefore theorized everything is moving away from us, but that might only be in our part of this vaccum.

Nature seems to be pretty consistant in terms of scale, I've often wondered what our view of this place might be if we scaled down to the size of an atom and looked up at our night sky..

When we understand "Dark energy" and "Dark matter" we might be closer to answering this baffling question.

Just my personal view

[JulianO]

that sounds awfully like the Steady State theory, doesn't it?

It does - but its only a tiny bit of the picture. Other things like the CMB, the acceleration and other things like BAO all point away from a steady state universe.

[JulianO]

In my view, light has mass and a finite speed in which it moves through a vaccum due to all the other stuff clutering up the late universe. It's not hard to imagine faster speeds of any particle if there was not much to interact with it early on.

Light has mass - or at least momentum. What other stuff might be cluttering up a vacuum? Light has to interact with it to slow it down. There was a lot more to slow it down in the early universe, in fact up to 300,000 years light was bashing into everything without getting very far!

From what I understand, we think Gravity came along late in the game, so it was a "flying apart universe" untill Gravity showed up which is where I can imagine the original inflation idea came from in the first place.

Well only if you consider 10^-43 seconds after the big bang as late in the game. Gravity was one of the first things to separate out in the big bang.

Since our galaxy is about 13.2bn years old and we can only see a certain distance in the 370 years of looking up, it's a BIG ask to assume we would even begin to understand what happened.

We can see out to a good fraction of that, nearly all the way for specific objects.

Hubble discovered red shift when looking at distant galaxies and therefore theorized everything is moving away from us, but that might only be in our part of this vaccum.

Hubble charted the recession velocities of galaxies, and found a linear relationship between their distance from us and the red shift. Others have now extended it further, and found its not linear, but accelerating. In either case they are using a good fraction of the visible universe to make such a statement.

Nature seems to be pretty consistant in terms of scale, I've often wondered what our view of this place might be if we scaled down to the size of an atom and looked up at our night sky..

When we understand "Dark energy" and "Dark matter" we might be closer to answering this baffling question.

Just my personal view

We understand Dark matter quite well, although we;re not exactly clear what it is made of yet (lots of ideas - just need proving). Dark energy is more elusive. More understanding would certainly be useful though!

[DarkStar7]

And yet it matches the WMAP black-body data with an accuracy that is unmatched by any other scientific theory in the history of human thought.

http://map.gsfc.nasa.gov/media/ContentMedia/990015b.jpg

The error bars on the original plot were so small that they couldn't be plotted on the same scale, and the match with the theory of Inflation was so good that it received a spontaneous standing ovation when it was first presented.

Seriously. Humanity has never ever come up with a theory that matches the experimental evidence so well. Never. Your claim that it is "rubbish" is a little unconvincing, and needlessly rude.

The theory requires dark energy to exist, which is probably vacuum energy, which is all that is required.

Please be clear I rubbish only 'inflation' which is simply a mathematical construct to explain observation.. A bit like the epicycles which were used when we were forced to believe that the Earth was the centre of the universe.

The universe is expanding, it is accelerating, the cosmic background radiation is all around us. The trouble is no one has appreciated the effect of vacuum energy.. the dark energy that negates the need for inflation to occur very quickly 13.7billion yrs ago. It is obviously a continuous process that uses the uncertainty principle.. ( energy/time relationship)

The assumption has been made by inflation proponents that if we run time back the galaxies all rush together at large energies to a specific location of infinitesimal small size. The infinitesimal point is not one point but an infinite number of infinitesimal small points, in other words spread everywhere!

If all masses grew from vacuum energy then galaxies etc further back in time contained less mass.

The universe looked the same 13.7billion yrs ago as it does today, but our current view was born from a seed of quantum uncertainty in the quantum foam. It was a surprise when it was found that the universe is expanding, it was a surprise to discover energy comes directly from the vacuum it. They are observed and are scientific fact. There is potentially enough energy in one quantum fluctuation to produce any fermionic particle.This is what is so frustrating for me. There is no need for super luminal inflation.

[Williams]

JulianO, Cheers Since I'm not a scientist and haven't studied this topic at any sort of serious level, I can only visualize what might have happened. yes I was imagining plank times for gravity. If we don't think outside the box for things we cannot prove, we'll get stuck. For example, If the big bang happened, the moment all particles were born they got rules. What im saying is perhaps since all particles are already old now, they may never have the same rules as the first moment of creation.. It doesn't matter how many particles you smash together in the LHC, the particles are different compaired to the originals..

Maybe we'll find out one day that dark energy is the creator of the vaccum and responsible for the inital inflation? perhaps in it's original form it was "Light Energy" and we're just seeing the remnant leftovers.. who knows, but it's fun to think about and thats why I'm here cheers.

[themos]

Only more data will show us what the correct way of thinking is. I find there's been too much speculation for my liking recently.

[Williams]

I find there's been too much speculation for my liking recently.

Yeah thats fair to say if that was intended for my general direction, I'll leave you to discuss the facts

[themos]

It was aimed at the science journalists and the science popularisers.

[scogyrd]

Thanks for the replies everyone. I think I understand now although there is one thing that confused me...

(The density of two gold bars is the same as the density of one gold bar)

While the density of two gold bars may be the same as one would the density of one gold bar be the same as another one that has expanded billions of times past its original size?

Also, my original question was going to be about the cosmic microwave background radiation, instead of nothing, and how that relates to the expanding universe so I think I'll ask that now.

Now, we're told that the cbr was created after the big bang so, presumably, there is only a finite amount and we're also told that the universe is expanding, more so at the edges, so if this is the case shouldn't we expect to see less of the cbr where the universe is expanding faster and the cbr is being replaced by the vacuum?

I suppose what I'm asking is how can a finite amount of cbr be uniform in an expanding universe that isn't expanding at the same speed everywhere???

I must apologise if you're getting bored of all these questions but I cant seem to find an answer to them anywhere else.

[themos]

I suppose what I'm asking is how can a finite amount of cbr be uniform in an expanding universe that isn't expanding at the same speed everywhere???

But it is expanding at the same speed everywhere. For any observer that measures 13.7 billion years since the big bang, they will see the same cbr.

I think,

[themos]

the universe is expanding, more so at the edges

Eh? No. The expansion is at some fraction of a percent per year, everywhere.

[Ptarmigan]

Similar with the expansive force, its very very weak, so you can completely ignore it on local and even galactic scales.

Thanks for that, yes, just making sure that I hadnt missed an interaction of local gravity with the expansion.

We don't see the effects on rulers as there isn't enough space in a 1 meter stick

Well I wasnt meaning a schoolboy ruler! I was thinking "rulers" as a collective noun to mean all our measuring devices including supernovae or even as a thought experiment, suppose I had a ruler to lay between here and the andromeda galaxy (massless cos it might otherwise collapse into its own black hole!)

[JulianO]

Well - you can see from plots like this one:

That the graph is fairly linear out to about a redshift of 0.1 (which is about a billion years ago, and 400 Mpc). As it gets to redshift 1, you can start to see the bend in it, which is where the expansive force is becoming more obvious.

At redshit 1 we are half way back to the begining of the universe, and about 3000 Mpc distance.