# Distinguishing between flatness

1. Dec 30, 2009

### Ranku

The universe is observed to be flat. This is due to its energy density, and also due to purported inflation. How do we distinguish between the contribution of each toward flatness?

2. Dec 30, 2009

### marcus

If I understand what you have in mind, then there is no need to distinguish because there are two types of causation.

The two causes are not mutually exclusive.

If inflation occurred, and was the main cause of spatial flatness, then inflation created the conditions for the energy density to be right.

The historical cause (a brief episode in the first fraction second) prepared for the immediate presentday circumstance.

And so it is the same thing. There is no need to sort out the responsibility and divide up the blame or credit for flatness

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You could look a bit more closely, if you want, at the idea of flatness depending on the energy density being right. What is the "right" density at any given moment depends on the percentage expansion rate----to have spatial flatness there must be a balance between expansion rate and density.

If in some historical epoch the density is higher , then (to avoid curling up) the expansion rate must be higher. But it must not be too high or flatness will be spoiled as well. The density must always be just right for the expansion rate and viceversa. There is a simple formula that describes this balance.

It is called the formula for the "critical density" because it tells you what the right density to have is, for any given Hubble rate H. The formula is easy to derive from the Friedman equation. Probably you can look up wikipedia for "critical density (cosmology)" and find the formula.

Basically it says that the density rho has to be proportional to H2, the square of the fractional expansion rate.

There is a beautiful feature that if you start off in perfect balance, then you stay. If you start off right, you stay right. So what inflation ensures is that you start off close enough to right, for practical purposes in (nearly) perfect balance----and then she will stay (nearly) flat.

So both are the cause and they are the same cause---one is the historical event, far in the past, and the other is the presentday circumstance stemming from that early event.
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Look at this:
http://en.wikipedia.org/wiki/Friedmann_equations
scroll down to the section on "the density parameter"
You will see the formula. They give the critical mass density. To convert mass density to energy density you multiply by c2. Just a conventional difference.

Last edited: Dec 30, 2009
3. Dec 30, 2009

### Ranku

So flatness itself is no proof of the occurance of inflation; flatness could well have been caused by the energy density alone.

And what is it that I hear about WMAP data ruling out the simplest inflationary models?

4. Dec 31, 2009

### Chalnoth

The energy density of what, precisely? Different sorts of energy densities do different things. Inflation is proposed as a particular sort of field that behaves at early times very much like vacuum energy, and that sort of energy tends to dilute away curvature.

Well, it doesn't really. It comes sort of close to ruling out a perfectly-flat primordial power spectrum, which isn't really an expected feature in inflationary models anyway. Basically, because inflation has to end, we expect there to be some deviation from a perfectly-flat primordial power spectrum. A perfectly-flat primordial power spectrum was a pre-inflation idea that doesn't really have any physical basis.

5. Dec 31, 2009

### Ranku

Energy density of dark energy + dark matter + regular matter + radiation

6. Dec 31, 2009

### Chalnoth

Those energy densities as measured today would not have caused the universe to approach flatness in the past. Before about 5 billion years ago, the trend would have been away from flatness in that situation.

7. Dec 31, 2009

### Ranku

Do we know if the universe was flat before 5 Gy ago, i.e., before it started expanding acceleratively due to dark energy? And if it was flat before 5 Gy ago, would that not be irrefutable proof of inflation? Or can the universe be flat before 5 Gy ago even without inflation?

8. Dec 31, 2009

### Chalnoth

The change in curvature due to dark energy over that time has been extremely minimal. In order for us to be unable to measure any deviation from flatness at the current time, our universe had to be massively, absurdly flat in the very early universe (for example, when baryogenesis was occurring).

9. Jan 1, 2010

### Ranku

Sorry, I'm not getting any of this :(. Could you just tell me if there is observational evidence that the universe was flat before 5 Gyr? And if so, can we distinguish between if that flatness at that time was caused by dark energy or inflation?

10. Jan 1, 2010

### twofish-quant

The way that the equations work, anything that is not-flat gets more and more not-flat as time goes on.

Now you might ask what happens if our understanding of gravity is wrong, which is a great question, but this sort of behavior tends to happen whenever you have any sort of attractive force. Once something is not flat, it gets more and more not-flat as time passes.

Dark energy doesn't help this. It makes the problem even worse.

The reason for inflation is that if the universe is "sort of flat" right now, at some point in the past it had to be really, really, really flat.

Last edited: Jan 1, 2010
11. Jan 1, 2010

### Chalnoth

If there is no observational evidence of deviation from flatness now, then there certainly isn't any evidence of any deviation as of 5 Gyr ago.

12. Jan 1, 2010

### Chalnoth

Huh? In what sense does it make the problem worse? It doesn't solve the problem, granted, but it does make the universe flatter as time goes on.

13. Jan 1, 2010

### twofish-quant

Never mind. I think I got my signs mixed.