# What caused inflation in the big bang theory?

1. Mar 27, 2004

### Royce

What caused inflation in the big bang theory?
I've read a few things that seem pure speculation designed to give a cause for something thought to necessarily have happened such as an antigravity force that faded at the end of the inflationary period. It seems too contrived to me.

2. Mar 28, 2004

### meteor

Habitually, inflation was explained being caused by a scalar field, the inflaton, that was the field that caused the acceleration. Then some theories proposed the existance of not one, but two scalar fields driving inflation (hybrid inflation and supernatural inflation are conspicuous examples). The last fad in cosmology is Loop Quantum Cosmology. In LQC there's inflation, but it's not caused by the inflaton or other scalar field, but is caused by quantum properties of the gravitational field itself

Last edited: Mar 28, 2004
3. Mar 29, 2004

### hellfire

Inflation is postulated to have been produced by a field with positive (and constant) energy density, but exterting a negative pressure. This is a characteristic of so called scalar fields.

In general relativity gravity couples not only to density but also to pressure, thus an antigravitational effect may take place if the pressure is acting against density.

This phenomenon is also assumed to take place now: some observations indicate that the expansion of space accelerates. If gravity due to energy density were the only acting force, then the expansion should decelerate. The accelerated expansion today is postulated to be produced by a cosmological constant (a vacuum energy density) which is a kind of scalar field.

The difference between now and inflation is, that the universe contains now other components (like matter) than a scalar field. During inflation, the scalar field was widely the dominant component. In such a case the expansion becomes exponential (the solution to the Friedmann equations is scalled deSitter model).

Note that due to the expansion of space and volume growth, the scalar field got more and more energy (since its energy density remains always constant). Inflation terminated when a part of the energy accumulated in the scalar field was transferred to the matter fields creating matter. This process is known as reheating.

Then, the expansion became driven not only by the scalar field but also by other fields. The strong antrigravitational effect faded and the expansion ceased to be exponential.

Inflation is of course a speculation, but it explains a lot of things and AFAIK it is difficult today to figure out a mechanism which could replace it.

(…I hope I did not write anything incorrect).

Regards.

4. Mar 29, 2004

### Njorl

The universal government payed its energy density debt by printing more space-time currency. That always causes inflation.

;)

Njorl

5. Mar 29, 2004

### pmb_phy

Basically inflation is antigravity in the sense that there is a gravitational repulsion. There are several ways for such a repulsion to occur. One is a non-zero cosmological constant. The other is vacuum energy and the third is as explained above, i.e. negative presssure. To see how pressure can act as a source in GR consider the weak field limit for a relativistic fluid which mass density $$\rho$$ and pressure p. Then

$$\nabla^2\Phi = 4\pi\G(\rho + 3p/c^2)$$

The necessary (but not sufficient) condition for a period of inflation is

$$\rho_{active} = \rho + 3p/c^2 < 0$$

which produces gravitational replusion since the right hand side of the first equation acts like a negative mass density. The term $$\rho_{active}$$ is the active gravitational mass density.

A similar thing happens with a positive cosmological constant.

Note: Regarding the inflaton - As I understand it, it is the vacuum energy of the scalar field which drives inflation and not the scalar field itself.

To see this from the man himself, i.e. Alan Guth, the creator of the infation theory, see

http://ocw.mit.edu/OcwWeb/Physics/8...AstrophysicsSpring2003/LectureNotes/index.htm

Go down to Guth's lecture and click on the material to the right which you'd like to see.

He also discussed the possibility of creating a universe in the laboratory. [:-)]

Last edited: Mar 29, 2004
6. Mar 29, 2004

### Mike2

And if you continue and cancel out $$\rho$$, then this only says that the speed of light must be less than the square root of negative 3. What?

7. Mar 29, 2004

### Royce

This, at least, I, as a non-scientist, can understand . Thanks to all of you. I wish I could say that I now understand it better but negative pressure, antigravity and scalar fields are hard for me to visualize and grasp. However, reading it again in different words has made it a bit easier to accept. Thanks again.

8. Mar 30, 2004

### pmb_phy

That just means that you can't cancel out $$\rho$$. $$\rho$$ is mass density and mass density can never be zero if there is pressure.

When you make an assumption which leads to something which is not physically meaningfull then that assumption is invalid

9. Mar 30, 2004

### marcus

I think I see the source of the confusion.
The symbol p (for pressure) looks like the symbol rho (for mass density)
if they were the same then you could divide out, or cancel out as you say.
and get a nonsense inequality about the speed of light

but rho and p are different so you cant do that cancelation
in fact they even have different units (unless you are working in a
system of units where c is dimensionless----like a system with c = 1)

to understand better, substitute A and B for rho and p
so the two look good and different

$$\rho + 3p/c^2 < 0$$

$$A + 3B/c^2 < 0$$

If they were the same, with A identical to B,
then
$$A + 3A/c^2 < 0$$
and you could divide out, assuming A non-zero,
$$1 + 3/c^2 < 0$$
and then
$$c^2 + 3 < 0$$
and then, as you say,
$$c^2 < -3$$

Last edited: Mar 30, 2004
10. Mar 30, 2004

### Mike2

Oops! My mistake, sorry.

11. Mar 30, 2004

### pmb_phy

Ah! Thanks marcus. Yes. That does seem to be the case. Thanks.

12. Mar 30, 2004

### Mike2

So are you saying that inflation stopped when mass was produced,... Like mass acted as an anchor to slow the expansion?

Couple quick questions? How fast was the inflation,... faster than light, at the speed of light?

Are you saying that there was no mass until inflation stopped, or slowed?

Thanks.

13. Mar 30, 2004

### hellfire

Mike2, I have to admit that my understanding of the subject is not deep (the math is heavy for me), but, anyway, may be I can try to answer your questions.

Before inflation there may be densities associated to other fields than the scalar field. This densities will drastically decrease and are negligible at the end of inflation (and before reheating) compared to the density of the scalar field (which has constant energy density).

The end of inflation is determined only by the behaviour of the scalar field. As already mentioned here, there is a false vacuum state during inflation (a state with more energy than the ground state) which decays in finite time. The phase of decay is known as 'slow roll' . During this phase the kinetic energy of the scalar field is negligible against the potential energy. This potential energy generates the exponential expansion.

After this phase the kinetic energy becomes relevant, the scalar field oscilates and transfers energy to the matter fields. This is the reheating process. How this transfer takes place is a question I cannot answer. I belive this is a heavy one (particle physics stuff involved).

The speed of inflation depends on the potential energy of the scalar field. The Hubble parameter H has a constant value during inflation and depends on the potential. The scale factor scales as a ~ exp(H t). One can find points in space receding at superluminal speeds. But note that this is not a specific feature of inflation, since superluminal recession takes also place today (and AFAIK in every cosmological model with a Hubble law).

Regards.

14. Apr 6, 2004

### Matrixman13

I look at inflation like this....

The inflaton field was the dominant field in the early universe. This field is normally in a low energy, ground state. But because of a random fluctuation, the energy spiked to the peak of its potential energy. This blew the fabric of spacetime outward at alarming speeds (many times faster than the speed of light.) Some may ask whether this violates relativity but it does not because it is accelerating space itself not traveling through space. the energy then slid back down to its ground state leaving the by product, matter. The matter that is now in the universe then slowed the expansion to a reasonable rate.

15. Apr 6, 2004

### Mike2

What does matter have to do with space? Is matter a form of space, an contraction of space that resists expansion?

Thanks.

16. Apr 10, 2004

### Newton

Last edited: Apr 10, 2004
17. Apr 10, 2004

### Newton

In fact very distant galaxies are receding from us at speeds greater than the speed of light today!

18. Apr 10, 2004

### Haelfix

A few misconceptions...

'Slow roll' is not necessary for inflation, it is however if there was only one round of inflation (but not two), it is an approximation in the differential eqns.

The original inflation model was taken to be the form of the Higgs particle (also minimally a scalar field), unfortunately it does not work. There is no way to end inflation with that model.

Nowdays, a veritable industry has gone into postulating the shape of the inflaton potential. There are literally hundreds of ways inflation can take place, none of them have much to do with particle physics as it currently stands.

As has been said before, generically its a way to cause exponential expansion of space-time, in order to smooth out any inhomogenities of matter fields, such that it ends up looking like what we see today.

The problem is always the same. Only the last few efolds carry observational consequence, so its very hard to falsify the hundreds of inflation models (only one of course can be correct). Only extremely sensitive probes of the CMB and galaxy structure can reveal differences, which is going to be a huge enterprise of Astronomy for the next 20 or so years.