# Inflation: Expansion of space

Tags:
1. May 14, 2015

### CassiopeiaA

A very fundamental doubt. Was inflation expansion of just space or the universe with whatever the state of matter it had?

2. May 14, 2015

### Staff: Mentor

The whole universe expanded, including all volumes inside.

3. May 14, 2015

### Chalnoth

The expansion of space is indistinguishable from the increase in distance between objects within space. They're two ways of describing the same phenomenon.

4. May 14, 2015

### Staff: Mentor

The latter. The details are very complicated and involve some very non-intuitive math and geometry, but the idea is that expansion causes distances between unbound objects to increase. This includes inflation.

5. May 15, 2015

### bapowell

Inflation can only occur if the universe is dominated by the right kind of energy density. This energy density needed to be uniform across the initially inflating region of the universe, and it needed to have the peculiar property that the density remained constant as the universe expanded. This constant energy density results in the hallmark accelerated expansion of inflation.

So the initially inflating universe had to be rather specially prepared -- the state of matter initially present was not arbitrary.

6. May 15, 2015

### CassiopeiaA

The energy density should be uniform, but how can it be constant during inflation?

7. May 15, 2015

### Chalnoth

It's not quite constant, but it does change very slowly. The super-short explanation is that there's a quantum field (called the inflaton) that has some potential energy. At some point, it takes on a particular value, and that value is represented by a specific energy density due to that potential energy. The tendency of the field is for its value to change in the direction of lower energy density. However, the expansion actually acts as a sort of friction, preventing the field value from changing quickly. If the parameters are balanced in the right way, such that this friction term is large, then this results in a nearly-constant energy density, which causes inflation.

If you want to read up on it in more detail, look around for, "slow roll inflation."

8. May 16, 2015

### bapowell

Energy is not conserved in general relativity.

9. May 24, 2015

### aboro

Chalnoth, I do not understand the basis for your answer (or perhaps the question that has been asked): I thought there is a distinction between the expansion of space between galaxies and over great distances as compared to what is happening locally. Thus, there is no expansion occurring between the moon and the earth. The moon is essentially the same distance from the center of the earth as it was a billion years ago. It is still about 3,000 miles between NYC and Los Angeles. The measurement for one mile today is the same as a mile being measured one billion years ago. Am I misunderstanding something?

10. May 24, 2015

### Staff: Mentor

Right. Which is equivalent to saying the distance does not increase.
Expansion of space and increasing distance are equivalent, that is the point. If one is zero then both are.

Actually, the distance between earth and moon does increase notably, but this is a classical effect from tides and irrelevant for this discussion.

11. May 26, 2015

### aboro

With all of our technology, we know that the the distance between the earth and the moon is 298,900 miles. If that distance is increasing because the Universe is expanding, is it taking light a longer amount of time to travel from the earth to the moon or has the light red-shifted as compared to the light that was traveling between these two objects a billion years ago?

12. May 26, 2015

### Staff: Mentor

Expansion is not causing the Earth and the Moon to move away from each other. Gravity is strong enough to prevent it. What is causing the Moon to recede from the Earth is the transfer of angular momentum from the Earth's rotation to the Moon's orbit through tidal effects.

13. May 26, 2015

### Quds Akbar

The space is what expanded, and that space was the universe. When one says that space expanded in inflation, it also means that the universe also inflated. I think Chalnoth made a good point, they're two ways of describing the same thing.

14. May 26, 2015

### aboro

My understanding about the expansion of the Universe is that it is observed when assessed at great distances (as between two galaxies) and that the cause of the expansion in unknown although the consensus is that dark energy may be the force that is causing galaxies to repel from each other. How do we know that the (unknown) forces at play in causing distant galaxies to be moving away from each other (i.e., being repelled from each other) is the same force that is allowing the moon to remain in sufficient equilibrium so as to only be affected by tidal forces and the earth's angular momentum?

15. May 26, 2015

### Chalnoth

The cause of the current expansion is the initial conditions for our universe. Those initial conditions are as yet unknown. The matter and energy in the universe (including dark energy) influence how this expansion changes over time.

The specific force that is at play with regards to how the universe expands is gravity, and carefully examining how gravity interacts with local bound systems in an expanding universe shows that there's basically no effect. For the most part, expansion is just inertia. Things are moving apart now because they were in the past. Bound systems like our galaxy don't have to compete with this expansion because the inertia of the expansion was overcome long ago when the system was first formed.

16. May 27, 2015

### Chronos

The 'force' of expansion is absolutely trivial compared to the force of gravity and other fundamantal forces in the universe. Were this not true spectral lines, kinematic motion and other such relevant effects in the universe would not match observed values. This is how science work calculate, predict, observe - then rinse and repeat ad nauseum.

17. May 27, 2015

### aboro

If I understand you correctly, you are saying that dark energy is not the cause of the expansion of the Universe. Inertia is.

If our galaxy no longer has to compete with the force of the Universe's inertia because that force was overcome long ago, is it still correct to say that this force does not and cannot cause the distance between the earth and the moon to expand? Stated differently, the only force affecting the distance between the earth and the moon is gravity. For the same reasons why the existence of the "ether" was repudiated by Einstein, cannot the same be said with respect to the presence of the Universe's inertia within our own galaxy (and other bound systems as well)?

18. May 27, 2015

### Staff: Mentor

Sort-of-inertia. Not the inertia of objects in space, but the evolution of spacetime itself.
That is right. Dark energy is speeding this up, but the universe would expand without dark energy as well.
That does not make sense.

19. May 27, 2015

### Chalnoth

Inertia isn't a force. It's just a statement of Newton's first law, "An object in motion tends to stay in motion." The universe is expanding today because it was expanding yesterday. No force is required for the expansion to continue.

One way to see this is to model a universe where there is a type of matter where the gravitational effect of its pressure exactly cancels the gravitational fact of its energy, which occurs when $p = -\rho/3$ (incidentally, the hypothetical cosmic strings have this property, so if our universe had mostly cosmic strings for energy density, it would follow this rule).

In such a universe, if we have no cosmological constant, the second Friedmann equation is:

$${\ddot{a} \over a} = -{4\pi G \over 3}\left(\rho + 3p\right) = 0$$

That is, in this hypothetical universe the second derivative of the scale factor is zero, which means that objects move away from one another at constant velocity, with no acceleration. In our universe, we have matter and radiation whose gravity pull things together, and dark energy whose gravity pushes them apart. So the motion of objects with respect to one another changes over time as gravity slows or speeds these objects.

20. Jun 2, 2015

### slatts

I think if I can put Chalnoth's and Bapowell's replies to CassiopeiaA's last question together, I'll be able to resolve some confusion I've had about descriptions of inflation models that are eternal to the future. Those descriptions have been plain English, but it's sounding like some exponent in the equations they've been talking about must be asymptotically approaching "1" (approaching "1" without ever quite reaching it). Could anyone familiar with mathematical descriptions of some of the eternal inflation models tell me whether I might be correct, or, if not, how any decrease in the density of the energy involved could otherwise continue eternally without fading into the purely inertial expansion that those multiverse models describe as being confined to their "local" (or "pocket", or "bubble") universes? (If the explanation involves derivatives rather than exponents, I should admit that my knowledge of them is still at the Wikipedia level.) Thanks.
.

21. Jun 2, 2015

### slatts

Thinking over my question, I'm thinking that the answer is likelier to involve one of those limits that show up as a subscript "lim"; without being able to read the entire equation, I've seen some that were verbalized as "in the infinite limit" by the physicist citing them. I've also noticed that there's some kind of distinction between equations that describe inflation as it happens initially and inflation as it affects the local universe forming within the inflaton field (or fields). If the latter are currently regarded as the end of the process, then a confirmation of it would suffice for an answer, since the absence of energy conservation saves a lot of speculation as to what's going on out there.

22. Jun 2, 2015

### Chalnoth

In the eternal inflation picture, while the field tends towards a lower energy state, quantum fluctuations bounce it around a little bit on its way there. So some regions increase a little bit in energy while others decrease. Any given region is more likely to decrease in energy than increase, but those that increase in energy expand faster and take up more volume in the end. If the parts that increase in energy expand quickly enough, then this process can continue forever.