# B What caused Inflation?

1. Mar 8, 2017

### Tanelorn

Is the cause of inflation unknown? Is it possible that it might have in part at least been caused by radiation pressure as a result of matter annihilating anti-matter at extremely high densities?

Does the theory of quintessence mainly try to say that inflation and dark energy are linked in some way? And that D.E. is a continuation of inflation? If so I have wondered if this was being proposed as a possibility myself, but I didn't realize it was being called Q.

Last edited: Mar 8, 2017
2. Mar 8, 2017

### phinds

It is not even known for sure that inflation HAPPENED, much less what caused it if it did happen.

Whether or not inflation, if it happened, was caused by dark energy is unknown but if it was then there was a state change in the form of dark energy at the end of inflation. Since we don't know what caused inflation, if it existed, OR what dark energy is, this is all just speculation.

3. Mar 9, 2017

### Orodruin

Staff Emeritus

4. Mar 9, 2017

### Chalnoth

Radiation actually causes more deceleration of the expansion than matter does, because it dilutes faster than matter.

Inflation models contain a field (typically a scalar field) which maintains a nearly-constant energy density over the course of the expansion.

5. Mar 9, 2017

### Staff: Mentor

I'm not sure the dilution rate is the key factor here. As I understand it, for the same energy density, radiation causes more deceleration because the deceleration parameter is governed by $\rho + 3 p$, and for radiation, $p = \frac{1}{3} \rho$, while for matter (more precisely, cold, nonrelativistic matter), $p = 0$.

6. Mar 9, 2017

### Chalnoth

Yes, the dilution rate very much is the key factor, as it's directly related to the relationship between pressure and density. This becomes relatively clear when you look at the first Friedmann equation, with constants omitted for clarity:

$$H^2 = \rho$$

If $\rho$ decreases rapidly, then the expansion rate decreases rapidly. If, on the other hand, $\rho$ remains approximately constant, then $H$ remains approximately constant.

7. Mar 9, 2017

### Staff: Mentor

Yes, but the question is the direction of causality, so to speak.

Yes, but that equation says nothing about rates of change. The question is what determines the rate of change.

But what determines how rapidly $\rho$ decreases? To find that out we need to look at the second Friedmann equation, which schematically says

$$\frac{\ddot{a}}{a} = - \left( \rho + 3 p \right)$$

So if we fix $\rho$ and compare a matter-dominated universe with $p = 0$ with a radiation-dominated universe with $p = \frac{1}{3} \rho$, we find that the magnitude of $\ddot{a} / a$ is larger in the second case (i.e., it is more negative), hence the expansion decelerates faster. In other words, the pressure of radiation causes faster deceleration (and hence faster dilution), not the other way around.

8. Mar 9, 2017

### Chalnoth

I don't think you can say that one of these caused the other. They're all mathematically equivalent ways of describing the physics.

The reason I say it's the rate of dilution that matters is that I think it's easier to understand. It's not easy to see why the pressure of a photon gas should impact the expansion, but it's easy to argue how the radiation dilutes with expansion and what effect that must therefore have.

First, the number of photons remains the same, but the volume increases. So the number of photons dilutes by $1/a^3$. The expansion further redshifts the photons by one factor of the expansion, resulting in a dilution of the energy density by $1/a^4$. That's step one.

Step two is a short description of General Relativity: this theory of gravity relates the amount of stuff there is in the universe to how much space-time is curved. Less stuff means less curvature. In an expanding universe, the space-time curvature manifests as the rate of expansion plus the spatial curvature (if any). This means that less stuff results in a lower rate of expansion. So matter/energy that dilutes more rapidly causes the rate of expansion to slow more rapidly.

9. Mar 9, 2017

### Chalnoth

10. Mar 9, 2017

### Staff: Mentor

But this is also highly counterintuitive, because less stuff should result in less gravity, which should mean less deceleration. A simple statement to the effect that, in GR, pressure is included in "stuff", makes it obvious (to me, anyway) why radiation causes more deceleration than matter with the same energy density: because there is more "stuff" present in the radiation, due to its pressure. Trying to explain why less stuff means more deceleration because of dilution seems more complicated to me.

I'll take a look.

11. Mar 9, 2017

### Staff: Mentor

I don't think this is right as it stands. Spacetime curvature is tidal gravity: the convergence or divergence of nearby geodesics. In a homogeneous universe, where there is no spatial variation in the geodesics at a given time, the convergence or divergence is determined, intuitively, by the rate of change of the expansion rate, i.e., $\ddot{a} / a$. It takes some more detailed explanation to see that the expansion rate itself, $\dot{a} / a$, also plays a role in convergence or divergence of geodesics. (This is the same more detailed explanation that Carroll is talking about when he says "The tricky part is explaining why “expanding at a fixed rate” means “accelerating.”") But even once you have the detailed explanation, that just says that both the expansion rate and its rate of change contribute to the convergence or divergence of geodesics. It doesn't say you can just ignore the rate of change.

(In more technical language, the Einstein tensor includes both $\dot{a} / a$ and $\ddot{a} / a$ terms.)

12. Mar 9, 2017

### Chalnoth

You can see it if you look through a derivation of the Friedmann equations. Once you place the curvature scalar into the right format, $H^2$ is a dominant term, with the other major one being the spatial curvature. I think there's a third term as well, but I'm not remembering offhand. But either way, the expansion itself is a major component of the space-time curvature.

13. Mar 9, 2017

### Staff: Mentor

There is; it's $\ddot{a} / a$ (or $\dot{H}$ if you write things in terms of $H$ and its derivative and fold part of $\ddot{a} / a$ into $H^2$).

But so is its rate of change. That was my point. Saying expansion rate contributes is one thing; saying it is spacetime curvature is another (and is wrong IMO since it ignores the rate of change of expansion rate).

14. Mar 13, 2017

### Tanelorn

Thank you for the replies. So in summary:
1. We do not know what causes inflation.
2. Matter anti-matter annihilation is not a cause of inflation.

What if 99.99% of all the matter and antimatter between any two points was annihilated instantly, would that look anything like what we call inflation as seen today? (Isnt inflation just a way to explain equal CMBR temperature everywhere?)

Does any definition of a white hole explain inflation? e.g. The link below is what I thought a white hole meant (If this is wrong please feel free to correct me):
https://www.physicsforums.com/threa...nation-for-the-big-bang-and-inflation.903820/
I still haven't been able to determine if white holes are crack pottery. (apologies if so)

Last edited: Mar 13, 2017
15. Mar 13, 2017

### Staff: Mentor

Only in the sense that we don't know exactly what the inflaton field was--we have no way of directly observing it. But we have a pretty good grasp on what kind of models can produce inflation.

Yes.

No.

No. It explains that, but it also explains other things that can't, as far as we know, be explained by models that don't include inflation (and models where the universe is dominated by ordinary radiation, whether it's from matter-antimatter annihilation or some other source, fall into the category of "models that don't include inflation").

No.

They're not crackpottery; they are mathematically valid solutions of the Einstein Field Equation. But no physicist, as far as I know, considers them physically reasonable, because there's no way to explain where the white hole singularity and its antihorizon (a horizon that you can't get inside, as opposed to the black hole horizon that you can't get outside once you're in) came from.

16. Mar 13, 2017

### bapowell

We don't know definitively what caused inflation but that's not to say we don't have successful models. A homogeneous scalar field that is potential energy dominated is a simple source of inflation. Neither of the sources you suggest are inflationary. The key is that the source must satisfy an equation of state $p \leq -\rho/3$ in order to drive the accelerated expansion that distinguishes inflation.

17. Mar 15, 2017

### Tanelorn

Thanks again guys.

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

p is pressure and ρ is energy density? And these are not related to matter and energy, but some unknown field which causes space itself to suddenly inflate?

Peter, I thought it was suggested many years ago that white holes were created and powered by black holes in another U?
So I set about trying to imagine a scenario in which a white hole could generate a flat U with equal temperature in all directions, and thought this would have to mean that the Anti Horizon would have to be many many orders of magnitude greater than the size of the observable U. Perhaps with inflation continuing to occur forever at the boundary of its Anti Horizon, and perhaps something like the reverse of the way a galaxy works with a SM BH at its center:

Last edited: Mar 15, 2017
18. Mar 15, 2017

### bapowell

The scalar field that drives inflation has energy just like any other field; the key is that the energy density is constant (or very nearly so). This results in exponential expansion.

19. Mar 15, 2017

### Staff: Mentor

It's been suggested as a speculative hypothesis, but there is no mathematical model of this in the literature that I'm aware of. The issue with the straightforward way of trying to do it, which is to simply "paste together" the black hole singularity in one Kruskal diagram with the white hole singularity in another Kruskal diagram sitting "on top" of it, is that spacetime curvature diverges at the singularity, so you don't have a well-defined spacetime manifold. I've never seen a model that fixes that issue. If you can find one in the literature, you're welcome to post a link to it.

It can't.

This wouldn't make our observable universe actually flat; it would just mean that its spatial curvature was small enough that it could have escaped our observation up to now.

In a white hole model, there would be no inflation. Inflationary models have no event horizon or antihorizon like the ones that appear in the Kruskal diagram of a black hole/white hole spacetime.

The diagram you tried to turn upside down here doesn't show time; it's a slice of the space outside of a static black hole, at an instant of Schwarzschild coordinate time. Turning it upside down doesn't reverse time; it just puts space upside down, which is physically meaningless.

20. Mar 15, 2017

### Tanelorn

Thanks bapowell and Peter

I thought that a white hole would affect space time the opposite of a BH, and that it would therefore be just the same as turning the diagram upside down. I guess things are not that simple. Also if the U was say 10^30 times larger than the observable U which I think Guth once suggested, things would like look pretty flat however the U was created.

Anyway, ok well thanks for taking the time.
I am just a part timer (and then some!), trying to design laser RF power supplies right now..