# The pre-inflationary epoch

1. Oct 11, 2015

### timmdeeg

I wonder whether the Friedmann equations are applicable to the pre-inflationary epoch and if there are any theoretical expectations regarding the spatial curvature at that early times.

I suspect the curvature parameter $k$ should have a certain value at that time already and which never will change in the future, correct?

Does - as the inflation has not yet started - this mean that the universe is static and if yes, static due to the cancelling of repelling and attractive gravity?

Thanks for any help.

2. Oct 11, 2015

### skydivephil

3. Oct 11, 2015

### marcus

Good paper to cite! Great example of recent research in pre-inflation cosmology.
There is a moment when H crosses from negative to positive (from contraction to expansion) So there is a moment when H = 0 and the universe is neither contracting nor expanding. It is not "static" in the usual sense---the bounce is extremely dynamic---but it is a moment when the opposite tendencies cancel---that could be what Timmdeeg was asking about.

The paper derives a quantum-modified Friedmann equation which makes it clear why there is a bounce at near-Planckian density and allows the critical turnaround density to be calculated. Timmdeeg asked about the Friedmann equation so he might be interested in that. I forget what page it's on.

4. Oct 11, 2015

### timmdeeg

No marcus, I didn't have this moment in my mind, but the universe prior to inflation being in a high energy state due to the inflaton field.
According to my impression the bounce models are very speculative and apart from this said moment isn't a static state per se.

5. Oct 11, 2015

### bapowell

Can you elaborate on what you mean by this? The inflaton would have been a subdominant component of the total energy of the pre-inflationary universe.

6. Oct 12, 2015

### timmdeeg

My question refers to the state of the universe before the scalar field started to roll down the potential energy hill. How would we describe this state? It seems obvious to describe it as a static universe, as long as it doesn't expand. But on the other side it seems nonsense to think of a static universe which contains vacuum energy only.

According to Friedmann any kind of energy density creates a time dependence on the scale factor, unless repelling gravity is balanced by attractive gravity. So, in case there exists a static state prior to inflation which kind of a vacuum energy wouldn't force the universe to expand?

7. Oct 12, 2015

### bapowell

If it contains only the inflaton (i.e. vacuum energy only) then of course it inflates. In order to not inflate, you must have other stuff in the universe that dominates the energy density. For example, prior to inflation, it's entirely possible to have had a radiation-dominated universe, with matter and inflaton subdominant. Remember -- to get inflation going, the inflaton must come to dominate the local energy density. Lastly, in order to not expand, you must have the right balance of matter/radiation and vacuum energy.
Regular old vacuum energy will work: recall Einstein's employment of the cosmological constant for just this purpose. However, I don't see a good reason to postulate a static universe prior to inflation, since the conditions for regular Friedmann expansion are much easier to achieve and understand.

8. Oct 12, 2015

### timmdeeg

Would you agree that a non-expanding universe containing nothing else than vacuum energy exists prior to inflation? But if so, how would you describe it?

Or perhaps do we simply have to admit that we don't know why it doesn't expand, although it contains vacuum energy only.

9. Oct 12, 2015

### bapowell

No, I'm trying to say that this is impossible. Vacuum energy contributes a constant energy density which leads to accelerated expansion in the Friedmann universe. The most generic pre-inflationary universe would be one containing matter, radiation and inflaton field (vacuum energy) with the latter subdominant so that the universe undergoes non-inflationary, radiation- or matter-dominated expansion.

10. Oct 12, 2015

### timmdeeg

Yes, but this possibility can be ruled out too (besides vacuum energy only), because matter was produced later (at the of inflation).

11. Oct 12, 2015

### bapowell

Yes, the inflaton decayed into the matter and radiation making up the observable universe; however, this does not rule out the possibility that matter and radiation existed prior to inflation. What observation could one make to rule out this possibility?

Remember, the inflaton, if it exists, is likely nothing more than a scalar matter field, not unlike the Higgs. There is no "vacuum energy only" solution that works because pure vacuum energy leads to eternal inflation -- it has no dynamics. The inflaton would have come into existence along with all the other kinds of particles at the big bang. In some part of the universe after the big bang, the inflaton field energy density was extraordinarily high, higher than the energy densities of all the other particles. This part of the universe underwent inflation, diluting all the non-inflaton energy density. Matter and energy is re-introduced as the inflaton decays towards the end of the inflationary epoch.

In fact, many cosmologists assumed that the inflaton existed in thermal equilibrium with other matter and radiation prior to inflation; these thermal interactions were perhaps key to the inflaton developing a VEV as the universe cooled.

12. Oct 13, 2015

### timmdeeg

Thank you for these helpful explanations, you are describing exactly what I've been missing.
Does "other matter and radiation prior to inflation" mean particles with and without rest mass of unknown nature, or how should I think of "...."?

I try in my own words, kindly correct if wrong:

The inflaton which is a scalar matter field has existed in thermal equilibrium with "other matter and radiation" prior to expansion. Due to inflation the "other matter ..." was diluted such that it can't be found in the observable universe. There is no causality between the "other matter and radiation" and the matter characterizing the scalar field in the sense that both co-existed without influencing each other.

If I understand you correctly, regarding this part of the universe there exists no universe prior to inflation, because inflation started at the same time when the high energy density inflaton field came into existence.

13. Oct 13, 2015

### bapowell

It would mean all particles (fields, really) that exist within the universe that couple to the inflaton. This is model-dependent.
I think you had it until the end: the inflaton and the other matter/radiation were in thermal equilibrium (by hypothesis) prior to inflation, so they certainly influenced each other.
No, I suggested earlier that the inflaton pops out of the big bang along with all the other fields. There can be inflatons in the universe without inflation! Remember, the inflaton must have sufficiently high potential energy to get inflation going, and this depends on the inflaton potential energy function. Take Linde's "chaotic inflation" model, $V \propto \phi^2$ where $\phi$ is the inflaton field. It's quite possible that $\phi$ sits at the minimum of the potential across some regions of the universe. These regions evolve according to the dominant energy density, say, radiation. But since $\phi$ is susceptible to thermal and quantum fluctuations, some parts of the universe will have inflatons that find themselves very high up on their potentials. If inflaton energy is dominant, these regions will inflate.

14. Oct 14, 2015

### timmdeeg

Ok, thanks for this excellent comprehensive description of the chaotic inflation model.

After some search I found one article only which mentions the curvature parameter:

Obviously the author means the initial (pre-inflationary) value of $k$, as he writes " inflation still can occur under that condition."
So it seems that $k=0$ is prefered. Probably this assumption is based on the "right" amount of "other matter and radiation" that fits to this conclusion, correct?

Last edited by a moderator: May 7, 2017
15. Oct 14, 2015

### bapowell

One of the merits of inflation is that you actually don't need to postulate spatial flatness as an initial condition. As long as inflation gets going, the universe is driven towards flatness regardless of the initial curvature.

16. Oct 14, 2015

### timmdeeg

Yes, therefore I was quite astonished about this sentence: "Normally, when discussing inflation, one considers the completely geometrically flat universe, k = 0"

17. Oct 14, 2015

### bapowell

Yes, because "when discussing inflation" usually we are focused on the observationally relevant part -- the last 60 e-folds or so. Many inflation models last for much longer than this, and so by the time the last 60 e-folds come around, there has been sufficient inflation to make k=0 a very safe assumption.

18. Oct 14, 2015

### timmdeeg

Ah this is the context, now it makes sense.

Thanks a lot for your patience.

19. Oct 14, 2015

### bapowell

My pleasure. Happy to help.

20. Oct 31, 2015

### timmdeeg

I agree totally after reading about chaotic inflation. This theory seems widely accepted among cosmologists. In the instant of time the universe comes into existence it has a certain spatial curvature und topology and starts to inflate immediately.There is no need for an initial state of thermal equilibrium. So, all my questions seem meaningless from this point of view.

What however is responsible for a value for $k$ and what selects the topology? It seems purely arbitrary (or the secret of the quantum fluctuation) and not subject of current theories.