Matter production during inflation

[nomadreid]

In his popular cosmology book "Que faisiez-vous avant le Big Bang" (sorry, it doesn't seem to have been translated into English) Edgard Gunzig presents a scenario for spontaneous matter production by inflation whereby virtual particle-antiparticle pairs were separated by inflation too far apart in too short a space of time for them to be able to recombine. The scenario seems a bit too simplified (as any explanation invoking virtual particles). Can anyone give me a slightly better version, or is the idea not well-founded?

 

[bapowell]

It's definitely well-founded that quantum fluctuations of the inflaton field give rise to classical curvature perturbations, but whether the picture of virtual particles getting pulled apart by the inflating space is a good physical picture is questionable. A better way to think is as follows: at each point in space, the inflaton field has a value. As inflation proceeds, quantum fluctuations cause the field to move up or down the potential, with the result that the inflaton field value varies across the inflating space. It is this inflaton fluctuation that we quantize as a free field and study. In some regions of space, the field fluctuation drives the inflaton to the vacuum and inflation ends. So on a spacelike hypersurface you will find regions of the universe that have stopped inflating. Some of these regions will have stopped inflating earlier than others; those that stopped inflating earliest will have reheated earlier, creating matter overdensities relative to those regions that stopped inflating more recently. What you end up with on this spacelike hypersurface, then, is a spectrum of density perturbations across a range of scales.

 

[nomadreid]

Thanks, bapowell. A description in terms of fields is preferable (to me) than in terms of virtual particles. If I understand correctly, the mass production seems to be the inflation equivalent of a sonic boom. This actually sounds like the contrary of the virtual particles explanation, in that your explanation deals with a "bunching up" rather than a "pulling apart". But I may be misinterpreting the answer...

 

[bapowell]

I think you might have. In what sense are you thinking the inflaton field is bunching up?

Take a spacelike hypersurface just after inflation. This is like a snapshot in time of the observable universe at the end of inflation. What I'm saying is that on this hypersurface, you will find a patchwork of different densities. The largest overdensities correspond to places in the universe that the inflaton field rolled to zero earliest, decaying into radiation. These regions then undergo the standard big bang cosmology, and structure formation can proceed. They get a headstart over those patches of the universe where inflation more recently ended. So the quantum fluctuation in this picture is not a virtual particle pair, it is a fluctuation in the field value of the inflaton.

 

[nomadreid]

Thanks for the clarification, bapowell. I believe that I now understand it better, although not one hundred percent. My idea of "bunching up" came from the correlation in a region between its quicker slowing down than its neighbours and the overdensity of energy. The role of the quantum fluctuations, if I understand correctly, was to induce a phase change in the overdensity, analogous to causing a supercooled fluid to crystallize. The potential energy of the inflationary field then converts into matter. Is this getting closer?

 

[bapowell]

Closer. The role of the quantum fluctuation is to drive different parts of the universe to the true vacuum at different times. The overdensity does not result directly from the quantum fluctuation, but from the decay of the inflaton field in those regions where inflation has ended.

If you'd like to think in terms of phase transitions, then inflation is 2nd-order. The supercooling occurs while the inflaton hangs out near the false vacuum, but there is no abrupt tunneling event to the true vacuum. Instead, the field rolls down and the quantum fluctuations either work to drive it back up towards the true vacuum or down to the false vacuum more quickly than the classical motion would direct.

 

[nomadreid]

Thanks again, bapowell. One thing that I wish to be clear on is whether, when you write that the quantum fluctuations can drive the state from the false vacuum "up" to the true vacuum (which we supposedly inhabit), you mean (since the false vacuum is higher -- in a graph with the Energy on the vertical axis -- than the true vacuum), that the fluctuations drive the state away from the false vacuum, sometimes towards the local maximum between the two local minima of the two vacua, so that it can possibly get into the trough of the true vacuum. If that is the case, I think the picture is getting clearer. If not, then I am in trouble.

 

[bapowell]

Ooops. Yeah, I got it backwards. Back up to the *false* vacuum, down to the *true*. Sorry about that!

 

[nomadreid]

All's well that ends well, so I think I now have a much clearer picture. Thanks a million.

 

[timmdeeg]

As inflation proceeds, quantum fluctuations cause the field to move up or down the potential, with the result that the inflaton field value varies across the inflating space. It is this inflaton fluctuation that we quantize as a free field and study. In some regions of space, the field fluctuation drives the inflaton to the vacuum and inflation ends. So on a spacelike hypersurface you will find regions of the universe that have stopped inflating. Some of these regions will have stopped inflating earlier than others; those that stopped inflating earliest will have reheated earlier, creating matter overdensities relative to those regions that stopped inflating more recently. What you end up with on this spacelike hypersurface, then, is a spectrum of density perturbations across a range of scales.

May I ask you, why have the regions where the inflation stops a little later and therefore are reheating later less density? Is that perhaps only due to dilution? What are the parameters on which the matter density created during reheating depends?

 

[bapowell]

They should be more dense because they've had more time to undergo structure formation.

 

[timmdeeg]

Thank you. Unfortunately I still wonder, why the regions where the inflation stopped an instant of time later are less dense due to this tiny delay. It's a fact however.
The structure formation you mentioned happened much later, so I fail to understand this argument in the context of my question. Any help is appreciated.

EDIT
After overthinking perhaps one could argue vice versa. The matter density in regions corresponding to the earliest reheating process decreased then due to expansion so that the matter density created a little later (latest reheating) occurs as overdensity compared to the former.

 

[Mordred]

Thank you. Unfortunately I still wonder, why the regions where the inflation stopped an instant of time later are less dense due to this tiny delay. It's a fact however.
The structure formation you mentioned happened much later, so I fail to understand this argument in the context of my question. Any help is appreciated.

EDIT
After overthinking perhaps one could argue vice versa. The matter density in regions corresponding to the earliest reheating process decreased then due to expansion so that the matter density created a little later (latest reheating) occurs as overdensity compared to the former.

The later inflation reheating, I would think though not positive would be hotter than the earlier reheated region. If I'm correct on that then the hotter region will try to balance out by flowing towards the cooler region, essentially starting flows in the plasma. This would result in perturbations, those variations in temperature should correspond to particles dropping out of thermal equilibrium sooner in the cooler regions as opposed to the hotter regions, clumping of energy/matter distributions would then start.