The Inflaton Field And Repulsive Gravity

[BOAS]

Hello!

I am reading "The Hidden Reality" by Brian Greene at the moment and I have a few questions about his discussion on inflationary cosmology that I do not feel he covered/I was able to understand from the text.

As far as I can tell, there is a hypothetical field called the inflaton that has uniform energy and permeates all space. This uniform energy gives rise to negative pressure and 'repulsive gravity'. What he refers to as quantum jitters are responsible for knocking the energy of the field down in certain places and from common sense, as space expands, the energy within the field is spread out among a larger area and thus decreases uniformly.

He also mentions that matter condensed out of the extremely high energy values the field inhabited at the very early stages of our universe.

Hopefully there are no gaping misunderstandings in what has been said, but based on that I have a few questions.

If the universe is truly infinite, doesn't this imply infinite energy? Since the field must permeate all of space to be considered uniform (unless it has a sharp boundary, and there are areas where the field hasn't had time to influence).

Following on from that, does this not imply that there will be a continuing gain of matter in the universe from it's condensing out of the field?

He also talks about if the universe is truly infinite, then we can have a 'quilted multiverse' where there are an infinite number of regions similar in size to our observable universe that have not been around long enough, and are separated by large enough distances so as to not exert any influence on each other and thus we would not know they are there. It seems to me that this is only possible if there is an infinite amount of matter/energy.

I understand that the book is intended to convey ideas rather than hard facts and that I'm very likely to have misunderstood some of it, but i'd be very interested to see some discussion on this.

Thanks!

 

[bapowell]

If the universe is truly infinite, doesn't this imply infinite energy? Since the field must permeate all of space to be considered uniform (unless it has a sharp boundary, and there are areas where the field hasn't had time to influence).

Yes.

Following on from that, does this not imply that there will be a continuing gain of matter in the universe from it's condensing out of the field?

I'm not sure what you mean by "continuing". After inflation ends, the energy "stored" in the inflaton is converted to radiation (this conversion passes through a phase of Bose-Einstein condensation of the field). If the universe is infinite and everywhere inflating, then after inflation the resulting radiation field will have infinite energy. But locally nothing unusual is going on: the energy of the inflaton is (mostly) converted into radiation consistent with stress-energy conservation.

He also talks about if the universe is truly infinite, then we can have a 'quilted multiverse' where there are an infinite number of regions similar in size to our observable universe that have not been around long enough, and are separated by large enough distances so as to not exert any influence on each other and thus we would not know they are there. It seems to me that this is only possible if there is an infinite amount of matter/energy.

Yes, this follows from your first question.

 

[BOAS]

I'm not sure what you mean by "continuing". After inflation ends, the energy "stored" in the inflaton is converted to radiation (this conversion passes through a phase of Bose-Einstein condensation of the field). If the universe is infinite and everywhere inflating, then after inflation the resulting radiation field will have infinite energy. But locally nothing unusual is going on: the energy of the inflaton is (mostly) converted into radiation consistent with stress-energy conservation.

Thank you for the response.

My use of the language is probably rather fuzzy, but here's what I meant (it actually hangs on another question or two); The amount of energy in the field has decreased over time, but as I understand it, it is still there and still subject to decrease - Therefore does this mean that matter is continuing to 'condense' out of it, or is this something that really only happens at high energies?

 

[timmdeeg]

The matter condensation in the early universe is sometimes described as a phase transition and compared with phase transitions like gas/liquid or liquid/solid. They happen under specific conditiones of pressure and temperature. Once the liquid is frozen further cooling can't create additional solid stuff.

 

[BOAS]

The matter condensation in the early universe is sometimes described as a phase transition and compared with phase transitions like gas/liquid or liquid/solid. They happen under specific conditiones of pressure and temperature. Once the liquid is frozen further cooling can't create additional solid stuff.

That analogy does make sense, thanks.

 

[bapowell]

My use of the language is probably rather fuzzy, but here's what I meant (it actually hangs on another question or two); The amount of energy in the field has decreased over time, but as I understand it, it is still there and still subject to decrease - Therefore does this mean that matter is continuing to 'condense' out of it, or is this something that really only happens at high energies?

Sorry for the late reply. You can think of the inflaton energy "going into" the expansion of the space (i.e. gravitational potential energy), but I've never quite felt comfortable with this explanation for two reasons 1) in a homogeneous universe, there is no gravitational field (although the inflaton fluctuations do impart some inhomogeneity) and 2) energy is simply not conserved (globally) in GR. Many see this latter "explanation" as a bit of a copout but it's nonethess a correct statement.

Regarding timmdeeg's interesting point about the phase transition: this is quite literally what is happening during inflation. It is much more relevant to the earlier models of inflation which involved so-called 1st-order phase transitions (here the inflaton is at a local max of its potential that is metastable) where the transition occurs abruptly as the field tunnels from the false to the true vacuum. You end up with regions of the universe that are inflating (false vacuum = old phase) and bubbles of true vacuum that go on to reheat and expand according to the standard big bang cosmology. In these models, the potential energy of the inflaton when it's at the metastable point (false vacuum) is associated with the latent heat of the phase transition: it gets liberated as the field decays to the true vacuum. These models involving 1st-order transitions ultimately failed, and have since been dubbed "old" inflation.

The "new" inflation models that followed these earlier failed attempts employed a 2nd-order transition -- so so-called "slow rollover" models where the maximum of the potential is unstable. In these models there is no "instantaneous" release of stored energy and instead of bubbles you get a universe in which different regions stopped inflating at different times. These regions also then reheated at different times and began to undergo conventional expansion at different times with the result that each region had a different density on any equal time slicing (instant in time). These are the celebrated inflation-induced density perturbations that reveal themselves as temperature anisotropies in the CMB.

Sorry, I realize this is far afield of your original question.

 

[BOAS]

Sorry for the late reply. You can think of the inflaton energy "going into" the expansion of the space (i.e. gravitational potential energy), but I've never quite felt comfortable with this explanation for two reasons 1) in a homogeneous universe, there is no gravitational field (although the inflaton fluctuations do impart some inhomogeneity) and 2) energy is simply not conserved (globally) in GR. Many see this latter "explanation" as a bit of a copout but it's nonethess a correct statement.

What do you mean that energy is not conserved 'globally' in GR? (why and what does 'globally' mean in context?)

Regarding timmdeeg's interesting point about the phase transition: this is quite literally what is happening during inflation. It is much more relevant to the earlier models of inflation which involved so-called 1st-order phase transitions (here the inflaton is at a local max of its potential that is metastable) where the transition occurs abruptly as the field tunnels from the false to the true vacuum. You end up with regions of the universe that are inflating (false vacuum = old phase) and bubbles of true vacuum that go on to reheat and expand according to the standard big bang cosmology. In these models, the potential energy of the inflaton when it's at the metastable point (false vacuum) is associated with the latent heat of the phase transition: it gets liberated as the field decays to the true vacuum. These models involving 1st-order transitions ultimately failed, and have since been dubbed "old" inflation.

I don't know any field theory and my QM knowledge is mainly superficial but when you say the transition occurs 'abrubtly' and mention tunneling, is this like the field jumping from one value to another without going through intermediary values?

The "new" inflation models that followed these earlier failed attempts employed a 2nd-order transition -- so so-called "slow rollover" models where the maximum of the potential is unstable. In these models there is no "instantaneous" release of stored energy and instead of bubbles you get a universe in which different regions stopped inflating at different times. These regions also then reheated at different times and began to undergo conventional expansion at different times with the result that each region had a different density on any equal time slicing (instant in time). These are the celebrated inflation-induced density perturbations that reveal themselves as temperature anisotropies in the CMB.

Where does the energy for reheating come from?

Sorry, I realize this is far afield of your original question.

I was completely unaware of the inflaton field 2 weeks ago, so it's all interesting to me.

Thanks.

 

[bapowell]

What do you mean that energy is not conserved 'globally' in GR? (why and what does 'globally' mean in context?)

It's a little complicated and you might wish to look into it for yourself. The basic problem is one of time: in mechanics, we learn that energy conservation results, via Noether's theorem, from time translation symmetry of the equations of motion. In GR, there is no such thing as a unique, globally defined timelike vector field, and so time translation symmetry is not a good concept globally. However, if we restrict ourselves to small enough regions of spacetime, then via the equivalence principle, we can use the geometry of special relativity and we regain our time symmetry (i.e. energy is conserved locally).

I don't know any field theory and my QM knowledge is mainly superficial but when you say the transition occurs 'abrubtly' and mention tunneling, is this like the field jumping from one value to another without going through intermediary values?

I mean it just like that. It's a tunneling problem where the field decays through a barrier.

Where does the energy for reheating come from?

From the inflaton's potential energy.

 

[joneall]

I am reading the same book, but have a different question. On pp. 316-318, Greene talks about where the energy of the inflaton field comes from. He says it comes from gravity.

"... a high-valued inflaton field drives the region it inhabits to rapidly grow, and in doing so creates an increasingly large spatial volume that is itself infused with a high-valued inflaton field. And because a uniform inflaton field contributes a constant energy per unit volume, the larger the volume it fills, the more energy it embodies. The driving force behind the expansion is gravity -- in its repulsive guise..."

Then -- "... as an inflation-filled region rapidly grows, the inflaton extracts energy form the gravitational field's inexhaustible resources...''

I do not understand, in 2nd last quote, what is THE gravitational field. Where is it? Is it part of the inflaton field. Is it curvature of space? If the inflaton field is expanding space, then it is essentially _creating_ space. I suppose the gravitational field comes along with the space. But then it sounds like the inflaton field is using gravity from space it has created to create more space in order to get more gravity in order to ... etc.

I clearly have misunderstood something here. But what?

Thanks in advance for any help offered!

 

[bapowell]

The problem could be that Prof. Greene is using imprecise language in order to explain things at a popular level. I too am confused by his statement, since there is no "gravitational field" in a homogeneous universe. He might mean that the energy is extracted more generally from space, but that too is a clumsy concept. If you read through the earlier posts in this thread, there is a discussion of how energy is not conserved in the universe at large.

 

[joneall]

The matter condensation in the early universe is sometimes described as a phase transition and compared with phase transitions like gas/liquid or liquid/solid. They happen under specific conditiones of pressure and temperature. Once the liquid is frozen further cooling can't create additional solid stuff.

I think you can also see this as the system's having reached a new energy minimum, where it stays put.

 

[PeterDonis]

I clearly have misunderstood something here. But what?

The problem could be that Prof. Greene is using imprecise language in order to explain things at a popular level.

I agree with bapowell here. This is often a problem with pop science books and articles. Brian Greene is a frequent offender, but he's by no means the only one. The only real solution to the problem is not to use pop science books and articles as sources if you actually want to understand the science.

 

[joneall]

I didn't know Greene was considered a pop writer. It is clear, tho, that they all sometimes cut corners. Comparing the three books I have read only lately (Greene, Carroll, Tegmark), it's easy to see that each one makes different simplifications. And sometimes that complicates the understanding.

Be that as it may, what then should I read without first taking a college course in general relativity? :) Suggestions?

Thanks!

 

[PeterDonis]

I didn't know Greene was considered a pop writer.

It's not the writer, it's the book. Even though Greene publishes peer-reviewed scientific papers, his books do not fall in that category. Nor do the popular books of any scientist, really, although some might come close. Some scientists are reasonably good at keeping to the rules, carefully distinguishing the actual science from their own speculations and opinions, even when they are writing popular books that aren't going to get reviewed by their peers. But others (and I would put Greene in this category) can't resist the temptation in their popular books to say things that they wouldn't be able to get away with in an actual peer-reviewed paper.

what then should I read without first taking a college course in general relativity?

I think Carroll's online lecture notes on GR are a good start:

http://arxiv.org/abs/gr-qc/9712019