Inflation and Monopoles: Exploring the Mysteries of Cosmic Expansion

[DiracPool]

1. Inflation--I've been doing a little study into cosmic inflation, and a question that many people (including myself) seem to have a hard time wrapping their head around is why was there a need for inflation rather than just assuming that the universe just started off flat, homogeneous, and even "temperatured." I can imagine a tiny sphere right around the time of the big bang whose geometry is (almost) perfectly flat and whose temperature is (almost) perfectly the same everywhere. I can then imagine this sphere (the universe) expanding at a steady rate to the point where at the size it is today it would have remained almost perfectly flat with an even temperature across the sky. However, when you present this scenario to a cosmologist they always seem to say "oh no, that could never happen." But then when they go into explaining why, I don't get the explanation.

The explanation always seems to go along the lines that 1) light wouldn't have time to communicate among the varied regions in order to keep the temperature even, and 2) that the inflation was needed to "flatten out" all the bumpiness in the pre-inflation situation. But my quandary is that, didn't we already take care of this in the description in the first paragraph? Is this just some kind of anomaly that just falls out of the mathematics that can't really be communicated visually? Or is it something like the size of the quantum fluctuations pre-inflation created a bumpiness in the primordial sphere I alluded to above such that it couldn't have started off that uniform, and that's the problem and that's why need the inflation concept? Or is it something else? I'm hoping someone can explain this fairly simply so that it makes sense, or can direct me to some literature/videos that do so.

2. Magnetic monopoles--Susskind has said that another problem inflation seems to solve is the monopole problem, saying that inflation diluted these monopoles to a concentration that may not be detectable (if my memory serves correct), and that is why no one has detected them. However, he also says that there was pretty much nothing pre the reheating epoch that existing other than the inflaton field. But now we also seem to have these monopoles existing before the reheating epoch as well as some "bumpiness" in the early inflaton field that needed smoothing or flatting out by the inflation process itself.

So my question is what, if anything, did the inflaton field consist of other than "inflaton potential energy" pre the inflationary phase and during the inflationary phase before reheating?

 

[Berenices]

Inflation arises as a prediction of GUT and resolves the horizon, smoothness, density and magnetic monopole problems of the 1970's.

Reference https://www.physicsforums.com/threa...es-in-the-standard-cosmological-model.105441/

I can't really say much more than that though I believe the inflaton was the most influential factor in those times.

 

[Orodruin]

But my quandary is that, didn't we already take care of this in the description in the first paragraph?

You might have taken care of it with the assumption that you started out with an even temperature in the entire Universe. The point is that this is not necessarily your initial condition. With inflation, you can allow for initial conditions that are not homogeneous and still end up with a homogeneous universe.

However, he also says that there was pretty much nothing pre the reheating epoch that existing other than the inflaton field. But now we also seem to have these monopoles existing before the reheating epoch as well as some "bumpiness" in the early inflaton field that needed smoothing or flatting out by the inflation process itself.

You (essentially) do not have anything else than the inflaton field precisely because of inflation. This is why inflation solves the magnetic monopole problem. The point is that the inflationary phase dilutes away anything which is not the inflaton field and thus right before reheating the inflaton field is the only thing that is around.

 

[bapowell]

2. Magnetic monopoles--Susskind has said that another problem inflation seems to solve is the monopole problem, saying that inflation diluted these monopoles to a concentration that may not be detectable (if my memory serves correct), and that is why no one has detected them. However, he also says that there was pretty much nothing pre the reheating epoch that existing other than the inflaton field. But now we also seem to have these monopoles existing before the reheating epoch as well as some "bumpiness" in the early inflaton field that needed smoothing or flatting out by the inflation process itself.

You raise a good question. The inflaton field existed along with all the other matter and gauge fields in the early universe prior to inflation. There may or may not have been monopoles prior to inflation (they might be created after depending on the particle physics model). In order for inflation to get underway, there needed to be a sufficiently smooth region of the universe dominated by the inflaton field energy. (Notice that there is a little bit of circularity in inflationary theory -- that one needs a suitably smooth and uniform region of the universe for inflation to render a larger smooth and uniform region of the universe.) If there were monopoles in existence prior to inflation, they must still have been sufficiently dilute in some region of the universe so as not to spoil the uniformity needed for inflation to begin.

The other possibility is that the operative particle physics model does not produce monopoles prior to inflation, but after. Recall that monopoles are formed in GUTs as topological defects -- places in the universe where various scalar fields take on different vacuum expectation values (VEV). Inflation results in a smooth universe, with all such VEVs correlated and so at most we expect to see one monopole per horizon volume.

 

[DiracPool]

You might have taken care of it with the assumption that you started out with an even temperature in the entire Universe. The point is that this is not necessarily your initial condition. With inflation, you can allow for initial conditions that are not homogeneous and still end up with a homogeneous universe.

Ok, I think that may be what I was looking for. If everything actually were completely smooth an homogenous at the very beginning, maybe we wouldn't need inflation at all, but that wasn't very likely due to, perhaps, quantum fluctuations very early on pre the inflationary epoch? So what inflation gives us is the opportunity to take a perhaps somewhat bumpy primordial sphere and smooth it out? In other words, it just allows for a wider variety of heterogeneity in the pre-inflationary universe?

 

[bapowell]

Inflation takes an initially small homogeneous patch and inflates to a size greater than or equal to the observable universe.

 

[phinds]

Inflation takes an initially small homogeneous patch and inflates to a size greater or than or equal to the observable universe.

As stated, that seems to imply that the entire size of the currently observable universe was caused by inflation, with no further added size due to the expansion, and accelerated expansion, of the universe. I'm sure that's not what you mean, but my point is that it's not clear WHAT you mean, exactly.

 

[bapowell]

The universe is homogeneous across distances at least as great as the cosmological horizon. One way of understanding that is to suppose that during inflation length scales grew to be at least as large as 1/H.

 

[phinds]

The universe is homogeneous across distances at least as great as the cosmological horizon. One way of understanding that is to suppose that during inflation length scales grew to be at least as large as 1/H.

I have no idea what that means nor how it addresses what I said. I don't doubt that it DOES, I just don't understand it. Are you saying that a meter wasn't a meter at the beginning of inflation?

 

[bapowell]

Sorry for the confusion. What I'm saying is that if $L_0$ is the proper size of the pre-inflationary patch, then $e^N L_0 \geq 1/H$, where $N$ is the number of e-foldings of inflation.

 

[phinds]

Sorry for the confusion. What I'm saying is that if $L_0$ is the proper size of the pre-inflationary patch, then $e^N L_0 \geq 1/H$, where $N$ is the number of e-foldings of inflation.

I wonder, could you possibly address my post #7 in English, not math?

 

[bapowell]

As stated, that seems to imply that the entire size of the currently observable universe was caused by inflation

I don't understand what this means. Expansion, inflation or otherwise, has nothing to do with the size of the observable universe. Perhaps maybe you can clarify what you mean by this. All I am saying is that the initial, pre-inflationary patch must have been stretched by inflation to a size at least as large as the present observable universe. Of course there is additional, non-inflationary expansion beyond this. But we need *at least* enough inflationary expansion to explain the homogeneity observed on horizon scales.

 

[phinds]

I don't understand what this means. Expansion, inflation or otherwise, has nothing to do with the size of the observable universe.

This seems to be saying that the volume that is currently encompassed by the observable universe was always the size it is now, because expansion and inflation had nothing to do with making it the size it is (and I don't know what else could have).

Perhaps maybe you can clarify what you mean by this. All I am saying is that the initial, pre-inflationary patch must have been stretched by inflation to a size at least as large as the present observable universe.

I agree w/ that but it seems to contradict the sentence directly above.

Of course there is additional, non-inflationary expansion beyond this. But we need *at least* enough inflationary expansion to explain the homogeneity observed on horizon scales.

Again, I agree.

 

[bapowell]

I agree w/ that but it seems to contradict the sentence directly above.

OK, good. In the sentence above I realize I'm not being very clear. What I'm trying to say is that the post-inflation particle horizon knows nothing about the amount of expansion that occurs during inflation.

 

[phinds]

OK, good. In the sentence above I realize I'm not being very clear. What I'm trying to say is that the post-inflation particle horizon knows nothing about the amount of expansion that occurs during inflation.

Well, again we agree. Seems we have, at least to some extent, been talking past each other in all this.

 

[bapowell]

Well, I'm happy to have helped you past 9000 posts at least ;)

 

[phinds]

Well, I'm happy to have helped you past 9000 posts at least ;)

Ha. I hadn't even noticed. Thanks

 

[Khashishi]

Do people actually believe in magnetic monopoles? The non-observance of magnetic monopoles is only evidence for inflation if magnetic monopoles can be shown to exist.

The initial conditions of the universe could have been expected to be close to uniform in temperature by a simple probability argument. If you assume every particle in the universe was given some random position and velocity (you have to make some assumptions), then there are vastly more configurations with uniform energy distribution than non-uniform. This quickly becomes a uniform temperature distribution.

 

[bapowell]

Do people actually believe in magnetic monopoles? The non-observance of magnetic monopoles is only evidence for inflation if magnetic monopoles can be shown to exist.

They are a generic prediction of most grand unified models. The lack of magnetic monopoles is not considered as evidence for inflation, rather, it is one of the puzzles that motivated cosmologists to propose inflation in the first place.

The initial conditions of the universe could have been expected to be close to uniform in temperature by a simple probability argument. If you assume every particle in the universe was given some random position and velocity (you have to make some assumptions), then there are vastly more configurations with uniform energy distribution than non-uniform. This quickly becomes a uniform temperature distribution.

By this line of reasoning it is vastly more likely that instead of a uniform universe you'd end up with just a single, fully functioning brain: see https://en.wikipedia.org/wiki/Boltzmann_brain

 

[Khashishi]

I don't accept the anthropic principle, so there is no reason to believe a Boltzmann brain is more likely than a uniform thermal bath. In fact, it is far less likely.

 

[DiracPool]

I don't accept the anthropic principle

Initially I hated the idea of the anthropic principle, I believed that there were UNI-versal laws that ran our universe and I wanted to find out what those were. However, the more I learn about physics and cosmology, the more the anthropic principle and the multiverse seem to be the inevitable conclusion.

 

[bapowell]

I don't accept the anthropic principle, so there is no reason to believe a Boltzmann brain is more likely than a uniform thermal bath. In fact, it is far less likely.

Yet you are conjecturing a statistical ensemble of possible states, many more of which are thermally uniform than not. Whether a Boltzmann brain is more or less likely than a uniform distribution of matter has nothing to do with whether or you not you accept the anthropic argument: it's a consequence of gravitational entropy.

Because you seem to be suggesting that a uniform thermal distribution is more likely than not, and therefore we have no need for inflation, please provide a formal justification of this argument.

 

[Chronos]

The Boltzmann brain concept is probably a leading example of logical reasons for dismissing the idea of a past eternal universe.

 

[Khashishi]

I think there are some constraints on the initial conditions of the universe that prevent it from having a high gravitational entropy. Our understanding of gravity breaks down at t=0. If we ignore gravitational entropy, then a random initial condition is likely to give us a very uniform universe. I can't justify ignoring gravitational entropy other than saying that we don't understand it well enough.

 

[bapowell]

If we ignore gravitational entropy, then a random initial condition is likely to give us a very uniform universe.

You keep saying this. Please provide a formal justification.

 

[yoron]

Pretty dar** cool bapowell :) Fun reading about that concept. I would put it the other way around though. What we have is 'linear time' (loosely speaking all of it naturally:), and that should then be the platform creating the logics we use. A 'pure field of probability' though implies no questions, and no outcomes either. You need that linearity to create the questions that you then want to answer. That would make our ideas of a brain a 'sub species' to probability in my thoughts, a symmetry break sort of, with probability as the 'know it all', although without questions. Well, as a thought :) (Actually I also tend to think of it as a symmetry, linear time constantly balanced relative probability)
=

Reading some more on it, don't think you need any 'anthropic principle' for it? You just need some sort of principle going from simple to complex. Doesn't have to do with 'intelligence' per se, even though it's nice that we're here, and can discuss it. Maybe Boltzmann brain isn't that far from my view either? I put linear time as the firstmost proponent though, although how to describe what exist in that 'eternal instant' without a time is unknown to me.
==

What I mean isn't that 'simple to complex' should be seen as 'linear time', just as 'probability' isn't time either. But time is what makes us notice the buildup from simple to complex, and probability is where time doesn't exist to me, although somethings probability is defined mostly through statistics, which implies time needed too. But all logic we use, use time. (It's somewhat of a contradiction at first sight, considering that you can ignore 'time' in mathematics, but no more of a contradiction than a 'pure field of probability' could be seen as, to me that is.)

 

[Torbjorn_L]

The Boltzmann brain concept is probably a leading example of logical reasons for dismissing the idea of a past eternal universe.

Why would there be a conflict? It is only if you can't distinguish between a BB fluctuation and other observers you will have a problem, and then only if selection bias is in play.

We are good as long as the outcome of an observable universe fluctuate into existence and then stay permanently is less likely than our universe. Inflation fix that, since it ends locally all the time, spawning off local universes faster than most anything else we can imagine.

 

[Garth]

I think what Chronos is saying is that in an past eternal universe/multiverse not only Boltzmann brains appear, an infinite number of times, but anything else logically possible you can possibly conceive of does as well an infinite number of times.

There is no way to test such an hypothesis and as a theory of anything is a theory of nothing it is totally outside the province of scientific inquiry. Good for science fiction though!

Garth

 

[Torbjorn_L]

I think what Chronos is saying is that in an past eternal universe/multiverse not only Boltzmann brains appear, an infinite number of times, but anything else logically possible you can possibly conceive of does as well an infinite number of times.

No, "logically" possible is too weak, it is philosophy and wrong, we know physics is lawful.

And not everything of fluctuation physics is possible, as I noted inflation cuts off "last Thursday" solipsist philosophy as well (the universe fluctuated into existence last Thursday with a 14 billion year perfect 'memory' of events. The regulation of slow roll inflation (which Planck now has more or less confirmed both by model test but even better with model-less observation) is perhaps one of its most exciting consequences.

That slow roll inflation and its potential multiverse outcome is testable in a semiclassical, local statistics way is known since 1987 (Weinberg's model and predicted test). In fact I understand better observation has failed the test a few years back, i.e. it would be perverse to claim it isn't testable since it has been tested. Maybe it shows multiverses isn't what we see, maybe it didn't account properly for the physics. (The details of how Weinberg did it is arguable.)

I don't presume to know what happens when you need to "inflate" (heh) statistics to infinite many distributions. My dim understanding of the problem in quantum physics is that quantum Hilbert spaces are assured to be complete metric spaces due to the inner product structure imposed by the probability amplitude (squared wavefunction). I don't see why an explicit simple quantum field in a semiclassical universe (slow roll inflation) would be any different. Hence a local approximation should be sound.

 

[Garth]

Inflation isn't short on falsifiable predictions, but that's the problem, there are too many of them.

Falsify one and an alternative is proposed, and then another, and then another...

Garth

 

[Chronos]

Garth, that is strangely reminiscent of string theory - a theory suffiiciently flexible to accommodate any observational evidence. I instinctively find such ideas repulsive and useless.

 

[bapowell]

Inflation isn't short on falsifiable predictions, but that's the problem, there are too many of them.

Falsify one and an alternative is proposed, and then another, and then another...

Garth

Then I would argue those aren't falsifiable prediction, or at least, they don't get at generic predictions of inflation but rather deal with predictions of specific models (like whether the scalar tilt is such and such). I can think of one generic prediction of inflation: superhorizon correlations in the EE polarization anisotropy.

 

[palmer eldtrich]

Then I would argue those aren't falsifiable prediction, or at least, they don't get at generic predictions of inflation but rather deal with predictions of specific models (like whether the scalar tilt is such and such). I can think of one generic prediction of inflation: superhorizon correlations in the EE polarization anisotropy.

Can you explain this in laymans terms? "superhorizon correlations in the EE polarization anisotropy'

 

[bapowell]

I'll try. Please let me know if I stray too far off the path here. CMB photons observed on Earth today are polarized. They can be either E-mode (curl-free) polarized or B-mode (curl) polarized. CMB photons are not polarized initially: when CMB photons move through an overdensity, they become E-mode (or scalar) polarized. We can use the pattern of E-mode polarization found in the CMB to reconstruct the field of density perturbations in the early universe. When we measure the polarization of CMB photons from across the sky, we find that there are interesting correlations in the polarizations of photons arriving on Earth from different directions (E-mode from one direction correlated with E-mode from another direction gives EE). The larger the angular separation of the photon directions, the larger the size of the overdensity that caused the polarization. What we find, remarkably, is that there are photon correlations indicating overdensities that were truly large -- larger than the size of the observable universe when the CMB was created. (The CMB was "created" around 350,000 years after the big bang. The size of the observable universe is roughly the distance that light had traveled in those 350,000 years (with the help of the expansion).) So these correlations bespeak an acausal process: the generation of an overdensity larger than the distance light could have traveled since the big bang. Inflation generically creates such "superhorizon" perturbations (overdensities).

 

[skydivephil]

Thanks for that Bapowell. Is this something that alternatives to inflation such as Ekpyrosis, VSL, CCC, string gas cosmology etc can explain as well or is it unique to inflation?