Cosmology Confusion

[Badly Shaved Monkey]

The recent discovery that neutrinos may have mass reminded me of my persisting confusion over the basis of the cosmological Big Picture, i.e. whether the Universe is open or closed.

As I understand it, Omega is the average density. For various reasons, among which is a desire for 'neatness', it is assumed that it will turn out to be equal to 1, the 'critical' density that lies between external expansion and eventual re-collapse. But ordinary baryonic matter is only a small fraction of this. But the reasons for it being equal to 1 are compelling so the search is on for the missing density.

1. Is the limit on the amount of baryonic matter, which is derived from theories of Big Bang nucleosynthesis independent of neutrinos having mass?

2. Dark Matter and Dark Energy have each been invoked for various reasons. DM would add to the density of baryonic matter to raise Omega nearer to 1, but does DE also add to the average energy density? In other words, if we add BM + DM + DE might we have accounted for enough mass-energy to bring Omega to 1?

3. But, DE is thought to be driving a new phase of cosmic acceleration. Now this is where I get really confused. If DE is the missing component that brings Omega to 1, how does that square with expansion getting faster instead of approaching a zero-rate asymptotically?

4. And I still get muddled between the connection between geometry and density. Indeed I now seem to be more muddled. Does Omega<1 equate to an open Universe and a hyperbolic geometry; Omega=1 equate to an asymptotically halting Universe and a flat geometry; Omega=1 equate to a closed Universe and a spherical geometry? Or are the fate of the expansion and the geometry independently determined?

5. Am I right that Cosmic Inflation is thought to explain the flatness? Am I also right in saying that Inflation is also thought to explain how nearly-nothing can blow up to make a Universe and the fact of it starting from nearly nothing also means that its total energy is nearly zero, which means that energy-density should be almost exactly matched by gravitation, Omega = 1 and we should have an asymptotically halting expansion? In other words, if inflation is true should it mean that Omega must be 1?

p.s. the reports I read were vague as to how much a neutrino was supposed to weigh, indeed which type of neutrino was being considered.

 

[Yllanes]

The recent discovery that neutrinos may have mass reminded me of my persisting confusion over the basis of the cosmological Big Picture, i.e. whether the Universe is open or closed.

We have been quite confident that they have mass for a few years now.

As I understand it, Omega is the average density. For various reasons, among which is a desire for 'neatness', it is assumed that it will turn out to be equal to 1, the 'critical' density that lies between external expansion and eventual re-collapse. But ordinary baryonic matter is only a small fraction of this. But the reasons for it being equal to 1 are compelling so the search is on for the missing density.

The most compelling reason is that it has been measured
to be almost 1, with an uncertainty interval that includes that value.

1. Is the limit on the amount of baryonic matter, which is derived from theories of Big Bang nucleosynthesis independent of neutrinos having mass?

Everything adds to the stress-energy momentum. That's the thing with graviation, everything (aside from dark energy) adds up. If you have an electric field, that affects the curvature of spacetime, if you have a neutrino, mass or no mass, that affects the curvature. The energy density is the important thing, not whether it is in the form of matter. Of course, the fact that m > 0 for neutrinos is important for several things, but I don't have time to go into much detail now.

2. Dark Matter and Dark Energy have each been invoked for various reasons. DM would add to the density of baryonic matter to raise Omega nearer to 1, but does DE also add to the average energy density? In other words, if we add BM + DM + DE might we have accounted for enough mass-energy to bring Omega to 1?

There are two kind of DM. One is ordinary matter that is, well, dark. That is, everything but stars. This is included in the baryonic matter part of Omega (and sums about 4%). The other kind, the strange kind, sums 20% of Omega. The 75% that lefts is almost everything contributed by DE (radiation has a negligible contribution).

3. But, DE is thought to be driving a new phase of cosmic acceleration. Now this is where I get really confused. If DE is the missing component that brings Omega to 1, how does that square with expansion getting faster instead of approaching a zero-rate asymptotically?

Because it is repulsive. Omega determines the curvature of space and whether the universe is open or closed. Without a cosmological constant (the DE), the curvature also determines the fate of the universe. A closed universe necessarily implies an expansion and a subsequent contraction, etc. But with Lambda (DE), you can have a closed universe that expands forever, because Lambda is repulsive gravitation.

4. And I still get muddled between the connection between geometry and density. Indeed I now seem to be more muddled. Does Omega<1 equate to an open Universe and a hyperbolic geometry; Omega=1 equate to an asymptotically halting Universe and a flat geometry; Omega=1 equate to a closed Universe and a spherical geometry? Or are the fate of the expansion and the geometry independently determined?

See above, Omega determines the geometry, but with Lambda, the geometry does not determine the fate.

p.s. the reports I read were vague as to how much a neutrino was supposed to weigh, indeed which type of neutrino was being considered.

I assume you are referring to the MINOS experiment. They don't measure the mass of a neutrino, the measure the difference between the masses of the different neutrinos. For those of you who don't know what this is all about, the thing is that neutrinos were thought to have m=0 and travel at c. (m = 0 <=> v =c always). But then they were observed to oscillate. A neutrino can change types during its journey, which means time passes for them which means v =/= c, which means m =/= 0.

ETA: I forgot to answer: They measured delta m2 = 0.0031 eV². This value is important (and will be more important when the experiment is fully operative), but I don't have time to go into details.

 

[jpowell]

5. Am I right that Cosmic Inflation is thought to explain the flatness? Am I also right in saying that Inflation is also thought to explain how nearly-nothing can blow up to make a Universe and the fact of it starting from nearly nothing also means that its total energy is nearly zero, which means that energy-density should be almost exactly matched by gravitation, Omega = 1 and we should have an asymptotically halting expansion? In other words, if inflation is true should it mean that Omega must be 1?

Inflation is mostly invoked to explain the horizon problem. Basically the universe looks the same in all directions, and roughly the same at each point (isotropy and homogeneity), yet different regions of spacetime are not casually connected, so shouldn't have been able to communicate with each other, yet why are they the same? Inflation solves this problem by assuming that for a very short period of time in the early epoch the universe expanded very very quickly (much faster than it does today) and hence this smoothed out our little patch of the universe.

It doesn't explain the geometry of spacetime, nor does it explain "how nearly-nothing can blow up to make a Universe" because that doesn't really make sense when you consider the universe in GR.

 

[Badly Shaved Monkey]

Thanks.

Let's see if I've got this right. DE contributes to Omega, and probably is sufficient to make it 1, but it also contributes/constitutes a non-zero Lambda. Omega=1, means the Universe is geometrically flat, but Lambda<>0 means that it will expand indefinitely.

What about question 5 about Inflation.

 

[Badly Shaved Monkey]

Inflation is mostly invoked to explain the horizon problem. Basically the universe looks the same in all directions, and roughly the same at each point (isotropy and homogeneity), yet different regions of spacetime are not casually connected, so shouldn't have been able to communicate with each other, yet why are they the same? Inflation solves this problem by assuming that for a very short period of time in the early epoch the universe expanded very very quickly (much faster than it does today) and hence this smoothed out our little patch of the universe.

It doesn't explain the geometry of spacetime, nor does it explain "how nearly-nothing can blow up to make a Universe" because that doesn't really make sense when you consider the universe in GR.

Thanks. Your reply crossed with my reply to Yllanes.

I know Inflation is a solution to the Horizon problem, but are you saying that flatness is not also implicit within it? Have I got homogenity, i.e. evenness or flatness in one sense confused with flatness in the geometric sense? In other words, could an Inflated universe be anything from spherical to hyperbolic, but, whatever it is, it would be homogeneous and isotropic?

 

[Yllanes]

Thanks.

Let's see if I've got this right. DE contributes to Omega, and probably is sufficient to make it 1, but it also contributes/constitutes a non-zero Lambda.

Yes, I'm sorry I was a bit confusing. DE and Lambda are the same thing, an extra term in Einstein's equations.

Omega=1, means the Universe is geometrically flat, but Lambda<>0 means that it will expand indefinitely.

Well, Lambda < 0 would have the opposite effect. It just so happens it is positive. Consider a universe with no mass, no energy, nothing... only Lambda. Then the size of the universe would be something like this: R=exp[Lambda*t], an exponential growth. This is called de Sitter universe. Our universe will very likely suffer this fate in the future, because energy is spreading along more and more space and eventually the density will be so small that the asymptotic behaviour is the de Sitter cosmology.

When Einstein originally introduced Lambda, it had a very different meaning ('the biggest blunder of his life'). He introduced artificially and tweaked its value so that the universe be static. Then Hubble saw the expansion... Had Einstein not added that term, he would have predicted the expansion of the universe without leaving his desk, a remarkable feat. Once the expansion was stablished, Lambda was dumped and three cosmologies (Friedmann) were proposed. Closed, flat and open (flat is also open). The cosmology was determined by the geometry. This prevailed for a long time (check some common gravitation books and that's what you will see, Landau & Lifshitz don't even talk about Lambda, Misner, Thorne & Wheeler discuss it but not as the real universe). Recently, the existence of Lambda was empirically proven and everything changed. Now it has more or less the opposite effect to what Einstein used, but it seems to exist.

 

[jpowell]

Thanks. Your reply crossed with my reply to Yllanes.

I know Inflation is a solution to the Horizon problem, but are you saying that flatness is not also implicit within it? Have I got homogenity, i.e. evenness or flatness in one sense confused with flatness in the geometric sense? In other words, could an Inflated universe be anything from spherical to hyperbolic, but, whatever it is, it would be homogeneous and isotropic?

Yes. Delving into pure mathematics for a moment. A sphere is homogeneous and isotropic, simply because every point looks the same, a plane is also homogeneous and isotropic because every point looks the same, and a hyperbolic surface (which is hard to imagine) has the same properties.

Isotropy does not imply flatness. (Edit: Just to clear things up isotropy includes homogeneity.)

 

[Yllanes]

Have I got homogenity, i.e. evenness or flatness in one sense confused with flatness in the geometric sense? In other words, could an Inflated universe be anything from spherical to hyperbolic, but, whatever it is, it would be homogeneous and isotropic?

I see jpowell has the inflation issue tackled, so I won't go into it. I just want to remark that homogeneity and isotropy are the two starting assumptions that give rise to the three models (closed, flat and open). We don't discuss any other possibility because these are the only ones consistent with those assumptions. Briefly, everything comes down to the definiton of a metric tensor. If we constrain this tensor to describe an isotropic and homogenous universe, then, aside from a size factor, the metric only leaves us with the choice of one sign, which determines open or closed (flat would be the limiting case with the size factor going to infinity). The choice of the sign and the magnitude of the size factor are determined by the density, assumed constant everywhere. This is a wild assumption at first (after all, pretty much all space is empty) but it makes sense if we go to really big scales.

For the sake of completeness, I must remark that nontrivial topologies (read: strange shapes for the universe) have been empirically discarded, at least for our 'neighbourhood'.

 

[Badly Shaved Monkey]

Thanks. I need to think this through to make sure I've got the hang of it.

I may be back!

 

[Yllanes]

I may be back!

And we will be waiting.

 

[jpowell]

Thanks. I need to think this through to make sure I've got the hang of it.

I may be back!

My only warning to you is that a lot of this stuff is not easy to understand if you apply "common sense" to it. The extreme situations in General Relativity are so far outside of ordinary human experience it is very hard to truly understand what is going on. In my opinion it's only by understanding the mathematical models at the heart of the theory that you can understand what the theory is about.

I would be happy to reccomend some introductory textbooks on the subject, but which ones and whether you will be able to understand them depend on your current knowledge of mathematics and physics.