Discovering the Universe's Flatness: Insights from an Amateur Astronomer

[CCosmin]

"Flat Universe"question.

Hello, everyone!

I'll start by saying that astronomy or physics are not my majors here; I'm a freshman Med School student, however I've recently started amateur astronomy as a hobby. Naturally I had to increase my knowledge on this subject so I started visiting different astronomy sites and youtube videos and I came across this video. At around the 40 minute mark, Mr. Krauss states that the Universe is flat when looking at the CBR. I didn't read too much into it because I still have my own studies to attend, however, if someone here could simplify it, like, for example: The 2D Universe on the surface of a balloon is expanding in 3 dimensions or something like that.

Sorry if this request sounds dumb or wastes anyone's time, but I tend to have these moments where I HAVE to realize how something fits.

Thanks! :)

 

[fhqwgads2005]

The concept of "flat" geometry is a little difficult to picture in 3 dimensions, in fact, it really is impossible. The best one can do is think about the implications of things being flat or curved. For now, let's just think of the universe as having 2 spatial dimensions. So let's just say we're stuck on some flat sheet that can be bent and folded however we decide.

When solving Einstein's equation, which relates the curvature of some spacetime to the energy contained in that spacetime, for the shape of the entire universe, we actually get 3 possible solutions, depending on the makeup of energy in the universe (proportions of energy due to matter, radiation, and "vacuum" energy). The only stipulations on these solutions are that the universe be homogeneous and isotropic -- that it looks essentially the same to any observer at any point in space -- which means there can't be an "edge" to the universe, since things would look very different to some observer standing near the edge. This means there are 2 general shapes the universe can have -- closed, or open. Closed would be like standing on the surface of a sphere (or balloon), because there's no edge. You can walk in one direction forever and never reach an edge. You would come back to where you started over and over again. Also strange things would happen like parallel lines would eventually intersect (think of lines of longitude on earth). The other option is an open universe, meaning the universe must simply be infinite in every direction in order to prevent the existence of some edge. There are two options for the open universe, saddle shaped (example in a link at the bottom), or flat. In this case, if you walk in the same direction forever, you'll never get back to where you started.

Now, how do you distinguish between saddle and flat? Geometrically, if you had a circle of radius r1 and a larger circle of radius r2, and measured the distance between those circles in flat space, you'd get d = (r2 - r1). But in a saddle shaped universe, you'd actually get something LESS than (r2 - r1). This is because the space between r1 and r2 is curved. Also, for the spherical (closed) universe, you'd get something MORE than (r2 - r1) for the same reason.

The "flat" solution to Einstein's equation is actually sort of a critical point between the spherical and saddle shaped geometries. It's like a fine line between the two. Now, it turns out, by measuring the CMB, we can measure the proportions of energies in the universe, which comes out to be about 70% "vacuum" energy, and 30% mass energy. And, this means that as precise as we can measure, the universe is right on that fine line between spherical and saddle shaped -- meaning it's flat!

Now, what crazy coincidence caused the universe to be exactly on that line between an open and closed universe (as far as we can tell with the precision we have)? The current explanation is a period of rapid expansion, called "inflation" in the very first instant after the Big Bang (something like 10^-36 seconds), which expanded the universe so quickly it just flattened out. Actually, since then, it has only become less flat, but we still won't likely be able to tell it's not.

If you're still interested in how to think in different numbers of spatial dimensions, I highly recommend the book Flatland by Edwin Abbott.

Saddle shape:

http://wapedia.mobi/thumb/25d7510/en/fixed/470/391/Saddle_point.png?format=jpg

 

[CCosmin]

So the "flat" part comes from the condensed line in the middle of the CBMR image, which represents the initial (and possibly current) direction of the expansion. I've got a better image in my head, but still correct me if I get it wrong. :)
Also, I seem to recall Carl Sagan's video about Flatland and the possibility of a 4th dimension in which this Universe could be expanding.
I'll see if I can get a hold of it somehow.

Many thanks!

 

[phinds]

fhgwgads, that's a very nice discourse; wish I could have done it that well.

I do take issue with your statement

Actually, since then, it has only become less flat, but we still won't likely be able to tell it's not.

If we knew to a certainty that "it has become less flat" then we WOULD know that it is not flat, "less flat" being a bit like "less pregnant" --- you can't becomes less so; you either are or you aren't.

 

[fhqwgads2005]

I'm not sure what you mean by the condensed line... The CMB is very uniform throughout the universe, except for very small local fluctuations called anisotropies. These are used to determine the energy densities of the universe, and from that, the geometry.

Expansion has no direction, the universe expands in all directions evenly from every point in space.

 

[CCosmin]

I saw a picture of the CMB that showed a red horizontal area in the middle. I think it was just set to really high contrast. That must have set me off track, but in the end I got your ideea. :)

Again, many thanks!

 

[fhqwgads2005]

Ahh, I think you mean the raw microwave images. The line you see in the middle is just due to the microwaves produced by our own galaxy. These aren't part of the CMB, even though they give off the same wavelengths. That big line in the middle is usually removed using complex statistical methods in order to see the CMB on its own.

see here
https://docs.google.com/viewer?a=v&...g_VHyG&sig=AHIEtbT65KUsnkjtJ8y5XSzeOVpbBwsNjA

 

[fhqwgads2005]

fhgwgads, that's a very nice discourse; wish I could have done it that well.

I do take issue with your statement

If we knew to a certainty that "it has become less flat" then we WOULD know that it is not flat, "less flat" being a bit like "less pregnant" --- you can't becomes less so; you either are or you aren't.

I meant theoretically... you can prove through the math of GR that the universe flattened by a factor of something like 10^60 after inflation. Observationally of course, we can only tell it's flat to something like 0.5% uncertainty.

 

[PatrickPowers]

The "flat" solution to Einstein's equation is actually sort of a critical point between the spherical and saddle shaped geometries. It's like a fine line between the two. Now, it turns out, by measuring the CMB, we can measure the proportions of energies in the universe, which comes out to be about 70% "vacuum" energy, and 30% mass energy. And, this means that as precise as we can measure, the universe is right on that fine line between spherical and saddle shaped -- meaning it's flat!

The flat geometry has been declared the "standard model." I don't know why: I was not consulted :-). It seems impossible for observation to prove that the universe is flat. Essentially you have to show that the curvature is equal to zero, and you can never measure the curvature to infinite precision so this can't be done. To "prove" the Universe is flat you would have to argue that some contradiction arises if the Universe is not flat. But that is always tricky.

My best guess is that the feeling is that it is close enough to flat for all practical purposes, so let's assume that and move on. Or perhaps it's being so close to flat is considered too much of a coincidence, so there must be some as-yet-undiscovered reason the Universe is flat.

 

[Chronos]

The universe is in a perpetual state of near perfect equilibrium. Were this not true it would, by now, have almost immediately recollapsed, or, expanded into a state of nearly zero density. Nobody can quite wrap their head around this weird, stuck in the middle coincidence.

 

[revo74]

Now, what crazy coincidence caused the universe to be exactly on that line between an open and closed universe (as far as we can tell with the precision we have)? The current explanation is a period of rapid expansion, called "inflation" in the very first instant after the Big Bang (something like 10^-36 seconds), which expanded the universe so quickly it just flattened out. Actually, since then, it has only become less flat, but we still won't likely be able to tell it's not.

Was inflation posited simply to explain the flat Universe or is there evidence for it that stands alone?

 

[bapowell]

Was inflation posited simply to explain the flat Universe or is there evidence for it that stands alone?

Inflation also addresses the horizon problem (essentially the uniformity of the CMB despite the fact that its comprised of [itex]\sim 10^5[/itex] causally disconnected regions) and the monopole problem (the absence today of heavy relics like monopoles).

Inflation is also a theory of structure formation. The predictions of simple inflation include a nearly scale invariant spectrum of adiabatic, Gaussian temperature fluctuations in the CMB. So far, observations support these aspects of simple inflation, and competing theories of structure formation, like cosmic strings, have been ruled out as the primary source of inhomogeneity. Still, non-inflationary theories can be constructed that also agree with the data.

However, there is one observation in particular that favors inflation over other theories of structure formation. The hallmark feature of inflation -- accelerated expansion -- results in correlations between regions of the universe that would appear to violate causality according to standard cosmology. In other words, correlations are observed in the CMB that exist on scales larger than the horizon. Both temperature and polarization anisotropies exhibit correlations on superhorizon scales. I emphasize polarization because superhorizon correlations in temperature anisotropies can be generated causally (via late-time processes like the integrated Sachs-Wolfe effect), whereas polarization anisotropies require a mechanism like inflation that can causally correlate regions of the universe that lie outside the Hubble radius.

Lastly, inflation predicts a large scale spectrum of primordial gravitational waves, which can in principle be detected by measuring B-mode polarization in the CMB.

 

[Nabeshin]

Inflation also addresses the horizon problem (essentially the uniformity of the CMB despite the fact that its comprised of [itex]\sim 10^5[/itex] causally disconnected regions) and the monopole problem (the absence today of heavy relics like monopoles).

Inflation is also a theory of structure formation. The predictions of simple inflation include a nearly scale invariant spectrum of adiabatic, Gaussian spectrum of temperature fluctuations in the CMB. So far, observations support these aspects of simple inflation, and competing theories of structure formation, like cosmic strings, have been ruled out as the primary source of inhomogeneity. Still, non-inflationary theories can be constructed that also agree with the data.

However, there is one observation in particular that favors inflation over other theories of structure formation. The hallmark feature of inflation -- accelerated expansion -- results in correlations between regions of the universe that would appear to violate causality according to standard cosmology. In other words, correlations are observed in the CMB that exist on scales larger than the horizon. Both temperature and polarization anisotropies exhibit correlations on superhorizon scales. I emphasize polarization because superhorizon correlations in temperature anisotropies can be generated causally (via late-time processes like the integrated Sachs-Wolfe effect), whereas polarization anisotropies require a mechanism like inflation that can causally correlate regions of the universe that lie outside the Hubble radius.

Lastly, inflation predicts a large scale spectrum of primordial gravitational waves, which can in principle be detected by measuring B-mode polarization in the CMB.

Bravo.

 

[revo74]

Inflation also addresses the horizon problem (essentially the uniformity of the CMB despite the fact that its comprised of [itex]\sim 10^5[/itex] causally disconnected regions) and the monopole problem (the absence today of heavy relics like monopoles).

Inflation is also a theory of structure formation. The predictions of simple inflation include a nearly scale invariant spectrum of adiabatic, Gaussian temperature fluctuations in the CMB. So far, observations support these aspects of simple inflation, and competing theories of structure formation, like cosmic strings, have been ruled out as the primary source of inhomogeneity. Still, non-inflationary theories can be constructed that also agree with the data.

However, there is one observation in particular that favors inflation over other theories of structure formation. The hallmark feature of inflation -- accelerated expansion -- results in correlations between regions of the universe that would appear to violate causality according to standard cosmology. In other words, correlations are observed in the CMB that exist on scales larger than the horizon. Both temperature and polarization anisotropies exhibit correlations on superhorizon scales. I emphasize polarization because superhorizon correlations in temperature anisotropies can be generated causally (via late-time processes like the integrated Sachs-Wolfe effect), whereas polarization anisotropies require a mechanism like inflation that can causally correlate regions of the universe that lie outside the Hubble radius.

Lastly, inflation predicts a large scale spectrum of primordial gravitational waves, which can in principle be detected by measuring B-mode polarization in the CMB.

Is there any way to confirm inflation with empirical data?