sábado, 26 de novembro de 2011

5. Galaxies and Clusters - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe



This lecture throws some concepts and history at you a little too fast. The course guidebook could be much more helpful if it included everything that Sean covered. But maybe there is a limit on the amount of pages per lecture. Yes, Sean does go that fast. Astronomy is my background and even I had to hit reverse several times to keep up.

So far we've assumed the universe to be smooth everywhere. So we plugged special relativity's space-time into general relativity's dynamic universe to get the Friedmann equation. That told us a great deal about the universe, but we would not be here if the universe was totally smooth. This lecture talks about the non-smooth universe and how it implies the existence of dark matter.

We see lumps in the early universe of 1 part in 100,000. To talk about how that imbalance causes formation from the atomic scale to the cosmological scale is nearly pure speculation. We really don't know much about how our own solar system formed. The solar nebulae hypothesis is so bland it makes me cringe every time I hear it. It's perfectly all right to talk about what we think happened, but it should be presented with the caveat of near ignorance on the real details.

Billions of years in gravity fields produces stars and galaxies which appear not to have enough visible ordinary matter, nor even ordinary matter to account for the dynamics of galaxies and their clusters. This work of Rubin and Zwicky is all in the course guide, so I tend to concentrate on what gets left out of the guide or what is not presented clearly.

It's funny how the famous character of Fritz Zwicky is presented differently in this course then in Alex Filippenko's course. I guess it's just expected from the nature of the lectures, but Alex gives respectful insights as he also pokes fun at some of the legendary Zwicky stories. Sean passes over without any mention of it. But Rubin agrees with Zwicky that five times the amount of ordinary matter is needed to account for the observed dynamics. Some of the techniques are not very clear or described too quickly, like the temperature gradient.

Is the dark matter ordinary? According to theories on the composition of light elements and the cosmic microwave background, the matter is not ordinary.

Since we observe the universe as flat, we call the overall energy density ρ (rho) from Einstein's equation that would make a flat universe, the critical density. But we can only account for 5% of the ordinary matter required for that critical density. Dark matter adds up to only 25% of that required for the critical density. So their total of 30% is close enough to 100% that for years it was thought that we would just discover the remaining ordinary or dark matter that makes up the missing 70%. But the critical density and overall energy density are constantly changing, even with respect to each other. The current total of 30% is a strange number because it is very close to 100%. It could be much much less than that. In the past it was actually much greater, which implies we are currently in a transition to a much smaller percentage. But that seems to be very strange and unlikely.

Only ten years ago astronomers explained it by thinking we just didn't have a good measure of the universe. The recent discovery of dark energy indeed does account for that missing 70% to make the universe flat. Yet like dark matter, its composition is in some mysterious form.

We now have under our belts, a picture of the entire universe, which is a pretty good one really. It's an impressive fact that we even have such a picture, since 100 years ago we knew almost nothing that was correct about the universe on very large scales. Yet now we have a picture that fits the data quite well.

The parts we've talked about are basically the fact that when you look into the sky, you see that it's filled with galaxies, so the universe is big. By a galaxy, we mean some collection of stars moving under their mutual gravitational attraction, maybe 100 billion stars per galaxy. There's perhaps 100 billion galaxies spread throughout the observable universe, and they're all moving away from all the other ones. So the universe is getting bigger as a function of time.

A crucial fact about this distribution of galaxies through space is that it's more or less uniform. The universe is smooth on very large scales, which is an incredibly helpful feature as far as cosmologists are concerned, because that means they can approximate the universe as being absolutely smooth. That's exactly what we did when we looked at what Einstein said about space and time and how they are joined together in one thing called spacetime in his Theory of Special Relativity. The idea that spacetime is dynamic, so that it can expand and have a geometry which can change with time, this is Einstein's Theory of General Relativity.

So if you have a universe that is perfectly smooth and looks the same everywhere, than what you can do is plug that into General Relativity and ask how such a perfectly smooth universe changes as a function of time? How does it expand, where does it come from, where will it go? We did that and derived an equation, the Friedmann equation, which relates the energy density in the universe to the way that space is curved and to the way space is expanding.

In today's lecture, we're going to go a little bit beyond that. We see a picture from the SDSS (Sloan Digital Sky Survey) of how galaxies are distributed in our local region of the universe. We said that they look pretty smooth, which was a good approximation and was very helpful. Today we will admit and take seriously the fact that they're not completely smooth. There is in fact structure there. Some of these galaxies are clumped together into groups, clusters, walls, sheets, or filaments that stretch across the observable universe.

At first glance, as cosmologists, we say that this is kind of annoying that the galaxies are not perfectly smooth, since we can really solve a lot of problems in terms of writing down equations and finding solutions, if everything really were perfectly smooth. On the other hand, it's certainly good news that there are local structures in the universe, that the density is not absolutely constant throughout space. We are much more dense than the air around us, which in turn is much more dense than the space between the stars. So there's structure in the universe, and today we're actually going to take advantage of that structure, by using it to weigh the universe, to find out how much stuff there is, in particular how much matter there is in the universe.

Of course we've already given away the punchline, so what we'll find is that there's a lot of matter in the universe, more than we seem to be able to account for with ordinary matter, with atoms, hydrogen, helium, that we're familiar with in the periodic table. Yet today we won't get quite that far. We'll just give evidence that there's a lot of mass in the universe, much more than we see directly. Yet it will take future lectures to show that we're actually pretty sure that the mass which we don't see, is some absolutely new kind of particle.

So lets think about the process by which the universe went from being very smooth, to having structures in it, to having galaxies and clusters of galaxies. We see an iconic image in cosmology, the picture of the Cosmic Microwave Background (CMB), which is the leftover radiation from the Big Bang. When the universe was less than about 400,000 years old, it was opaque, hot, dense, and giving off light. Yet that light didn't get very far, as it just kept bumping into free electrons. Yet once the universe was older than 400,000 years, it became transparent, and that light streamed across the universe unimpeded. That goes with this image we see right here.

This is a snapshot of what the universe looked like when it was about 400,000 years after the Big Bang. Now it's about 14 billion years after the Big Bang, so a lot of time has passed, and we can see the effects of this passage of time. This picture actually shows the slight differences in temperature from place to place in the CMB. The blue areas are a little colder, while the yellow and red are a little bit hotter, yet only very slightly so!

The amount of variation in temperature of the CMB is only about 1 part in 100,000. So what that means, is that there were slight variations in the density of stuff back at that time. The density of the universe from place to place, some 400,000 years after the Big Bang, was nearly perfectly smooth, yet not exactly so. We may have had 100,000 particles in one region of space, and 100,001 in this other region, and 99,999 in that region, tiny variations over an ultimately very smooth distribution.

So in lecture 11 we'll be talking in great detail about what kinds of patterns we see in the CMB, how they got there, and what we learned from them. Today we'll just mention that the universe was a lot more smooth back then than it is today, where we see galaxies in some places, yet no galaxies in others. There's a huge amount of contrast between the density in a galaxy and the density outside.

So what happened from the microwave background era to today, is gravity. It worked on these tiny perturbations, these tiny ripples, in the density of space, to increase their magnitude. Gravity works as a contrast knob where you turn up the contrast in the universe. You take dense regions and they become even more dense, and less dense regions in the universe become even less dense.

What happens in that region where there's 100,001 particles is that the force due to gravity is a little bit more than in the region with only 100,000. So the region with one extra particle, pulls things toward it. Then it has two extra particles, so it has a little bit more mass, so it can pull even more things to it. This is a very slight effect and takes literally billions of years to happen. Yet due to this effect, we go from an almost perfectly smooth distribution, to one that, though still very smooth on large scales, on small scales has stars, planets, and galaxies.

So that happened over the last 14 billion years. Gravity turned up the contrast knob on the universe, and it did so in a hierarchical fashion. What that means is, on smaller scales, things can happen more quickly. It takes less time to build up a density region in some very tiny region of the universe, than it does over megaparsecs. Such dense structures that are millions or billions of light years across, will literally take millions or billions of year to create, respectively.

So the universe forms in a bottom-up way. You first form planet and star sized things, than galaxy sized things, clusters of galaxies, and beyond. So it's no surprise that we see more structures on small scales than we do on large scales in the universe.

We mentioned before that when you actually go and look out into the sky, what you see are a collection of galaxies. So here again is the Hubble Deep Field, an image of a randomly selected part of the sky. There's not anything special or especially interesting in that region, but the universe is more or less the same everywhere, so it doesn't matter.

We take a picture in some region of the sky and we see that it's filled with galaxies. One thing we notice about them, is that they're very pretty, beautiful, and aesthetically pleasing. Personally Sean has always wondered just why that is the case? He's really sure why we find galaxies beautiful, and it's hard to imagine some explanation of this from evolutionary psychology! A million years ago when we were hunters and gatherers, we didn't know what galaxies were looking like. So it's hard to imagine some kind of pressure on us, so that we would look at the galaxies sometime in the future and find them to be beautiful. Yet beautiful they certainly are!

The other thing is that the galaxies look different. Some are red, blue, smooth, or irregular. Partly this is because we are looking at galaxies from different moments of time. When you look at the sky, because the speed of light is finite, one light year per year, you're looking backwards in time. If you see a galaxy that is a billion light years away, you're seeing it as it looked a billion years ago. So it's not surprising in some sense, that the galaxies look different. We're taking snapshots of them at different stages in their evolution.

Yet on the other hand, even today the nearby galaxies that are all the same age, still do look different. Galaxies have a slightly individualistic character, which is going to be important once we get to talking about what we can learn by studying individual galaxies.

So what we're caring about in this course, dark matter and dark energy, is how to weigh the galaxies. How do we know how much stuff there is in a galaxy? Well the simplest thing to do is just look and count. To say, well you know there's 100 billion stars and that the average mass of the star is something like the mass of the sun, you're going to guess there's about 100 billion solar masses worth of stuff in a typical galaxy.

Yet it's always possible that, since even 100 years ago, people recognized that there was stuff in galaxies that we couldn't see directly. So you want a better way to get a handle on the total mass of the galaxy. How do you do that? Of course, the answer is given to us again by gravity. Einstein showed that gravity is universal. Everything that exists in nature, everything that has energy, will give rise to a gravitational field. So even though you don't see it directly, you can tell how much stuff there is in a galaxy, by measuring its gravitational field. The more mass there is in the galaxy, the stronger the gravitational field will be.

Now in fact, we don't really even need Einstein's laws to tell us this, since Newton's laws could have done it. Einstein invented a theory of gravity that is better than Newton's theory, that can describe things which Newton's theory can't describe. The expansion of the universe is not something that makes sense for Newtonian gravity, for Isaac Newton's space and time were fixed in absolute structures. He couldn't have talked about the Big Bang as some actual expansion of the universe itself.

However, Newton could have talked very easily about a galaxy, since it's in a regime of a part of the universe where Newton's theory of gravity is an excellent approximation for what is really going on, according to Einstein. So we can think about Newtonian gravity. We can think about the fundamental law of Newtonian gravity which is the inverse square law. According to this, if you have two objects, they exert a force on each other, proportional to their mass. So the heavier they are, the larger the force is. It's also inversely proportional to the distance between them, squared. So as things get further apart, the gravitational force between them gets less and less.

That means that as one object is orbiting around another one, when the orbiting object goes further away, it needs to orbit more slowly in order to follow an ellipse around the object it orbits. So in the solar system, this is perfectly clear. Mercury is moving around the sun very quickly, since it's the closest planet. The earth is moving at some medium speed, and Pluto is moving very slowly. It's not just that it takes Pluto longer, because it has longer to go, but it is actually moving more slowly around the sun, since the force of gravity is much weaker out there where Pluto is.

This is, in fact, how we measure the mass of the sun! We can't put the sun on a scale and weigh it. Yet what we can do is to look at the velocity with which planets are orbiting around the sun, and measure its gravitational field. Knowing the latter will tell us the mass of the sun.

So lets do the same thing with a galaxy. Let's measure the velocity of things moving around a galaxy. We see a picture of Andromeda, and we'd want to look at stuff that is on the outskirts of the galaxy. The difference between a galaxy and the sun, is that the galaxy is not all concentrated in one small region. It's clear where the sun is, and outside the sun, there's not a lot of mass.

Yet a galaxy is more spread out. It's much more diffuse. So you want to look at objects that are as far away as possible, since they would be testing the accumulated gravitational field from everything that they are orbiting. If you want to make sure you're getting all the mass, you want to go as far away as possible. The prediction from Isaac Newton would be that the further you go away, the slower things are revolving around the galaxy.

If you measure the speed at which they're rotating, you can figure out the mass. So this project was undertaken in the 1970s, by an astronomer at the Carnegie Institute in Washington, named Vera Rubin. She measured what are called rotation curves of galaxies. So she observed gas and dust that orbits around a galaxy. Her optical images in visible light, only show part of the galaxy, the biggest, most massive part.

Yet if you also use radiotelescopes, there is stuff you can also see, little wisps of gas and dust, further outside. So she could use those as gravitational tests for what the gravitational field is. What Rubin found is that even though she looked at gas further and further outside the visible galaxy, the velocity of the orbiting gas, did not decrease. As she went further out, the stuff kept orbiting at the same velocity, more or less.

The simple interpretation of this, is that as you go further out, you're feeling the effects of more and more stuff. You have not succeeded in getting outside the entire galaxy. There is still stuff outside. However, we've looked at gas that is far outside anything we can visibly observe inside the galaxy. So the conclusions from Vera Rubin's observations of the rotation curves of galaxies, is that there's stuff creating gravity in galaxies that we don't directly see. This extra stuff is distributed in a much bigger, puffier halo around the galaxy.

So if Rubin is right, and current cosmologists think she certainly is, the galaxy that we see is a decoration. It's a lit up little thing, inside a much bigger structure. A halo made of dark matter. If you plug in the numbers, what you find, according to Rubin's calculations, is that most of the stuff in the galaxy, most of the mass, most of the grams or ergs, is actually in dark matter, and not in the visible matter.

There's certainly also the possibility that we don't understand gravity. Perhaps Newton's theory does not apply in this regime. Yet that would be a big surprise, and we'll talk about limits on that later. So for right now, the simplest explanation is that there really is dark matter there.

Yet that's a surprising result, the first evidence that we have for dark matter being an important part of galactic dynamics. So we'd like to check that, since whenever you get a result that is this important, which says there's a whole new kind of stuff out there in the universe, you don't just accept it and move on. You want to find more evidence that there's something like that going on, or that contradicts it.

So what you can do is look at rotation curves of clusters of galaxies. Rubin measured the rotation curves around individual galaxies, which actually have good and bad features for such a purpose. The good features are the galaxies are very organized. They're very regular, and it's clear there is a disk, that you're looking at stuff which is outside the visible matter, and you can see what you're doing, basically.

Yet clusters are a little bit messier. They're not in disks, but are more disorganized into somewhat spherical shapes, so that you might not be able to measure as cleanly what is actually going on. You need to be a little bit more clever about the techniques you use to weigh the total amount of stuff in the cluster. We see a picture of a cluster of galaxies, where we see at least dozens of different galaxies. In fact a typical cluster will often have hundreds of galaxies in it.

The good part about clusters, even though they're a little bit messy, is that they have a good chance to be a fair sample of the universe. The worry when you look at an individual galaxy, is that they are all different. Some are small and ratty, while some are big and very smooth. Clusters are all big enough, that over the lifetime of the universe, there isn't time for different kinds of stuff to be segregated. Within a cluster, you basically are getting a fair sample of every kind of thing in the universe.

The analogy that astronomers sometimes use is that you're trying to measure the density of people in the US, in different places. Yet the data you have, is not the total density of people, but what you have is the membership directory for the American Astronomical Society, broken down by city. You can see for example, that there's a giant metropolis called Pasadena, California, and there's a tiny suburb called Los Angeles, California! There's a lot more astronomers in Pasadena, since Caltech and the Jet Propulsion Laboratory are there, than there are in Los Angeles.

Yet the problem is, the reason you reach this untrue conclusion, is because you didn't use a fair sample of the universe. Astronomers do not completely, accurately trace the population at large. They are a biased sample. So the good thing about clusters of galaxies is that they are not a biased sample. You get a big enough chunk of the universe, and what you see, should be representative of what is actually going on.

So the next picture we see is a computer simulation, not a photograph using data. It's the result of a computer trying to figure out how we went from an early universe with an almost smooth cosmology, to the late universe where we see these structures lighting up. The good news is that these simulations do a very good job of matching the data, so that we can understand in our computers, where different types of matter might be.

An interesting thing about these galaxies, is that they're helping us to answer the question of where the ordinary matter is located in galaxies. It might be that there's dark matter, and we'll say that there is. Yet even without dark matter, you can still say that just because you've seen a galaxy that's lit up, shining with stars, it doesn't mean that this is where the ordinary stuff is. What if there's just gas in between the galaxies? How do you know?

Again, clusters provide the way to answer that question, because they are a fair sample of the universe. What happens in a cluster is that the gas in between the galaxies is pulled into the center of the cluster, because of the force of gravity. So even if that gas is dark, and is not shining and forming stars, even if in the desolate cold of intergalactic space, it would be completely invisible, in the cluster where it clumps together, it heats up. The gas bumps into other gas and goes up to a very high temperature, so starts to emit x-rays.

We see an image from the Rosat x-ray satellite, of a cluster of galaxies which have a much smoother distribution than if we just saw it in visible light. We see that in between the galaxies which we thought we were observing, there's a lot of stuff there. This is the hot x-ray gas in between the galaxies.

We can do the calculation and ask how many hydrogen atoms for instance, are in the hot gas in between the galaxies, versus the hydrogen atoms actually in the galaxies, shining in the form of stars. The answer is that there's more mass in between the galaxies in ordinary matter, just in hydrogen atoms, than there is in the stars in the galaxies themselves! About 2/3 of the total amount of ordinary matter in a cluster, is in between the galaxies themselves!

So because we believe that clusters are a fair sample of the universe, that tells us that when we were weighing individual galaxies, we were missing a lot of ordinary matter. Forget about the dark matter, we didn't even get a fair sample of the ordinary matter, since most galaxies are not even in clusters. They're out by themselves and we can measure it, yet we had no way of knowing what the total amount of invisible hydrogen was. In a cluster of galaxies, we can find that. It's lit up, because it is heated up, and now emits x-rays.

So we can find out where the stuff is, in a cluster of galaxies. There is a complementary way of doing it, so not only can we look at x-rays being emitted by the hot x-ray gas, but we can also look at the shadow that the cluster casts on the CMB. This is coming from way back when the universe was only 400,000 years old. If a microwave from the CMB passes through a cluster of galaxies, it will scatter off of that hot gas. So when we look at the cluster, we see a dark spot instead of the CMB, because it's been scattered by the hot gas. That is another way, besides using the x-rays, to measure the amount of stuff, and we get a consistent answer. We find that 2/3 of the ordinary matter in a cluster of galaxies, is not in the galaxies themselves.

OK, so that tells us where the ordinary matter is located. Yet what about this dark matter stuff? Should we weigh the clusters of galaxies and get the same answer? Well it turns out there are two different ways to weigh the clusters of galaxies, one is to do the sort of analogous thing to what Rubin did with rotation curves. Unfortunately, clusters are not aligned in a nice little disk, so you can't get a nice little rotation curve. Yet what you can do, is measure the individual velocities of every single galaxy. There's a theorem in classical Newtonian physics, that the average velocity of every galaxy moving around, is related to the total mass inside. The more mass you have, the faster they will be moving. That is the analogous statement to the fact that the more mass you have in the galaxy, the faster something will be orbiting around it.

So this was first looked at, actually back in the 1930s, very long ago, by Fritz Zwicky, who was a Caltech astronomer at the time. He looked at the Coma cluster of galaxies, measuring their individual velocities. He plugged in the numbers and said, "Look, there's no way to explain these numbers on the basis of the matter we see. There must be matter there which we don't see."

He wasn't absolutely taken seriously at the time. It was sort of too early, and he was on the spot, before people were ready for it. People figured, "Well there was stuff there that we just don't see. There's hydrogen or whatever, ordinary stars and planets that we haven't taken into account. Someday we will find them" Today of course, we can do better. We can take account of the stars and planets, and we confirm that don't find enough.

The other thing to do is look at the temperature profiles of the hot gas, to find out the temperature of the gas, starting from the center of the galaxy, and moving our way outward. Not only does this tell us how much gas there is, but also the total gravitational field of the cluster of galaxies. That total gravitational field, depends on the total amount of mass.

The answer once again is completely consistent, namely that even though there's a lot more matter in hot x-ray gas in between the galaxies, than in the galaxies themselves, it is still not nearly enough to account for the total amount of matter in the cluster of galaxies, either by the dynamics of the galaxies zooming around, or by measuring the total amount of gravitational field, using the x-ray profile of the cluster. We get the same answer, which is that the total amount of mass is something like five times what we actually have in ordinary matter. This seems to be very good evidence that there needs to be something new in there, something that we call dark matter.

This kind of argument doesn't completely rule out that it's not some very sneakily hidden ordinary form of matter, but that it's pointing in that direction. So what can we learn from that? Is it possible that we're missing something? Is it possible that there is some dark form of ordinary matter that we haven't seen? It is certainly possible, just from what we've said so far.

In later lectures, we'll put an absolute upper limit on the total amount of ordinary matter in the universe. We'll do that by going back to the very early universe when it was one minute old, or a few hundred thousand years old, look at the relics we get from the early universe in the form of helium, lithium, and other light elements, and also in the form of the CMB. It turns out that properties of these relics from the early universe, depend on the total amount of ordinary matter in the universe, in a very specific way. Back then, ordinary matter was not separated into stars, gas, dust, and planets. It was all absolutely smoothly distributed.

So once and for all, we can get a measurement of the total amount of ordinary matter. We'll find that it's very consistent with what we think is there, from what we see from hot gas in clusters of galaxies and elsewhere. In other words, we have more or less, a rigorous argument that the matter which we now think must be there, from the dynamics of clusters of galaxies, cannot be ordinary matter hidden in some clever way. It has to be something new.

So lets' explore one way of thinking about what this answer is. We keep talking about the fact that the total amount of dark matter is about five times as much as the total amount of ordinary matter. Yet what units is that in? How should we think about this? Well remember the Friedmann equation is used to govern the expansion of the universe. It relates the total energy density on average in the universe, rho(ρ), to the expansion rate (H) and to the curvature of space (K):

((8πG)/3)(ρ)=H² + K

In other words, if you know (ρ) and (H), then you can tell what (K) is, right from the equation. In yet other words, there is one particular value of the (ρ), which for any given value of (H), will mean that the universe must be flat. In other words, there is a critical value of (ρ) that says if we measure (H), and know that the actual (ρ) is equal to that critical value, we know that the spatial value of the geometry of the universe must be Euclidean, flat, with no curvature.

This is not to necessarily say that we have that (ρ), but that is "a" density that we can define using the Friedmannn equation. So this is very convenient for astronomers, to measure the (ρ) that we see, in units of how much density you would need to make the universe flat, the so-called critical density.

It turns out that the ordinary matter we see in the universe, which we'll eventually show is limited very strongly by Big Bang nucleosynthesis and the CMB, and what right now we're inferring from the matter we actually see, is about 5% of that critical density. Ordinary hydrogen atoms and other forms of stuff in the periodic table, makes up about 5% of what you would need to make the universe spatially flat.

So the other stuff in the universe, the dark matter that we see evidence for in clusters of galaxies, then makes up about 25% of the critical density, which is about five times as much as the ordinary matter. So that's a very interesting result, because 5% + 25% = 30%. We see in matter, both ordinary and dark, about 30% of what you need to make the universe spatially flat, about 30% of the critical density.

The reason why that's an interesting number, is that 30% is close to 100%, yet it's not equal to it. So this number could have been anything, like one billionth of 1%, or several trillion percent! It could have been any number, yet it's 30%, which is pretty close to being 100%.

That makes us suspicious. So 10-20 years ago, talking to most cosmologists, they would have said, I bet that we just haven't found all the matter yet. Once we go and do better survey's of the universe, we'll bring that 30% all the way up to 100% and be much more aesthetically pleasing to have exactly the critical density, than if we had only 30% of it."

In the back of their minds was one other fact, which is that this 30% is a number which is not a constant. It changes with time as the universe expands. So the energy density changes in time in a very specific way, in a matter dominated universe, but the critical density also changes, and they change with respect to each other.

So if it's the critical density that we need, and if we only have 30% today of it, then in the past we had a much closer value to the critical density. Things were very close to being spatially flat. So if we really lived in a universe that had 30% of the critical density and nothing else, we would be right in the middle of a transition regime from a spatially flat universe, where the curvature was negligible and you couldn't measure it, to a universe that was highly spatially curved, and the density would be going from almost the critical density and swooping down to almost zero percent of it.

That's very strange to find us living today, in some important part of the universe's history. For a long time, it was just thought that we don't have evidence that we don't exactly have a good measure of the total amount of matter in the universe. Less than 10 years ago of course, in 1998, the true answer was revealed. The answer is that there is stuff out there, that is not matter. It's dark energy, that makes up almost precisely the 70% that we need to make the universe spatially flat. We do have the critical density in the universe, yet most of it is not matter, but something even more mysterious.

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