PHYSICS 107. Lecture 27 What s Next?

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1 PHYSICS 107 Lecture 27 What s Next? The origin of the elements Apart from the expansion of the universe and the cosmic microwave background radiation, the Big Bang theory makes another important set of predictions: the abundance of the elements. There has been a long program of research in astronomy to figure out what atoms are actually out there, and how many of each kind of atom there is. In the early universe the speeds of the particles are so fast and the densities are so high that nuclear reactions are happening very often. This enables nuclei to be built up from protons and neutrons. This happens at a temperature of about K. This is when the universe is about 1 second old! Here is a sample of the most important reactions that lead to the production of H (which of course is just a proton), 2 H, which is a bound state of a proton and neutron), 3 H (a proton and 2 neutrons this doesn t make it to the present days because it has a half-life of only yrs), 3 He ( 2 protons and a neutron, but rare) and finally 4 He (2 protons and 2 neutrons). p + n d + γ d + d 3 He + n 3 H + p 3 H + d 4 He + n p + d 3 He + γ

2 n + d 3 H + γ p + 3 H 4 He + γ n + 3 He + γ d + d 4 He + γ 3 He + 4 He 7 Li So there is also a tiny amount of 7 Li produced in the first few seconds. Heavier elements are not produced in the Big Bang because at mass numbers A = 5 and A = 8 there are no stable nuclei, so when those nuclei are produced they break apart immediately and this prevents heavier elements from forming. We are able to calculate the abundances of all these light elements very accurately. The computer calculations are very similar to the very well-developed science of chemical reactions. There is one very important prediction that comes out: the universe should be about 92% regular hydrogen ( 1 H) atoms and 8% 4 He atoms (by number), which is about 74% and 25% (by mass). This turns out to be a very accurate prediction. In addition, deuterium is present at the level of about 27 parts per million, again in excellent agreement with the Big Bang theory. Everything else should be much more rare than hydrogen and helium, and they are. These three predictions: the expansion of the universe, the cosmic background radiation, and the abundance of the light elements, are the 3 main predictions of the Big Bang theory, and all have been verified in detail. The other heavier elements have been made in stars and supernova explosions much later in the age of the universe. The heavier elements tend to clump together to make planets, so they are much more prevalent on earth than they are in the

3 universe as a whole. Predicting all the elemental abundances is a very complicated and ongoing field of research, but there are no really big mysteries remaining in it. The Future Now run to the final question. What's going to happen? Does the universe expand forever? Does it come to a steady state? Does it fall back on itself? We can formulate this question a little more precisely by making a plot of the radius of the universe a(t), again using the word radius in quotation marks. If a(t) just goes on increasing forever then indeed the universe will continue to expand, and we will get further and further away from all the other galaxies forever. But there is also the possibility that a(t) will peak and then start to decrease, perhaps even going back to zero at some stage, a big crunch instead of a big bang. It's just exactly these two possibilities that are present in the solutions of Einstein's gravitational equations for the evolution of the universe. The solutions are named after their discoverer Alexandre Friedman. (Einstein wrote down the equations, but he did not find all the solutions.) What Friedman showed was that the scenario that ultimately plays out depends on the density of the universe, that is, the energy per cubic centimeter. If this energy density is high enough then the galaxies and other matter are attracting each other sufficiently to stop the expansion, and turn it back around. But if there is not enough energy density in the universe then the expansion will indeed go on forever. It's much like the problem of the escape velocity for a rocket. If we shoot it up fast enough then it will escape the Earth's pull and fly off into space and never come back. But if we don't give enough of a push it will fall back to earth. It depends on the speed it is going. These two possibilities are connected with the curvature of the space in which we find ourselves. The general theory of relativity predicts that space can actually be curved, in the same sense that the surface of the earth is. If you think of drawing a triangle on the surface of the earth with two vertices at the equator and one at the North Pole, you'll see that the sum of the three angles is greater than 180. This is called positive curvature. It can also happen that the sum of the three angles is less than 180. This is called negative curvature. Flat space is a third alternative in

4 which the sum of the angles is always 180. There is a nice picture of these triangles on two-dimensional surfaces in the book. Of course the real universe is three-dimensional, which unfortunately makes the geometry very hard to draw or to visualize. Fascinatingly, the shape of the universe is also connected to the expansion. If the curvature is flat or negative the universe must expand forever, according to the gravity equations. It's only possible for the expansion of the universe to stop and then start shrinking if the curvature is positive. These alternatives are shown in the accompanying figure. Actually, the figure is plotted in terms of the relative size of the universe, with units. You can think of the vertical axis as the distance to the nearest galaxy. Furthermore, these alternatives have a precise connection with the density of the universe. There is a critical value of the density, given by the equation role critical equals ρ crit = 3 H 2 / 8 π G. This is only about g/ cm 3, which is only about 6 H atoms per cubic meter. (But remember there is a lot of space between stars and galaxies.) If the density is greater than this value, then the universe should be closed and the expansion will eventually stop. If it's less than the critical value than the curvature is negative and the universe expands forever. If

5 the density is exactly equal to the critical density, then the universe is flat and again it will expand forever. Longer Distances The way to investigate the curvature is to look for changes in Hubble's constant H as a function of time. If H is getting bigger, then the expansion is accelerating, while if it is getting smaller, then the expansion is decelerating. We can check this by looking out at more and more distant objects, since that is like looking backward in time. For increasingly distant objects, the red shift z gets bigger and bigger. They also get fainter and fainter, but plotting the redshift versus the brightness for very distant objects is the key to understanding if the expansion is speeding up or slowing down. Starting in the 1990s, this became possible. The idea was to look at the red shift of supernovas which are very bright explosions of stars. It turned out that the intrinsic brightness of so-called type Ia supernovas is very predictable, which means we have a good way of telling how far away they are. This means we can plot the redshift as a function of how far away an object is. I won't go into the details but suffice it to say that the apparent brightness of a supernova does not go down as fast as one would expect as a function of the distance as measured by the red shift z. The curve of brightness versus red shift can be used to settle the question of the shape of the universe, and it appears, to a very good approximation, to be flat. This means both that ρ = ρ crit and that the universe will expand forever; not only that but it appears from these observations that the expansion is actually accelerating! The figure plots the brightness (which astronomers refer to as the magnitude, or mag for short) versus the redshift parameter z. Each point represents a single supernova. As z gets bigger, the supernovas are further and further away, but they do not get fainter as fast as one would expect. This is the evidence for the acceleration of the expansion of the universe.

6 The discovery of the acceleration came as a huge surprise, though the possibility was always there in the equation for the expansion of the universe. It requires a form of matter or energy that exerts a kind of negative pressure, pushing the galaxies apart much faster than one would get from an expansion that is counteracted only by ordinary matter, which always exerts a positive pressure. No one expected that such a form of matter should exist, since there is no evidence for

7 it in other observations. For the same reason it s not even clear that we should call it matter all we can say is that it is some kind of energy and we can t see it anywhere else but in the expansion. So it goes under the name of dark energy. The shape of the brightness versus redshift curve has now been investigated in such detail that we can use it to determine the density of ordinary matter that exerts a positive pressure, and also to determine the density of this other kind of matter that exerts a negative pressure the dark energy. Because the universe is flat the actual total density of matter must be equal to the critical density ρ crit, as we mentioned above. Breaking this down into ordinary (positive pressure) matter and dark energy, it turns out that the amount of ordinary matter is about 32% of the total density and the dark energy is 68% of the total density. This is not good because the actual matter that we see in the universe is only about 4.6% of the total density ρ crit. Dark Matter This gave rise to the hypothesis that there must be other matter, so-called dark matter that we just can't see, but it's somewhere out there in the sky. This must be stuff in addition to the particles in the standard model (unless they are combined in some way that we don t understand at all) because it certainly cannot have electric charge. Electric charge necessarily leads to electromagnetic radiation, and it's exactly that that we don't see from this dark matter. It certainly feels the gravitational interaction because that's what is contributing to the red shift curve. There is now a lot of independent evidence for the existence of dark matter, all of which comes from its gravitational effects. The first evidence is in the speeds of rotations of galaxies. The outer reaches of galaxies tend to rotate much faster than we would expect based on the visible matter, and the additional mass provided by the dark matter explains this commonly observed phenomenon in observations of galaxies. Another effect that is now ascribed to dark matter is the prevalence and strength of gravitational lensing. All matter bends the paths of light in its vicinity which causes a kind of focusing effect when light from a distant galaxy passes through a region of high mass on its way towards us. The strength of this lensing effect is much greater than one would get if only the visible matter was causing. The pattern of anisotropy in the cosmic background radiation also supports the

8 presence of dark matter. Finally it appears that dark matter plays a very important role in the formation of galaxies. Current models of galaxy formation are in pretty good agreement with what we see looking out into the sky, but only if dark matter is there to help things out. If there were no dark matter it would take much longer for galaxies to form, and the history of stars and galaxies would have been quite different. So we are pretty confident these days of the existence of dark matter and of the amount of it. It's about 27% of the total energy density in the universe. However we still have almost no idea what it is. Dark Energy That leaves us with 68% of the universe coming from the amazing and strange dark energy. It's dark because we do not see it anywhere in the universe. It seems to have no function other than to accelerate the expansion of the universe. It doesn't seem to clump together with other matter like dark matter does. So far, there are not even really any serious proposals for trying to determine the nature of dark energy. Is it some kind of other particle? Does it have something to do with quantum tunneling? Could it be particles going in and out of existence, providing a kind of background energy that so far we just don't know how to detect? Science is a continual process of expanding the known into the unknown, always trying to enlarge the area so we understand, and spread the boundaries of knowledge outwards. But that means that there's always a boundary between the known and the unknown. So that's where we are now at the end of our course: standing at that boundary looking out at a mystery.

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