4.3 The accelerating universe and the distant future
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1 Discovering Astronomy : Galaxies and Cosmology 46 Figure 55: Alternate histories of the universe, depending on the mean density compared to the critical value. The left hand panel shows the idea graphically. The right hand panel illustrates the idea as a graph.note that all the different histories have the same slope (i.e. expansion rate) today 4.3 The accelerating universe and the distant future Lecture 10 : Cosmic Perspective 22.4 In this final lecture, we look at how the expansion of the universe seems to have evolved, and what the future might be like. First we will look at cosmic dynamics and its connection to the density of the universe; then we look at the ancient accelerating universe and the theory of inflation ; and finally the modern accelerating universe and the distant future. Cosmic Dynamics. What will happen to the expansion rate over time? We would expect that gravity should slow it down. But we don t know what caused the expansion, so maybe there is some other effect that will speed it up? We should be open minded about the change with time, and see what evidence there is. First lets look at the effects of gravity. The critical density. The greater the average density of matter, the greater the deceleration caused by gravity. There is a critical density crit that we can calculate from general relativity. Above this, gravity is strong enough that eventually the expansion stops and the universe recollapses. Below this, the expansion continues forever. In todays terms, the critical value is crit = kg m 3. Note that this applies to the everage density. Within a galaxy, the density is much higher. To get a sensible estimate we have to average over many galaxies and all the gaps in between. The ratio of the actual density to the critical density crit is so important its given a special symbol and referred to as the density parameter: = crit Future histories. If gravity is all that matters, the sketches in Fig. 55 illustrate the three possibilities - recollapse, expand foerever, or just balanced in between. The right hand sketch ilustrates the possibility of an accelerating universe, which we will return to later. If we knew the value of, we would be able to predict how the expansion will change in the future. But it also would allow us to deduce what happened in the past, and as you can see from Fig. 55, it would substantially change our estimate of the age of the universe. Shape of the universe. General Relativity tells us that matter makes space curved. The degree of curvature for the Universe as a whole also depends on the average density of matter, and the critical value is the same as for the dynamic behaviour. If =1, i.e. = crit, then there is no curvature; space is flat and infinite. If > 1 then the curvature closes up, and space is spherical and finite.
2 Discovering Astronomy : Galaxies and Cosmology 47 Figure 56: Left : Alternate spacetime curvatures, depending on the value of the density parameter. Right : Measuring spacetime curvature using the ripples in the CMB. If < 1 then the curvature is negative and space is hyperbolic and finite. These possibilities are sketched in Fig. 56. So how dense IS the universe? We could estimate this in three ways : (i) Count the number of galaxies per unit volume that we see locally, and add up the mass contributions from the stars and gas that we believe to be typical. If we do this, we find i.e. a density that is about 0.3% of the critical value. (ii) Next we can allow for the dark matter we believe is present. As we saw earlier, we think every galaxy has about ten times as much dark matter as stars, and judging by the motions in clusters of galaxies, the total amount of distributed dark matter is probably a hundred times as much as what we see in stars. This suggests that the true density is 0.3. (iii) Next we can calculate the amount of ordinary matter needed to explain the light element abundances from nucleosynthesis in the Big Bang. This gives The fact that this is much less than from method (ii) is why we believe the dark matter is non-baryonic. So it seems that even with all the dark matter, is less then one, suggesting that the universe has hyperbolic curvature, is infinite, and will expand forever... but only just. The density is suspiciously close to the critical value - it could have been a millionth or a million times critical... So what shape IS the universe? The geometry (curvature) of the Universe can be deduced from the angular size of the ripples in the CMB, compared to their expected physical size. Fig. 56 shows the observations. CMB fluctuations have a characteristic scale of about 1 on the sky. We understand the expected physical size quite well, because the flucuations are due to waves casued by gas pressure, which is relatively simple physics. We also know exactly what distance CMB photons are coming from. The calculations then show that the physical and angular sizes match up for a a simple universe in which the universe is very precisely flat, not curved at all. This implies that =1to a high degree of accuracy. How do we reconcile this with our earlier density estimate of =0.3? The contents of the universe. It seems the universe is made of : 0.3% stars 4% ordinary matter 26% dark matter 70% something even weirder than dark matter
3 Discovering Astronomy : Galaxies and Cosmology 48 Figure 57: The isotropy problem. The left hand panel shows the standard universe. In this figure, distance is horizontal, and time goes up. The scale of the axes is set so that a ray of light makes a line of 45. Consider the light from two gas clouds, emitted at the time of formation of the CMB. We can see light from both these clouds, but between the Big Bang and this time, no light ray from one cloud can have reached the other. The right hand panel shows how inflation solves this problem. The two gas clouds actually started out very close to each other, and can easily have been in contact. making 100% of the critical density in total. What matters is not just the density of mass, but of overall mass-energy. So the 70% even weirder stuff is some sort of dark energy. Three problems. In the 1970s, it was recognised that there were three major problems with cosmology as we have sketched it so far. The idea of inflation - an exponential expansion in the very early universe - was proposed by Alan Guth iun 1981 to solve these problems. Problem 1 : flatness. Why is the density so close to being exactly 100% of the critical value? Or, why is the universe flat? (Same question...) is this just a cosmic coincidence or is there a missing ingredient? Problem 2 : isotropy. Why do opposite sides of the sky look much the same in the CMB? Simple calculations of the expanding universe show that patches of sky a few degrees apart should never have been in communication with each other. How did they know to be so similar? The problem is illustrated in Fig. 57. Problem 3 : structure. Why were the initial fluctuations in the very early universe just right for growing into the clusters and galaxies we see today? We already have the general idea that quantum physics predicts some random fluctuations, but how big will they be, and what distribution of sizes will they have - i.e. how many big ones versus how many small ones? Older versions of cosmology had to put in these fluctuations by hand to get the answer right.. Explosive expansion. The problems were all solved in 1981 by Alan Guth who proposed the idea of cosmic inflation. Some versions of Grand Unified Theory (GUT) say that spacetime can have phases rather like the phases of matter (gas, liquid, solid) and that in some phases even empty space has positive energy. Guth s idea was that the very early universe (10 38 sec) went through a phase transition which suddenly put extra energy in and started it expanding. This would be a runaway effect, because the bigger space got, the more energy it released! The effect was an expansion of by a factor of over a period of sec. The inflation ends at another phase transition. The basic idea is illustrated in Fig. 58. So how does this help our three problems? Solving the three problems. The flatness problem is solved by sheer scale. If the universe started closed and spherical, as it expands, it gets harder and harder to distinguish from flat, as illustrated in Fig. 58. The isotropy problem is solved because two regions that we thought were well separated
4 Discovering Astronomy : Galaxies and Cosmology 49 Figure 58: Left: size of universe versus time, contrasting the standard model and the inflation model. Right L Ilustration of how a greatly expanded sphere becomes asympotically flat. in the standard model were actually very close in the pre-expanded inflationary model, so were in contact and could have been very similar. This is shown graphically in Fig. 57. Finally the structure formation problem is solved because the inflation model makes very definite predictions, and they turn out to be just right for what is needed to seed the growth of structure. Tiny random quantum fluctuations in the very early universe get stretched out to much bigger fluctuations, and spread put into a range of sizes. The detailed predictions of the theory match what is required by the structure simulations extremely well. Caveat Emptor? The way that inflation explains the old cosmological problems is very impressive. But to be really sure its correct, we need another independent way of checking whether its right, or a striking prediction that we can test. Another future Nobel prize waiting! Cosmic kinematics today. So it seems likely that in the past the universe went through a very brief but explosive inflation phase, but this ended so that presumably the universe is now coasting, but also presumably decelerating due to mutual gravitational attraction. Previously, we tried to work out how much the universe is decelerating indirectly by (a) estimating the mass in the local universe, and (b) measuring the curvature of the universe. Can we just measure the change in expansion rate with time directly? Astronomers tried this for years but it finally started working in the 1990s. Distant supernovae. You need a standard candle that you can see at very large distances; the apparent brightness then tells you its distance. You can then compare the observed redshift with the redshift you would have expected if Hubble s law v = H 0 D just continued unchanged. Galaxies or quasars are no good as standard candles - they cover a big range of brightness. Supernovae can do the trick, but they are rare. We need to monitor thousands of galaxies repeatedly; every so often you will catch a supernova going off. The first projects that did this massive monitoring came up with a big surprise - see Fig. 59. The supernova results show that Figure 59: Expansion history of the universe as deduced from the supernova results.
5 Discovering Astronomy : Galaxies and Cosmology 50 the universe is not decelerating at all - it is accelerating! Dark energy fuelling. The reason for the acceleration is connected with the dark energy that we identified earlier as being necessary to make the mass-energy add up to 100% of the critical value. Like the vacuum energy associated with inflation, it can drive expansion, overcoming gravity : but this is a component that is only coming into play much later in the life of the universe. The amount of dark energy has changed with cosmic epoch. We are living at a time when it is just starting to take over... We don t really understand dark energy yet, and so we don t know how to predict the future evolution of the universe. It is also possible that multiple universes burst into being in their own inflationary epochs... but we are straying into untestable speculation. The state of cosmology. We end with a summing up of where we have gotten to in our understanding of the universe as a whole. Here are the key points : Big Bang cosmology is one of our most precise and best tested theories. Old cosmology predicted the microwave background, and explains the abundance of the elements, and the the changes in galaxies and quasars, but requires a strange dark matter. New cosmology explains flatness, isotropy, and the growth of structure, but requires a strange dark energy. We now know the parameters of the theory precisely; Big Bang theory is an accurate machine But... we don t know what dark matter and dark energy actually are... This is a very strange state for a theory to be in - so incredibly successful and yet relying on an unsolved puzzle - what are dark matter and dark energy? This is one of the big issues of modern science.
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