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**Introduction to Astrophysics**

Lecture 17: Cosmology: the expansion of the Universe

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Cosmology Cosmology is the study of the Universe as a whole. It attempts to answer a series of all-encompassing questions: What are the properties of the present Universe? What does the Universe contain? What is the future destiny of the Universe? How was the Universe created in the first place?

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**The Cosmological Principle**

“There are no preferred observers in the Universe.” The cosmological principle implies that galaxies should, on average, be distributed uniformly within the Universe. The Universe should have a constant density at any given time. The Cosmological Principle is an idealization. On a local scale different locations in the solar system are clearly different; you’d rather be on the surface of the Earth than in the centre of the Sun. It is an approximation which is believed to be true on large scales.

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**Distance units reminder**

The precise choice of distance unit depends on the application. For stellar physics a parsec (equal to about three light years) is a useful measure as the nearest stars are about a parsec away. For properties of a galaxy, a parsec is too small a number and we use kiloparsecs. We are about 8 kiloparsecs from the galactic centre. If we talk about populations of galaxies, such as the separation between them, we need an even bigger unit, the megaparsec (equals a million parsecs). This is a good unit because the typical separattion between nearby galaxies is about a megaparsec. In cosmology it is sometimes necessary to go one further and talk of gigaparsecs, equal to a billion parsecs.

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Galaxy motions At the start of the 20th century, the new technique of spectroscopy, allied with the large telescopes which had begun to become available, enabled observers to use the shifting of spectral lines to measure the velocities of galaxies. This was first done by Vesto Slipher in He measured the velocity of the Andromeda galaxy (M31), and found it moving towards us at 300 kilometres per second.

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**Spectrum of a very distant galaxy (redshift 3.511).**

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Hubble’s Law Andromeda turned out to be unusual in coming towards us. Over the next 20 years Slipher measured spectra of 40 more galaxies, and found that the vast majority were receding from us. Edwin Hubble, working with Milton Humason, was able to measure many more spectra. He discovered what we now know as Hubble’s Law. Edwin Powell Hubble

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Hubble’s Law What Hubble discovered was that the velocity of a galaxy was proportional to its distance from us: v = H d where H is a constant, now known as Hubble’s constant.

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**Hubble’s Law What does it mean?**

1) It certainly does mean that galaxies are currently moving apart from one another. Our Universe is expanding! 2) It almost certainly means that the Universe has a finite age, and expanded to its present size from a highly dense initial state, sometimes called the Big Bang. 3) It does not mean that there is a centre to the “explosion”.

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Hubble’s Law Hubble’s Law has just the right form that every observer sees all galaxies receding away such that the Hubble Law is satisfied.

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Hubble’s Constant Hubble’s Law states that v = H d. The proportionality constant is Hubble’s constant, and its value tells us how fast the Universe is expanding. But what is that value?

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**H = v/d Hubble’s Constant**

Ever since Hubble’s first observations, attempts have been made to measure the Hubble constant. It has been a seventy year quest which is perhaps only now beginning to reach a close. H = v/d Typical velocities are measured in kilometres per second. Typical galaxy separations are measured in megaparsecs So H should be measured in kilometres per second per megaparsec.

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**Hubble’s Constant H = 500 km s -1 Mpc -1**

Hubble’s original measurement gave a Hubble constant of H = 500 km s -1 Mpc -1 That is, a galaxy one megaparsec away is expected to be receding at 500 km s-1 Mpc-1. We now know that this is far too high, because Hubble drastically underestimated the distances to his galaxies.

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Present attempts The correct answer is now believed to be between 50 and 100 km s-1 Mpc-1, though there is still controversy as to its exact value. The highest profile project is the Hubble Telescope Key Project on the Hubble constant, led by Wendy Freedman. They are settling on a value around 70 km s-1 Mpc-1. It may however be some time before the disagreements are finally settled.

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**What governs the expansion of the Universe?**

The main force that determines the evolution of the Universe is gravity. In particular, gravitational attraction acts in order to slow down the expansion of the Universe. The extent to which gravity slows down the expansion depends on the amount and properties of material in the Universe providing the gravitational attraction.

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Three possible fates Before thinking about the Universe, let’s try a simpler problem of throwing a rock from the surface of the moon. If you throw a rock upwards, one of three things happens: You throw at less than the escape velocity (2.38 km s-1). The rock goes up and comes back down. You throw faster than the escape velocity The rock flies off into interstellar space, eventually at a fixed velocity. You throw at exactly the escape velocity The rock flies away forever, but gets slower and slower as it does so.

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Now the Universe ... Exactly the same three possibilities exist for the simplest models of the Universe. Assuming gravity is the only important influence, gravity will cause the expansion to slow down. Whether it is able to slow it to a halt depends how strong the gravitational force is. The different possibilities were first discussed by the Russian mathematician Alexandre Friedmann in 1922, and later independently by Belgian priest Georges Lemaitre. Alexandre Friedmann

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**Three types of Universe**

1. Open Universe This is the case where the gravitational attraction is not enough to stop the expansion. The Universe expands forever. This situation happens if the density of material in the Universe is low, as then there is less gravitational attraction.

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**Three types of Universe**

2. Closed Universe In the high-density case, there is enough gravitational attraction to halt the expansion. Collapse is then inevitable.

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**Three types of Universe**

3. Critical Universe If the density lies exactly on the dividing line, then the Universe expands forever, but the expansion becomes slower and slower. If the density of matter in the Universe is at this level, we say that we have a critical density.

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**Three types of Universe**

Closed Critical Open Size Time

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**What Universe do we live in?**

One of the key goals of cosmology is to decide which type of Universe we live in. This requires determining the density of the Universe. It has long been known that the density is within an order of magnitude of the critical density, just from adding up all the visible material Given that the answer could have been anything, that was taken as strong indication that the Universe had the critical density.

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But ... Nowadays doubt has been cast on whether any of the standard choices is able to describe our Universe. In 1998, observations of distant supernovae suggested that the Universe is accelerating! Since gravitational attraction will inevitably slow the expansion, none of the models will be capable of explaining that.

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Cosmology 2005 The currently-favoured cosmological model does not rely on gravity alone. There is also a repulsive force which drives everything apart, and which currently is more important than gravity. This repulsive force is said to be caused by a cosmological constant, which, loosely speaking, means the energy associated with empty space. And if you know what that means you should tell someone, because no-one else does.

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**The destiny of the Universe**

It now appears that the Universe has quite a bit less than a critical density of material – perhaps about one third. On its own, that would imply that gravity is not able to stop the expansion. The extra repulsion from the cosmological constant makes recollapse even less likely. According to our best current understanding, therefore, the Universe will survive forever.

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The course quiz! Takes place during the class on Friday 2nd December. It will start promptly at 9am. If you arrive late you lose that time. There will be 40 multiple choice questions and you will have 40 minutes to complete them. The quiz contributes 60% of the total assessment for this course. The material covered will be up to and including this lecture. The material in example sheets is also part of the syllabus.

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