To talk about physical cosmology, let us first define what cosmology means and what it meant to humans in ancient times. Cosmology means the description of our universe as a whole, its origin and its fate. If I talk about the "physical cosmology" I deliberately restrict myself to talk only about the visible (or observable) universe. This can be quite a difference. Now we force ourselves to believe (i.e. argue with) only what we see!! However, what we see, can itself mean different things. In modern science, what we see, mean what we can measure or detect with any of our scientific apparatus.

You probably see where this leads to: Over the course of history the observable universe has tremendously expanded!! This experience alone should make us feel humble or not? If we compare what humans in ancient Greece knew as the universe and what we know now, we should acknowledge that in 100 years from now our observable universe may look somewhat different (using an understatement here). You see that this experience also makes it quite understandable that an overarching cosmology developed which tried to put this observable universe into a context by

either claiming religious revelation to give a picture

or by theorizing what our observations may mean.

In ancient times these two ways were not always recognizable as separate paths to knowledge. However, depending on the culture from which we have the records we can more or less clearly distinguish between the two. This introduction should show what I would like to emphasize in my brief overview of physical cosmology:

the key observations and we get them

and the models to describe the observations

In particular, we can immediately see how in cosmology there had to be a number of paradigm shifts. The expanding observations definitely invited them. However, there is the other side of us which tends to hold us back, because it may be so comforting to stay with the old picture. To understand modern cosmology and where we might be with respect to further paradigm shifts we have to briefly talk about the most important earlier ones.

Let's start with the old Greeks: At that time the visible universe consisted of the Earth up to the horizon and the sky above. This led to a model with a flat Earth and the sky like a giant tent above the Earth. You can easily see how our simple experience may have contributed to this picture. The entire universe (cosmos) also included non-visible things such as heaven (beyond the sky) and the underworld (below Earth). However, this is only one possible analogy, and I don't want to dwell on it farther here. This belongs to a different realm. Let us for some time just keep Heaven and Earth, and I will come back to it with the second paradigm shift. What I really want to study now is: How did this paradigm (flat Earth) shift to a spherical Earth? If you think about a round Earth (and for a short while forget about your knowledge of gravity), what does it feel like to stand on this round ball? Does it seem to make sense? This is the material the inertia is made from which tries to keep us in line with old paradigms.

There were several key observations:

1) Lunar eclipse: round shadow of the Earth; here is already an interpretation involved in the observation itself!! So we have to be careful. (Aristarch of Samos)

2) Stars are at different heights in Greece, northern Europe and Egypt; a ship emerges from the ocean at a distance with the mast and sail first (Aristotle)

3) Eratosthenes used the effects on the sun to determine the size of the Earth. In zenith at noon at summer solstice in Syene (Assuan), while he could measure a shadow in Alexandria (800 km farther north).

Which of the 3 reasons is the most compelling one? Let us try to shoot holes into each reason and see what happens.

Now we do not only have a new paradigm (which by the way was not unanimously adopted by everybody), but we also have a size with which we can start to measure the universe: This is the second important point here, namely get a sense for distances and sizes in the universe.

Now the paradigm was:

• Earth round and in the center

• all other objects are in Heaven and circle around the Earth (and the point is they are on circles, because Heaven is supposed to be perfect)

This scheme worked for the stars, the sun and the moon. However, the planets seemed to defy the simple picture. They wandered around in loops and went back and forth. That is why they are called planets (in Greek: wanderers). But instead of using this observation as indication for trouble with the paradigm, great thinkers tried to squeeze the observation into the existing framework. This is by the way an interesting lesson about what happens, if you try to do this: the model becomes more complicated than warranted by the observations. This criterion on models is known as "Occam's razor" after a medieval philosopher. We try to cut out unnecessary assumptions.

Ptolemy perfected the model along the old paradigm with small circles on big circles. Thus the universe looked like a giant clock with complicated gears. (Explain epicycles, if needed). In addition, Venus and Mercury had to be artificially restricted to staying close to the Sun.

-> Sun larger than Earth

-> complicated model

Already Aristarch and then finally Copernicus put the Sun into the center. For Copernicus the main argument was that the Sun was more important, and "God would have put the Sun into the center".

Pros and Cons (Table)

Galileo brought observations into the discussion:

• Jupiter's moons: mini solar system

• phases of Venus: experimentum crucis

Copernicus also brought us a gift: His model contained the method to determine distances of the planets from the sun. Let us explore this method briefly:

Venus, Mars

Now we know the (relative) distances of all planets, if we are able to measure the distance of the sun from the Earth. This task was already accomplished by Hipparchos. (Use the size of the Earth's shadow on the moon and get the distance of the moon. Then measure the angle between the sun and the moon at exactly half moon to get how much farther the sun is from the Earth.)

However, there were 2 important scientific problems left for the Copernican model, and these were pointed at by Tycho Brahe:

1) Copernicus's model was not more accurate than Ptolemy's; Copernicus had to add epicycles to cope with this challenge! So Occam's razor applied also here.

Kepler: Using Tycho's exact data of Mars, he showed that

• the orbits are ellipses with the sun at one of the foci 1st

Kepler's effort led to a beautiful harmonic geometrical model of the universe. Everything seemed to fit within geometrical reasoning. However, there was no reasoning yet what the driving action behind all these geometrically confined motions might be. Kepler came awfully close by guessing that there was some driving force in the sun which decreased with distance (just from his 2nd and 3rd law).

Only Newton made the bold step towards reasoning with forces. In order to do so he had to abandon Aristotelian physics. (Newton: gravity as explanation) Let me step out of this historic discourse at this point and go on with the geometric reasoning to finish our idea of distances and sizes in the universe. We will come back later to the "physical" reasoning.

2) More importantly Tycho pointed out that the stars did not show any parallax.

Explain parallax;

Bessel in 1838 measured the first parallax of a star: 0.7" of an arc!!!

Brahe reached an amazing accuracy: 0.1 degree

small angle: 0.1 degree: 0.8 cm from 5 m (Dime)

No parallax observed! Closest star 0.7'' -> We need 500 times better accuracy!!! 0.015 mm seen from the rear of the class

Where is the closest star in our solar system model? In San Francisco!! One would have to measure the size of this class as seen from San Francisco. This was an enormous step which increased the known universe by many orders of magnitude!! The method gives us a more practical distance unit:

1 Parsec = distance from which 1 AU (distance of Earth from Sun) is seen as 1 arcsec. This is also equivalent to: 1 Parsec = 3.26 light years.

a) Geometric methods: We can measure parallaxes reliably to Å 0.02". So this method works up to Å 50 Parsec or 150 LY. The European Space Agency (ESA) has sponsored one satellite to improve this situation: Hipparchos

b) Spectroscopic methods: Standard candles. It was found by observation that we can use stars as "standard candles" to determine their distance. If a lamp (candle) has a certain luminosity the light intensity we measure decreases with the square of the distance

If we know L and measure f, we can determine the distance r.

We observe stars with different colors (Sun: yellow; Betelgeuze: red; Rigel: white/blueish). What does this mean? If turn on a heater element, it starts with red, then getting hotter it turns yellow, white -> blue. Color is a function of temperature. Taking the light spectrum we can exactly determine the temperature of a hot opaque object, such as stars. We organize the color of stars according to a letter sequence from hot to cool:

Oh, Be A Fine Girl/Guy Kiss Me (Right Now, Smack)

As this is the main effect which determines their luminosity stars are organized on one line in a Color - Luminosity diagram (the so called Hertzsprung-Russell diagram). Measuring the color we know the luminosity and thus can determine the distance.

This method gives us distances to several 10s of kPc.

Using the spectroscopic method the first attempt was made to map out our "universe", as it was thought at that time. Already Herschel had counted stars on the sky (without knowing their distance) in the 17th century. He came to the conclusion that we live in the center of a disk-like assembly of stars, our Milky Way galaxy. The band across the sky told us of the disk structure, but there was the impression of being in the center again (which we seemed to had got rid of since Copernicus). At the end of last century Kapteyn counted the stars again and added distance determination. Again the same picture: in the center of a disk, the radius Å 15,000 LY. This picture held until Å 1920.

Shapley showed that we are again not in the center of everything, this time of our Milky Way. What had fooled observers was the interstellar gas and dust, which acts like fog. Imagine standing in a street with streetlights in fog. Where do you might think you are with respect to the ends of the street, if you don't know anything else?

Shapley counted Globular clusters of stars in the sky and measured their distance. They turned out to be more than 20 kPc away and center around a point far from the sun (Å 20 kPc towards Sagittarius). He used gigantic standard candles to come to his conclusion: Cepheid variable stars. This is a special class of stars, which are closer to the end of their lives, which are not stable, they contract and expand. When they are larger, they are cooler and vice versa, i.e. they emit less light when large. These stars are among the most luminous on the H-R diagram and thus can be seen at large distances (up to 10's of millions of LY). What makes them standard candles is the fact that their pulse period depends on their size and thus on their luminosity. More luminous stars are slower, like a longer pendulum is swinging slower, or a larger bell has a lower pitch meaning a lower frequency or longer period of the sound wave. This was found by Henrietta Leavitt early 1900 by plotting L and P for Cepheids in the Large Magellanic cloud, thus assuming that they are approx. at the same distance. By simply measuring the pulse period of these stars we know their luminosity from cross-calibration with the other methods.

We see that the distance get less and less accurate the farther we go, simply from the fact that each new method has to build on the one which does not reach far enough. Therefore, the errors will tend to stack up!!The last lecture left us with a known universe which only held our Milky Way itself. This was the accepted view until 1920, when a great scientific debate was fought between Shapley and Curtis. Shapley maintained there is only our Milky Way and all the other milky patches in the sky belonged to it, while Curtis fought for independent island universes (galaxies) beyond the realm of the Milky Way. (Debate at the 75th anniversary at the Smithsonian to commemorate) The debate was finally settled by Hubble, who used the Cepheid method, which was successfully used by Shapley (irony: this method defeated his ideas) earlier to show that the solar system is not in the center of the Milky Way. Hubble found that the Andromeda galaxy and other such clusters clearly had to be beyond the reaches of the Milky Way. This was another great paradigm shift: It opened the universe way beyond the Milky Way and made the M.W. just one out of zillions of galaxies - another humbling experience.

Starting from the parallax measurement which can be performed very accurately, we have to go to several layers of different methods. Each method has to be calibrated by using distances from a method which only works closer to home. We see that the distances get less and less accurate the farther we go, simply from the fact that each new method has to build on the one which does not reach far enough. Therefore, the errors will tend to stack up!! This a haunting experience even today, and every opportunity to make the error bars narrower is sought. This is also the background of a debate about size and age of the universe, triggered by recent observations with the Hubble space telescope. (Eicher, 1994)

It was Hubble who detected another breathtaking truth about the galaxies: they seem to flee us, with speeds ever increasing the farther away they are. He used the Cepheids to get the distance. To determine the speed of the galaxies he used the Doppler effect of spectral lines. He discovered a relation which was named after him:

v = H*d with H being the Hubble constant

This so-called redshift is the final cornerstone of the distance ladder, it reaches as far as we can take spectra of galaxy light. So it can be used itself again as a method for distance determination. This method has recently been employed by M. Geller and J. Huchra at the Harvard Smithsonian Institution to map the universe. The result of this mapping is a distribution of the galaxies in the universe which is by far not uniform, they are rather found in large groups. Structures such as the "Great Wall" of galaxies were identified, and the universe as a whole looks more like - foam as produced by soap bubbles. The galaxies are found along the sheets of the bubbles with huge empty voids between them.

Now let's turn to a few different aspects of the galaxy flight:

1) What does it mean, if everywhere around us the galaxies are fleeing at a larger speed, the farther away they are from us? Are we in the center of an explosion? - Certainly not! The view is the same from any one galaxy in the universe. Actually the galaxies behave like the raisins in a rising yeast dough. This picture is much more what the universe is like: The entire space is expanding and taking all objects with it. The objects are not racing through space!!!

Typical values of the Hubble const. are: H = 50 - 100 km/sec per MPc. This leads to ages: 50 -> 20 Billion years

100 -> 10 Billion years

(simple estimate: 100 km/sec per 3.3 MLY; to flee at speed of light * 3000 -> 10000 MLY thus we are looking for how long it took light to cross the space from that distance to us, i.e. 10000 MY or 10 Billion years).

Now physics tells us: there is a beginning of the universe, even a beginning of time and space, since before that very instant there was nothing, literally nothing, which we can grasp with our physical senses.

Let us take another look at our result: We are talking about distances. What is the largest distance from which we can see a galaxy? - That distance at which the galaxies flee at c (the speed of light). Beyond this point there is no way that we will be able to see any galaxy. Thus we get a natural boundary of the observable universe, and this is for the first time a boundary which cannot be extended by physical methods. However, we should make the distinction that we are talking about the observable universe and not the universe.

Hubble's result also solved a mystery which was pondered by the German physician and amateur astronomer Olbers in the last century, known as Olbers' Paradox. He wondered what an infinite universe would look like

In an infinite universe our sky would always be as bright as the surface of the sun! So our universe may still be infinite in size, but we cannot see far enough back in time. Our observable universe is finite.

Hubble had a very hard time selling his new model. The reason: his universe was far too young.

The distance ladder was off by an order of magnitude when Hubble compiled his results. With H Å 500 km/sec per MPc his universe would have been younger than 2 Billion years, younger than the Earth and younger than the sun. Better observations have led to a more consistent picture today. However, the debate goes on in a very fierce way. A Hubble constant close to 100 km/sec/MPc presents a universe which would still be younger than the oldest known stars, the ones in globular clusters. Although the determination of the speed of the galaxies with the Doppler effect is fairly accurate, the distance measurements have still large error bars. And this is a point of emphasis with the Hubble space telescope.

Another point may be the age of the stars. How do we know that? We can use the H-R diagrams of star clusters to also determine the age of its star population. Stars burn their main fuel, hydrogen into helium, on the main sequence. The difference between stars with different temperature and luminosity is their mass, i.e. their amount of fuel. The luminosity or energy output of massive stars is much larger than that of small stars

The rich are squandering, while the poor are skimping. Thus the luminous stars die long before the small ones. From the end point of the main sequence we find the age of the star population; these are the stars just at the end of their main fuel supply, and provides us with an excellent estimate of their age. However, also here some uncertainties of the modeling enter the results. Anyway 10 Billion years would indeed be too young!

Such difficulties has led some astronomers to thinking about alternative models: A steady state universe, as proposed by Bondi and Hoyle. To make it steady state during the observed expansion the continuous creation of new material was invoked. In addition to using an ad hoc assumption, this model faced several obstacles:

For example, there is indeed an evolution of galaxies observed with more distant galaxies appearing younger, or the quasars as the infant galaxies being at the greatest distances. This would not fit into a continuous creation of new matter and new galaxies everywhere. We will see a few more blows against this model as we go along.

Another question arises from Hubble's new view of the universe: will it expand forever? With all the galaxies there is a lot of mass in the universe. All this mass is connected by the universal force of gravitation. What is the consequence? - The Hubble relation needs a deceleration term, i.e. the expansion speed should faster than the linear relation suggests for the oldest and thus farthest objects in the universe. Taken to the extreme, the expansion may be stopped at some time by the force of gravity. This problem is equivalent to the escape velocity of a space-going rocket. Only above a minimum velocity will the rocket leave the planet.

For a more massive planet a faster escape velocity is needed. In the universe all the mass is spread out. We can compute the influence of the matter on a galaxy at the perimeter of a spherical volume ( the influence of the matter outside cancels out):

For a given Hubble constant there is a mass density which makes the universe collapse again after some time. If the density is higher than the critical density the universe will contract and end in a final crunch (closed universe), and if it is lower the universe will expand forever (open universe). The view is the Newtonian universe. We have a more accurate description of the effects of gravity by Einstein. However, the concepts are easier to grasp in Newton's picture, and the main result comes out correctly. In Einstein's picture space is curved by gravity. The closed universe is a hypersphere or analogous to a balloon (Demo: Balloon) (if you travel far enough in one direction, you will finally come back to good old Earth), whereas the open universe is more like hyper-saddle.

The universe on the border line between these 2 states is a flat universe, which just expands asymptotically. Unfortunately the measurements of H and the mass density are still poor, and plots of the Hubble relation do not reveal the deceleration in a way that we can really measure it. Our information does not reach deep enough and is too inaccurate.

So far we have worked with one set of observations: The distance scale together with the Doppler effect. Such a set of observations may hold the final clue of a model, if we can repeat the experiment!! In the case of the universe we face a very special problem: While the model of stars, star clusters and even galaxies can be compared and tested with many examples, there is only one universe, and we may never peak beyond. This is a serious problem for a science which relies on tests by experiment. The only way to test our model in an independent way, is to look for consistency with other independent predictions of the model. This is exactly what improved the confidence in the Big Bang model.

In the 50s Hermann, Alpher and Gamov took Hubble's model further back in time and came to a stunning conclusion: The universe would have had to consist only of light (or energy) in very early times, because in this squeezed state it had to be extremely hot.

This prediction was verified in the mid 60's by Penzias and Wilson of Bell Telephone, when they tried to improve satellite communication. They found a hiss in their antenna which they finally identified as the predicted cosmic background. Slide: Antenna

This observation is so profound - the earliest electromagnetic radiation of the universe - that NASA built an entire satellite to study this radiation

It measured a textbook thermal radiation spectrum

with a slight anisotropy (blueshift - redshift)

This is the first time we have an absolute reference frame of our universe: we are moving with respect to this rest frame of the Big Bang (motion of the Earth, solar system, Milky Way). Other than this anisotropy the radiation is extremely homogeneous, actually almost too homogeneous for our universe. If we remember the huge clumpiness of the universe structure as seen in the bubbles where the galaxies are found on the surface, this seemed in contradiction with the smooth background radiation, because the clumpiness had to come from somewhere. Finally, a very small clumpiness was found

This observation compiled from 2 years of Cobe data saved the Big Bang model from a major overhaul.

The background radiation comes from an age of the universe of 300,000 years. Is there any chance to go even further back in time? In order to get information about this early universe we have to resort to more detailed modeling. The clues we can tap here is the mixture of the elements in the universe, in particular, the very light ones H, He, Li, since they were formed in the beginning of the universe, when it was hot enough for nuclear reactions. We are talking about the cosmic cooking recipe.

However, the missing mass is not the only problem which seems to plague the standard Big Bang model.

- Flatness problem

In the relativistic terms our universe is very close to being flat: one order of magnitude off in density means nothing. In order to get to this condition now (at an age of 10-20 Billion years) it had to start out incredibly accurate (accuracy of 10^-15 at an age of 3 minutes). Consider the following: you want to aim the spaceprobe exactly into the asymptotic escape corridor.

- Horizon problem

We see exactly the same parameters of the universe in all directions, when observing the background radiation. However, if we compute the distance of the 2 opposite regions of space from each other at an age of 300,000 years (the time when the background radiation started to run), there was no prior communication between these regions at speeds slower than the speed of light! I.e. there was no connection and it becomes strange that everything is so homogeneous.

- Matter problem

Finally, there is 1 proton or neutron for every 10⁹ photons in the universe. Originally everything was photons. If they react in a hot environment exactly as many protons as anti-protons would be produced, which finally would cancel each other in collisions. Why is there left over matter after all?

A solution proposed in the 70's by Alan Guth and Andre Linde is the idea of an inflationary universe. Encouraged by the discovery of Salam and Weinberg that the electromagnetic and the weak nuclear force (2 of the total of 4 basic forces in the universe) can be combined to the higher symmetry of the electroweak force at higher energies, a combination even with the strong nuclear force into Grand Unified force is envisioned at even higher energies than we can produce in accelerators. However, this was available in the early universe.

The evolution of the early universe is thought of as a series of symmetry breaking into more separate forces, like the isotropic symmetry of the liquid water is broken into the more constrained symmetry of the ice crystals during the phase transition from liquid to solid. During such phase transitions the latent (melting) energy is freed up and becomes useable. The equivalent of this energy was held responsible by Guth and Linde for the additional push in the original expansion, which they phrased as inflation of the universe. Like the surface of the wrinkled balloon

Demo: balloon

is flattened, the geometry of the universe was made flat, i.e. almost exactly on the edge between open and closed. Everything in the universe was in contact with each other before inflation. We now can see only a tiny fraction of the entire universe (what we know as the observable universe). This of course has to have the same parameters everywhere, because it went through the same process. This solves the horizon problem. Finally, the symmetry breaking itself explains why there is an asymmetry between matter and anti-matter.

This is the point where we stand like Goethe's Faust:

However, let me close this lecture with a few different views on the universe by well-known physicists, which outline the diverse view of the two alternate Anthropic Principles:

"We still believe that the universe should be logical and beautiful;

we have only dropped the word 'God'"

"I would phrase it in a different way: In the past people had insight into a kind of intelligent being (intelligence), which created (structured) the universe, and they have personalized it and named it 'God'"

"God was a mathematician"