Lesson 10

Overview

About Lesson 10

This is the lesson where I am going to try to answer some of the big questions in astronomy about the nature of our universe. In this lesson, we are going to focus on cosmology, which is the study of the structure and evolution of the universe as a whole. There are a lot of questions that many of us want answered about the nature of the universe, and astronomers have come up with answers for many of them. They are not always answers that satisfy us completely, but they are the answers that our observations of nature provide us.

What will we learn in Lesson 10?

By the end of Lesson 10, you should be able to:

  • quantitatively relate the velocity of a galaxy and its distance using Hubble’s Law;
  • describe how Hubble’s Law implies an expanding Universe;
  • describe the evidence for the Big Bang as the origin of the Universe and the methods for estimating the age of the Universe;
  • describe the evidence for substantial amounts of dark matter in the Universe;
  • explain how observations of distant objects reveal the Universe is accelerating as it expands.

What is due for Lesson 10?

Lesson 10 will take us one week to complete.

Please refer to the Calendar in Canvas for specific time frames and due dates.

There are a number of required activities in this lesson. The chart below provides an overview of those activities that must be submitted for Lesson 10. For assignment details, refer to the lesson page noted.

Lesson 10 Requirements
Requirement Submitting your work
Lesson 10 Quiz Your score on this quiz will count towards your overall quiz average.
Discussion Forum: The Big Bang Participate in the Canvas Discussion Forum: "The Big Bang".
Lab 3 You will submit your lab report to a drop box.

Questions?

If you have any questions, please post them to the General Questions and Discussion forum (not email). I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.

Olbers' Paradox

Additional reading from www.astronomynotes.com


There is an old, simple question that can help us to understand a fundamental property of the universe. The question is usually called Olbers' Paradox, (after German astronomer Heinrich W. Olbers), and it can be stated pretty simply:

Why is the night sky dark?

The reason that this question is so important is because its answer can tell us about the distribution of stars and galaxies in the universe.

Consider the possibility that the universe is infinite and that it is filled with luminous objects (stars and the galaxies that contain them). If this is true, then every sight line from the Earth will eventually intersect a bright object. This means that if the universe is infinite and contains an infinite number of bright objects, the night sky will be bright! Since the night sky is dark, this tells us that one of our assumptions about the universe is incorrect. I made a pretty basic illustration of this, shown below:

Schematic of the distribution of stars in an infiniate universe and Olber's Paradox, stars are scattered on the left and grouped to the right
Figure 10.1: Schematic of the distribution of stars in an infinite universe and Olber's Paradox
Credit: Penn State Astronomy & Astrophysics

In the left panel, what is represented is the Earth in a 3D universe with stars arranged randomly around the planet. From one particular vantage point, you can draw sight lines from Earth to every star within your field of view. If the Universe is infinite and filled with stars all at different distances from Earth, then every single sight line should land on a star. So, in the right panel, this is illustrated; you should see in projection a night sky filled with stars. An analogy is standing in the middle of a large forest -- every direction you look, your line of sight should end on a tree, as shown in the image below.

Photo of Biogradska forest in Montenegro with light coming through the trees
Figure 10.2: Photograph of Biogradska forest in Montenegro
Credit: Wikipedia

Let's briefly consider the mathematics of this situation. You know from many discussions previously that every object appears fainter the more distant it is from Earth, and the brightness of that object drops off as 1/d2, or an object twice as far away is 1/4th as bright. If we picture spherical shells surrounding the Earth, though, the number of stars covering the surface area of one particular shell will increase by exactly the same amount as the brightness of the stars on that shell decreased, so the surface brightness, that is, the brightness per unit area on the sky, will be the same for every shell. There is an excellent public domain visualization of this phenomenon in the Wikimedia Commons; it shows the sky randomly filling with more distant, and therefore fainter objects, but since the number of faint objects is so large, the picture of the sky eventually fills with a light of uniform brightness.

This is the source of the paradox. If the universe is infinite and filled with stars, the surface brightness of the night sky should be the same as the Sun's, so the night sky should be as bright as the daytime sky. Even though this is obvious by simply looking at the sky, when you review the image of the Hubble Ultra Deep Field, there is clearly dark sky visible between every galaxy, providing further evidence that every sight line does not end on a luminous object.

Hubble image of the Ultra Deep Field (full size)
Figure 10.3: Hubble Image of the Ultra Deep Field

Based on what you have learned so far, you may have a few questions.

  • Does it matter that we considered stars and not galaxies? No, because the same logic holds for galaxies. If every one of your sight lines ended on a galaxy, the night sky would be bright.
  • Is there enough dust in the Universe to block our sight lines to some stars or galaxies? Yes, but if the Universe was infinite and with an infinite number of stars and galaxies, the light from those objects would heat up the dust causing it to glow brightly enough to light up the night sky.

The solution to the paradox (why is the night sky dark?) could be due to several different possibilities:

  1. The universe is finite, that is, it ends at some point.
  2. The stars run out at large distances.
  3. There hasn't been enough time for the light to reach us from the most distant stars.

We will find out shortly that we can actually estimate the age of our universe. Because the universe is not infinitely old, the answer is number 3 listed above. Since light takes time to reach us, we can see only those objects that are near enough to us that their light has reached us. Curiously enough, the first published solution to Olbers' Paradox is attributed to Edgar Allan Poe. In his essay Eureka, Poe says:

Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy - since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.

While we know the solution today for Olber's Paradox, it took until well into the 20th century for us to truly understand the nature of the Universe well enough to explain the answer to this question. In the rest of this lesson, you will find out how we came to understand the Universe and prove to ourselves the reason the night sky is dark.

Want to learn more?

The Wikipedia Page on Olbers' Paradox has a bit more background information on the history of this question if you are interested in finding out more.

Hubble's Law

Additional reading from www.astronomynotes.com


During his work studying galaxies, Hubble used Cepheid variable stars to measure the distances to a sample of galaxies. Even before the Shapley/Curtis debate and the discovery that spiral nebulae are external galaxies, observations had shown that the vast majority of galaxies had spectral lines redshifted from the laboratory values. If you recall from our work on the Doppler effect, a redshift in a spectral line indicates that the object is moving away from us. In a publication by Hubble in 1929, he showed that if you plot the distance to a galaxy (measured from Cepheid variables) and the velocity of the galaxy (measured by the shift in the spectral lines), the two quantities are directly correlated! See the reproduction of his plot below.

Edwin Hubble's plot of the Velocity-Distance relationship for galaxies, shows a linear relationship
Figure 10.4: Edwin Hubble's plot of the Velocity-Distance relationship for galaxies

Want to learn more?

Read Hubble's original articles! The astronomical community maintains an excellent resource meant primarily for practicing astronomers. It is the SAO/NASA Astrophysics Data System, and you can use it to search the astronomical literature. For example, if you want to find information on every article I have ever published, you can go there and stick my name in the author field. However, for a much more interesting search, you can go there and put in "Hubble, E" in the author field, and it will bring up the listing of Hubble's published works, including the paper in which he published the plot above.

Interpreting these diagrams

On the y-axis, you plot the velocity of the galaxy obtained from the spectrum. On the x-axis, you plot the distance to that galaxy, in this case obtained from Cepheids. If these two quantities (distance and velocity) had nothing to do with each other, then the diagram would look like what we call a "scatter plot." That is, it would appear as a bunch of points randomly placed in different locations. However, it is somewhat apparent in this case that you can draw a straight line through the points. What this means is that as the distance gets bigger, so does the velocity. In algebra class, you learned that the equation for a line that passes through the point (0,0) is:

y=mx

where y = the quantity plotted on the y-axis (velocity), x = the quantity plotted on the x-axis (distance), and m is the slope of the line. For the specific case of this relationship, we usually write the equation this way:

v= H 0 d

H0 is called the Hubble constant. It is the slope of the line that relates the distance of a galaxy to its velocity. If you know H0 and if you can calculate the velocity, v, from the spectrum, then you can use this equation to calculate the distance, d, to that galaxy. Let's quickly review how we measure velocities for objects that are receding from us. The equation that you saw in Lesson 4 for the Doppler shift was:

Δλ/ λ 0 = v r /c

Where Δλ is the difference between the measured wavelength for a line in the spectrum of an object and the wavelength for that same line observed in the spectrum of an object at rest. The other term on the left hand side, λ0, is the wavelength of that line in the spectrum of an object at rest. For objects at large distances from Earth where the distance is determined using Hubble's Law, we do not often refer to their recession velocities (e.g., "that galaxy has a velocity of 14,000 km/sec away from us") or their distances in Mpc (e.g., "that galaxy is 247 Mpc from us"), instead, we simply refer to the object's redshift, z. The definition of z is that it is the left hand side of the Doppler shift equation:

z= Δλ/ λ 0

For example, if you observe a galaxy with an H-alpha line at 680 nm, and you know the rest wavelength for that line is 656.3 nm, then its redshift is:

z= ( 680nm656.3nm )/ 656.3nm =0.036

Hubble's law, which says simply that a galaxy's velocity (or as is sometimes plotted, its redshift) is directly proportional to its distance, also tells us something important about the state of the universe. If the universe is static and unchanging, there should be no correlation between distance and velocity. However, if the universe is expanding, we expect a correlation between distance and velocity. The usual analogy used here is that of an explosion – the fragments of shrapnel produced are moving with a range of velocities, and the most distant objects from the source of the explosion have the largest velocities. Astronomers believe that Hubble's law is a direct consequence of the ongoing expansion of the universe and that the evidence suggests that the universe began in an explosion, which we call the Big Bang.

There are a couple of important caveats that apply to Hubble's Law. They are:

  1. Hubble's Law only works for distant galaxies. For nearby galaxies (in the Local Group), stars inside the Milky Way, and for objects in our Solar System, the relationship between distance and velocity does not hold. The reason for the discrepancy for nearby galaxies is the "peculiar velocity" of the galaxy, that is, its real velocity through space that is unrelated to the expansion. For distant galaxies, their peculiar velocities are small enough that they still lie on or near the line for Hubble's Law. For nearby galaxies, though, their peculiar velocity is larger than their velocity from the expansion, so their peculiar velocity dominates their total velocity, causing them to lie far from the line relating velocity to distance. For example, the galaxy M31 does not even show a redshift; it is blueshifted, showing that its peculiar velocity is pointed towards us, rather than away from us.
  2. Recall the concept of the "lookback time" for an object. For objects at very large distances from us, it is very common to see their distances referred to not in units like parsecs or light years, but in units of time. For example, astronomers will say, "The light from this galaxy was emitted when the universe was 10% of its present age, over 12 billion years ago." We base these descriptions on the redshift of the galaxy and the lookback time.

You can consider Hubble's Law to be the final rung in the distance ladder. If you know Hubble's constant accurately, then you can calculate the distance to any galaxy in the Universe simply by measuring its velocity (which is reasonably easy to do for any galaxy for which you can observe its spectrum). To calibrate Hubble's constant, though, you need to be able to plot the distances for a number of galaxies as obtained using other methods. While that may seem like an easy statement to make, it was an incredibly difficult task to accomplish. For decades, astronomers have argued over the precise value of Hubble's constant. This measurement was, in fact, one of the major reasons for building and launching the Hubble Space Telescope. It spent years observing Cepheid variables in distant galaxies in order to measure Hubble's constant as precisely as possible. The results were reported in 1999. See "Hubble Completes Eight-Year Effort to Measure Expanding Universe."

Note that in Hubble's diagram, above, he has data on galaxies out to 2 Mpc (that is, 2,000,000 parsecs). The diagram produced by the Hubble Key Project team used data on galaxies out to about 23 Mpc.

The Implications of Hubble's Law: An Expanding Universe

Additional reading from www.astronomynotes.com


Like Kepler's Laws, Hubble's Law is an empirical law. Hubble discovered a relationship between two measurable properties of galaxies: their velocities and their distances. Given this relationship, though, it naturally leads to several questions. These questions are:

  • What is the cause of this relationship?
  • Why should more distant galaxies have larger velocities?

On the previous page, we attributed the velocities of galaxies and the relationship between their velocities and distances to an explosion. Because all of the pieces of debris from an explosion originated at the same spot, the more distant ones must be moving faster to have traveled the farthest in the same amount of time. This is an acceptable analogy, but it is not perfect. It does, however, help us understand that the universe must be expanding. Our best interpretation of the relationship discovered by Hubble is that it implies that the space between galaxies is expanding.

Let's study this idea of an expanding Universe in a bit more detail. If all objects are moving outward at a constant speed, the boundaries defined by the outermost objects must be continuously growing. To be more precise about the expansion of the universe, we again resort to analogies. The first is this: picture dots on a very long rubber band. The dots are supposed to represent galaxies. If you pull on the rubber band, the distance between the dots will grow. If the initial distance between each dot is 1 cm (Dot B is 1 cm away from Dot A, Dot C is 2 cm away, and Dot D is 3 cm away) and you pull on the rubber band so that the dots are now 2 cm apart, then from Dot A, Dot B will be 2 cm away, Dot C will be 4 cm away, and Dot D will be 6 cm away. Dot C will have moved twice as far from Dot A in the same amount of time as Dot B did, and Dot D will have moved three times as far from Dot A in the same amount of time as Dot B did. Therefore, from Dot A's point of view, the more distant dots will appear to have moved faster than the closer dots (remember, the velocity of an object is the distance traveled divided by the time it takes to go that distance).  If we were to repeat the previous experiment, but measure the distances between the dots from Dot B's point of view, we would find that Dot B would draw the same conclusion as Dot A. That is, all the dots would appear to be moving away from Dot B, and the farther dots would appear to move faster.

image described in text
Rubber band / dot analogy of the expanding universe.  In an example initial state, galaxies appear as dots along a rubber band.  The blue and yellow dots are equidistant from the point of origin, as are the white and pink dots, albeit in opposite directions.  The orange dot is between the white and blue dot, and closer to the point of origin.  The green dot is between the yellow and pink dot, and farther from the point of origin.
Credit: Penn State Department of Astronomy & Astrophysics
image described in text
Rubber band / dot analogy of the expanding universe.  The universe's expansion, when doubled in size, causes all th dots to appear twice as far as they once were, from the perspective of the point of origin.  This means that the white and pink dots have appeared to move much farther from the point of origin compared to the blue and yellow dots, in opposite directions from the point of origin.  However, taking the perspective of the pink dot, the green dot has not appeared to move much compared to the white dot.
Credit: Penn State Department of Astronomy & Astrophysics

The analogy in the figure above allows us to draw several conclusions about the universe.

  1. The galaxies are not really moving through space away from each other. Instead, what is happening is the space between them is expanding (just like the rubber band expanded, separating the dots fixed to it from each other). As the universe expands, the galaxies get farther from each other, and the apparent velocity will appear to be larger for the more distant galaxies.
  2. The Earth and the Milky Way are not special in seeing that all galaxies appear to be moving away from us. If we were on a different galaxy, we would also see all the other galaxies appear to be moving away from us because of this expansion.

The next two analogies are similar to the rubber band / dot analogy, but we are going to think in more dimensions, since we know that the galaxies are not restricted to be found along a one dimensional line. Instead of a line, picture the dough for raisin bread. Inside the dough, all of the raisins are separated from each other. As the dough rises during baking, all of the raisins will move farther away from each other. Let's say that the size of the dough doubles. The distance between all of the raisins will double, and just like the dots on the rubber band, the more distant raisins will appear to have moved faster. This is represented well in the animated image from the NASA WMAP mission included below.

Animated image showing the rising of raisin bread dough
Figure 10.6: Animated image showing the rising of a loaf of raisin bread dough. This animation contains the same idea as in Figure 10.5, but expanded to three spatial dimensions instead of one.  The raisins in the dough are like the dots on the rubber band or galaxies in the Universe.  As the dough expands, the separation between the raisins increases, just like the separation between galaxies in our Universe.
Credit: NASA / WMAP

Both of the two analogies (rubber band and raisin bread) should allow you to picture that every galaxy (or dot or raisin) will see all other galaxies moving away if the space between them is expanding. We use one more analogy to try to explain the mathematics of the expansion of the universe and to answer another common question that arises in cosmology:

  • Why can't we observe the center of the expansion?

Picture a universe that consists only of the surface of a balloon. All of the galaxies and the stars in the galaxies are fixed onto the surface of the balloon. There is no way for the observers to perceive the region inside the balloon or the region outside the balloon, they are (and light is) constrained to travel only along the surface. In this analogy, as the balloon inflates, the galaxies on the surface of the balloon will move farther away from each other. Just like with the rubber band and raisin analogies, if you measure the distance between the galaxies before and after the inflation of the balloon, you will be able to show that the more distant galaxies will appear to move faster, just like Hubble's Law in our universe (and like the rubber band and raisin loaf experiments). Again, every galaxy will observe the same effect, and no one galaxy is in a special location. If you ask where the center of the expansion is, it is inside the balloon. This means that no location on the surface of the balloon (the universe according to the residents on the surface of the balloon) can be identified as the "center" of the universe.

We use this analogy to answer the question:

  • Where is the center of our universe?

The idea is that we live in a universe with three spatial dimensions that we can perceive, but that there exist "extra" dimensions (maybe one, maybe more than one) that contain the center of the expansion. Just like the two-dimensional beings that inhabit the surface of the balloon universe, we cannot observe the center of our universe. We can tell that it is expanding, but we cannot identify a location in our 3D space that is the center of the expansion.

Until this point, we have been describing the redshift of light as a Doppler shift. However, now that we understand the Universe to be expanding, we need to revise this description. The way we understand the cosmological redshift of galaxies is as follows. Picture a photon emitted by a distant galaxy towards the Earth. That photon has a specific wavelength. However, during the trip between the distant galaxy and Earth, the space between that galaxy and Earth has expanded. The expansion of space causes the wavelength of the photon to stretch, so when it arrives at Earth, it has a longer wavelength than when it left. Mathematically, this behaves exactly as if the photon was Doppler shifted. So, we interpret the galaxies as moving through space away from us. However, the proper interpretation is that the galaxies are at specific positions in space, and the space between them is expanding. An animation illustrating the cosmological redshift using the balloon analogy for the expansion of space is below.

Illustration of cosmological redshift using balloon analogy. In this animation, the wave drawn on the balloon represents the a wave of light with a specific wavelength.  As the balloon expands, the wavelength increases.  We believe this is how light behaves in the Universe. As the Universe expands, the distance between crests of the wave of light also expand, causing the wavelength to increase.  Light with a longer wavelength is redder, so light appears redshifted because of the expansion.
Credit: Penn State Department of Astronomy & Astrophysics

Does this mean that the Solar System is expanding? What about the Milky Way? Will Pluto get farther and farther from the Sun as the Universe expands? The answer is no, and it is a bit difficult to understand exactly why. Consider again a stable Main Sequence star. We discussed how in order for a star to avoid collapse, the outward force of the radiation pressure created by the nuclear fusion in the core balanced the inward pull of gravity. We can consider all objects and systems of objects in the universe subject to the same kind of balance of forces. The expansion of the universe can be thought of as a global force that is pulling on all objects. However, it is only strong on very large scales. At the scale of a galaxy, the gravitational force binding a galaxy together is much stronger than the "expansion force," so the galaxy does not expand. At the scale of the Solar System, the imbalance is even larger, so the gravitational binding of the Solar System easily overwhelms the "expansion force," keeping Pluto's orbital separation from the Sun the same over time.

The Age of the Universe

If we agree that Hubble's Law tells us that the universe is expanding, it also implies that in the past the universe was much smaller than it is today. If we assume that the expansion's apparent velocity (that is, how fast the galaxies appear to be moving apart) has been constant over the history of the universe, we can calculate how long ago the galaxies began their separation. This should tell us the time that the expansion began, which should give us an estimate of the age of the universe.

If the expansion of the universe is happening rapidly, then we expect the universe to be relatively young, because it has taken only a short time for the galaxies to expand to large distances. If, on the other hand, the universal expansion is progressing at a slow speed, then the age of the universe should be relatively old, because it has taken a long time for the galaxies to reach large distances from each other. We know how fast the universe is expanding, because we know the value of Hubble's constant (H0 ). The faster the universe is expanding, the faster the galaxies will appear to be moving away from each other.

You can actually calculate an estimate for the age of the Universe from Hubble's Law. The distance between two galaxies is D. The apparent velocity with which they are separating from each other is v. At some point, the galaxies were touching, and we can consider that time the moment of the Big Bang. If you take the separation between the two galaxies (D) and divide that by the apparent velocity (v), that will leave you with how long it took for the galaxies to reach their current separation. The standard analogy here is to consider that you are now 300 miles from home. You drove 60 mph the entire time, so how long did it take you to get here? Well, 300 miles / 60 mph = 5 hours.

  • So, the time it has taken for the galaxies to reach their current separations is t=D/v .
  • But, from Hubble's Law, we know that v= H 0 D .
  • So,  t=D/ v=D/ ( H 0 ×D )=1/ H 0 . So, you can take 1/ H 0 as an estimate for the age of the Universe.
  • The best estimate for H 0 = 73km/ s/ Mpc . To turn this into an age, we'll have to do a unit conversion.
  • Since 1Mpc=3.08× 10 19 km , H 0  = ( 73 km/s/Mpc ) x (1 Mpc/3.08 x  10 19  km) = 2.37 x  10 18  1/s .
  • So, the age of the Universe is  t = 1/ H 0  = 1 / 2.37 x  10 18  1/s = 4.22 x  10 17  s = 13.4 billion years .

From stellar evolution, we have estimated the ages of the oldest globular clusters to be approximately 12-13 billion years old. These are the oldest objects we have identified, and it is a nice check on our estimates for the age of the Universe that they are consistent. It would have been strange if we were unable to find any objects roughly as old as the Universe or if we found anything significantly older than the estimated age of the Universe. For many years, until about 10 years ago, however, there was a controversy over the age of the universe derived from Hubble's Constant. The best theories available at the time were estimating that the stars at the Main Sequence Turn Off in many globular clusters had ages of 15 billion years old or more. This creates a problem. How can the universe contain an object older than itself? Recently, however, advances in our understanding of the stars have led us to refine the ages of the stars in globular clusters, and we now estimate them to be about 13 billion years old. This means, though, that the stars in the globular clusters must have formed within the first several hundred million years of the universe's existence!

The Large Scale Structure of the Universe

Additional reading from www.astronomynotes.com


Using the power of Hubble's Law to measure the distances to large numbers of galaxies, we can investigate the distribution of these objects in the Universe. So far, we have only looked at a few nearby examples: the Local Group and the Virgo Cluster. The Local Group is surrounded by a few other groups that we have discussed, and the Virgo Cluster is only one of a few nearby clusters. What we find when we study the distribution of galaxies in more detail is that groups and clusters are common throughout the Universe. For example, the Coma Cluster is another galaxy cluster, but it is different from Virgo in that it is a very massive, very dense cluster that contains about 10,000 galaxies.

Labeled image of the Coma Cluster explained in text
Figure 10.8: Labeled image of the Coma Cluster from the Digitized Sky Survey

The Perseus Cluster is another large cluster of galaxies within 100 Mpc of the Milky Way. You can find a large number of additional images of galaxy clusters at APOD or at Hubblesite. However, most of them look similar to the images you have seen so far of Virgo, Coma, and Perseus.

Since we now know that the redshift of a galaxy is a measurement of its distance, after we take an image of a part of the sky, we can take spectra of all of the galaxies in that image to determine their distances. What we have found is that galaxies tend to clump together. Astronomers have invested a lot of effort in doing this not just in deep fields, but in large swaths of sky. In this way, we have not only mapped out the distances to the clusters themselves, but to the galaxies in front of, behind, and around these clusters. So, what do we find? Well, for example, look at the plot below of the distances to a large number of galaxies from the Sloan Digital Sky Survey.

Plot of sky coordinates vs. distance for galaxies in the Sloan Digital Sky Survey showing redshift
Figure 10.9: A plot of sky coordinates vs. distance for galaxies in the Sloan Digital Sky Survey
Credit: SDSS

To interpret the plot above, picture it as a slice of the sky as seen from Earth. So Earth is at the center of the image. Each point on the plot is a galaxy. The direction to that point indicates its location on the sky, and the distance from the center of the image indicates its distance from Earth. Another group completed a similar survey of the galaxies in the Universe called the 2dF Redshift Survey.

These pie slice diagrams show the distances to all of the galaxies in a narrow strip of sky. The densest groups of points are the locations of clusters like Virgo, Coma, and Perseus. What you should notice is that the distribution of galaxies is not random. That is, the clusters appear to form clusters of clusters! The structure that you see in the pie slice diagrams is often described as being like soap bubbles. That is, the galaxies lie along the walls of the bubbles, and inside the bubbles are voids where very few galaxies are found. The voids are not completely empty. For example, the Hubble Deep Field image was taken in the center of a void. The poor groups like the Local Group lie in the voids.

The Cosmological Principle

So far, we have been considering cosmology mainly from an observational standpoint. That is, we have been looking at the distribution of galaxies in the Universe and the relationship between their distances and their velocities. However, we can also consider cosmology from a theoretical standpoint. That is, given what we know about the laws of physics, how should the Universe behave? In the early part of the 20th century, scientists like Einstein were using the theory of General Relativity to describe the behavior of the Universe. Astronomers studying the Universe made a simplifying assumption that is now known as the Cosmological Principle. It states:

  • On the largest cosmic scales, the Universe is both homogeneous and isotropic.

Homogeneity means that there is no preferred location in the Universe. That is, no matter where you are in the Universe, if you look at the Universe, it will look the same.

Isotropy means that there is no preferred direction in the Universe. That is, from your current location, no matter which direction you look, the Universe will look the same.

Diagrams like the one above of the distribution of galaxies in the Universe seem to imply that the Universe isn't homogeneous and isotropic. In other words, the galaxies in one direction are not distributed in exactly the same way as the galaxies in another direction. However, if you look at the scale on the plot, the galaxies it contains only extend to a redshift of z < 0.2, which is equivalent to a distance of about 750 Mpc. When we study the most distant objects we can find at much larger distances from Earth, the structure appears to smooth out and become more homogeneous on the largest scales. For example, the all-sky map of the locations of objects detected by radio telescopes shown below reveals a much more uniform appearance. These objects are mostly expected to lie at higher redshifts than the ones in the pie slice diagram above, suggesting that when we consider the largest distance scales, the Universe appears to be homogeneous and isotropic. Thus, we currently find support for the Cosmological Principle in the distribution of galaxies in the Universe.

All-sky map of the locations of objects detected by radio telescopes represented by two gray circles
Figure 10.10: An all-sky map of the locations of objects detected by radio telescopes

A coherent model for the Universe: The Big Bang Theory

Additional reading from www.astronomynotes.com


Given the following information:

  • Hubble's Law implies the Universe is expanding;
  • We observe the galaxies in the Universe to lie in a filament / void structure, but overall to be distributed on the largest scales in a homogeneous and isotropic way;
  • General Relativity describes the behavior of space-time in the Universe;

Astronomers have adopted a model known as the Hot Big Bang model to describe the Universe that incorporates the information above. You can state the model pretty concisely—we propose that the entire visible Universe and all of its contents was contained in a tiny region that was originally the size of a pinpoint. At one instant in time, that very hot, very dense point began expanding, and it is now much larger and much cooler than it was at the beginning.

Using the mathematical formulation of General Relativity, you can show that for a homogeneous, isotropic Universe, the geometry of the Universe must be either flat (that is, it obeys the laws of geometry that we all learned in math class), positively curved, or negatively curved. These possibilities are illustrated (to the best that they can be approximated in a flat illustration) below.

Schematic diagram of the potential geometries of the Universe, 1D, 2D, and 3D
Figure 10.11: Schematic diagram of the potential geometries of the Universe
Credit: NASA / WMAP

Recall that in the flat geometry that you learned in school, you were taught that the sum of the interior angles of a triangle equals 180 degrees. In the bottom part of the illustration, you see a flat plane with a normal triangle drawn on the plane. The top part of the illustration represents a closed, positively curved or spherical geometry. In the spherical geometry, the sum of the interior angles of a triangle add up to more than 180 degrees. The middle of the illustration represents an infinite, negatively curved or hyperbolic geometry. In this geometry, the sum of the interior angles of a triangle add up to less than 180 degrees. In principle, if there was a large enough triangular object in the universe and you could measure its interior angles, you could determine the local geometry of the Universe. There are other tests you could also conceive. For example, in our familiar flat geometry, two parallel lines remain parallel for their entire length. In a spherical geometry, parallel lines converge, and in a hyperbolic geometry parallel lines diverge. Note that if the Universe is spherical, if you could travel in one direction long enough, you would return to your original position. In either of the other two cases, you would never return to your original position.

You should keep in mind that these different geometric effects are observable in our universe. If we can detect them directly, we can determine the details of the shape of our universe. One more realistic example is to consider using a standard ruler to measure how distance and angular size are related. Consider an analogy on Earth: if you look out your window and see a nearby tree and a more distant tree, even if they are the same real size, the nearby tree will appear larger to you. We know that in our familiar flat geometry, as an object gets farther away from us, it looks smaller. However, in the positively curved geometry, an object with a given size will look smaller and smaller as it gets progressively farther away, but at some critical distance, it will start to look larger again! So, if you can identify an object with a known size (say a galaxy), and you see that the sizes of galaxies shrink as they get farther away from us, but then their apparent sizes start to grow again for all galaxies past a certain redshift, we must live in a positively curved universe. In practice, this test is very hard to do, because we do not know of a good object that can be seen at large distances and is always the same size (that is, the diameter of galaxies is not constant enough to do this test well).

Another way to determine the geometry of the Universe is to try to measure the total quantity of matter it contains, since the amount of matter determines the geometry of the Universe. If we designate a critical density and we call that value ρ crit :

  • If the measured density of the universe, ρ ave > ρ crit then the geometry of the Universe will be spherical, and the Universe will be closed.
  • If the measured density of the universe, ρ ave < ρ crit then the geometry of the Universe will be hyperbolic, and the Universe will be open and infinite.
  • If the measured density of the universe, ρ ave = ρ crit then the geometry of the Universe will be flat, and the Universe will be infinite.

In the illustration above, the geometries are labeled with, for example, Ω 0  =1 . In this notation, Ω 0 =  ρ ave  /  ρ crit , so if Ω 0  =1 , this means the same thing as ρ ave  =  ρ crit .

Finally, we should address some limitations of the Big Bang model and some misconceptions to watch out for when discussing the Big Bang model. These are:

  • Because the Big Bang occurred approximately 13.7 billion years ago, we are only able to observe the Universe within about 13.7 billion light years of Earth. This boundary is referred to as our horizon. The Big Bang model only describes the Universe within our horizon. We expect that the Universe extends far beyond our horizon, and the Universe beyond our horizon may not have the same properties as the observable Universe within our horizon.
  • The Big Bang model does not suppose that an explosion occurred at one point that is the center of the Universe. Instead, the entire Universe was once a point, and it has now expanded in size to its current extent. So every point in our Universe now was once in the same location in the past. So, the proper way to consider the location of the "center" is that every single location in the Universe now can be considered to be the center of the Universe equally.
  • A very common question is to ask "What is beyond the edge of the Universe or what is the Universe expanding into?" The (unsatisfying) answer to this question is that the Universe encompasses everything and it as a whole is expanding, so there is no edge.
  • The Big Bang model does not claim to explain the cause of the initial expansion.

The Cosmic Microwave Background

Additional reading from www.astronomynotes.com


The Big Bang Model is sometimes challenged in some of the same ways we see evolution being challenged. Since astronomers provide evidence that the Universe is about 13.7 billion years old, those who believe in a young Earth also attack the validity of the Big Bang model. However, astronomers consider the Big Bang to be quite successful in explaining a number of observations of the Universe, and although it does have some limitations, its fundamental ideas are not in doubt. One of the strongest pieces of evidence that supports the Big Bang model is the presence of a Cosmic Microwave Background Radiation, or CMB, observed throughout the Universe.

Want to read more?

The American Astronomical Society has put together a concise booklet called "The Ancient Universe," which is subtitled, "How Astronomers Know the Vast Scale of Cosmic Time." This booklet is an excellent resource, and it provides in one place the multiple lines of evidence we have found to support the age of the Universe.

Consider the Universe shortly after the Big Bang. It was still quite small, so all of the matter present was extremely hot and extremely dense. The temperature was so high that atoms could not exist. Instead, the Universe was filled with electrons, atomic nuclei, and photons of light. At this time, the Universe was opaque, because the free electrons in the Universe scatter the photons of light. The analogy you often hear to describe this process is one that compares the passage of photons through the Universe to the passage of photons through the clouds in Earth's atmosphere. Clouds scatter light, too, so although you can see through the clear air to the base of the clouds, you can't see beyond the clouds because photons of light are scattered by the clouds. At some point in time during the Universe's early expansion, the temperature cooled enough for the free electrons to combine with the nuclei, creating atoms. This epoch of time in the Universe's history is referred to as recombination. After recombination, the Universe is no longer opaque, so all of those photons of light could freely move through space, eventually reaching Earth. Recall the phenomenon of lookback time—by looking to large distances in space, we are also looking earlier and earlier in the Universe's history. So, we should be able to see the transition from our currently transparent Universe to an opaque Universe at very large lookback times just like we can see through the transparent air to the opaque clouds on an overcast day. This is illustrated below.

Diagram comparing the surface of last scattering in the Universe and in the Earth's atmosphere
Figure 10.12: Diagram comparing the surface of last scattering in the Universe and in the Earth's atmosphere. The cosmic microwave background Radiation's "surface of last scatter" is analogous to the light coming through the clouds to our eye on a cloudy day. We can only see the surface of the cloud where light was last scattered. 
Credit: NASA / WMAP

In the illustration above on the left, you see that the right side is labeled with the temperature of the Universe at that time. At the time when recombination occurred, the Universe was filled with an opaque gas with a uniform temperature of approximately 3000 kelvin, so its spectrum was that of a blackbody of 3000 K. As those photons from that 3000 K blackbody have traveled through the Universe to reach Earth, they have been redshifted by the expansion of the Universe. When they reach us, the peak of the blackbody spectrum is not seen to correspond to a temperature of 3000 K, but to a temperature of 2.7 K, which is in the microwave part of the spectrum. Hence the name the Cosmic Microwave Background Radiation.

This is another area of astronomy that has generated Nobel Prizes. In the 1960s, two researchers from Bell Labs, Penzias and Wilson, detected a "hiss" in their radio telescope that seemed to be detected no matter where the instrument was pointed. After eliminating every possible source of the noise (a famous part of their story is that they also considered and rejected the pigeons living in their telescope and the pigeon droppings they left behind as a potential source of this noise), they concluded that they had detected a cosmic background. At the time, other astronomers had made theoretical calculations suggesting there should be a CMB and had predicted its temperature. By comparing their predictions to the results of Penzias and Wilson, they determined that this radiation provided evidence supporting the Big Bang Model. Penzias and Wilson won the Nobel Prize in 1978. However, the theorists who made the predictions about the nature of the CMB did not share the prize.

Since the work of Penzias and Wilson, NASA has launched two satellites to study the CMB in detail. There have also been a large number of ground-based, and even balloon-based, experiments to study this radiation. The Cosmic Background Explorer, or COBE, was launched in 1989. It studied the CMB for a number of years. COBE measured the spectrum of the CMB and found the data shown below.

Plot of the spectrum of the CMB from COBE data, shows as waves increase intensity decreases at a non-linear rate
Figure 10.13: Plot of the spectrum of the CMB from COBE data
Credit: NASA / COBE

This plot shows that the spectrum of the CMB is exactly the shape of a blackbody curve emitted by an opaque gas with a temperature of 2.726 kelvin. This and other results from the COBE mission were considered so important to the study of cosmology and the Big Bang model that John Mather and George Smoot were awarded the Nobel Prize for Physics in 2006.

The WMAP mission followed COBE, and it measured the CMB more precisely than COBE was able to do. Both missions found the same thing, though. The map of the CMB over the sky is remarkably smooth. Here is an image of the entire sky of the CMB as detected by WMAP.

A green oval
Figure 10.14: An image of the CMB over the whole sky as measured by WMAP
Credit: NASA / WMAP

This image may seem like a joke, but it is an accurate representation of the data. It shows that over the entire sky, WMAP measured the intensity of the CMB radiation to be uniform to about 1 part in 100,000. However, if you enhance this image after removing variations caused by the redshift and blueshift of the CMB caused by the Earth's motion through the Universe and removing the foreground microwave radiation from the Milky Way Galaxy and other bright point sources in the Universe, you can produce a map of the intrinsic anisotropies in the CMB. Below is the enhanced image.

WMAP image of the anisostropies in the CMB, shown as a multi-colored oval
Figure 10.15: WMAP image of the anisostropies in the CMB
Credit: NASA / WMAP

The areas of red and dark blue show the maximum deviations from uniformity. They correspond to differences in the temperature of the CMB of approximately +/- 200 microKelvin (that is 0.0002 Kelvin). Astronomers interpret these fluctuations as small differences in the density of the plasma that filled the Universe right after the Big Bang. Astronomers have devoted a great deal of effort to studying these anisotropies, because they allow us to further refine our model for the Universe. The way this process works is that astronomers can choose the parameters for a particular model of the Universe (for example, they set in the model the current value of Hubble's constant, the current density of normal matter in the Universe, etc.) and, based on those parameters, they can create a simulated map of the expected anisotropies in the CMB in a Universe with those parameters. They can compare their predicted map to the measured anisotropies from WMAP and determine how their chosen parameters match the real values for our Universe. In this way, this map has allowed us to refine our measurements for the cosmological parameters to higher precision than has been previously possible.

Want to Learn More?

Dark Matter, Dark Energy, and the Accelerating Universe

Additional reading from www.astronomynotes.com


So far, we have discussed the origin of the Universe and the age of the Universe, but not its ultimate fate. This has been a question that has been pursued for many years, and a number of theorists were considering possible ideas for the fate of the Universe concurrently with the development of the Big Bang model. If you compare college astronomy textbooks today to those published about 20 years ago or more, though, you will find that this part of the discussion of cosmology has changed substantially since about 1998. The reason is because newly discovered evidence for dark energy complicates the matter. Dark matter plays a role in determining the fate of the Universe, too.

We have already encountered dark matter during our discussion of the rotation curve of the Milky Way, but I will go into some more detail here. Recall that in the Milky Way, we find that the outer parts of the Galaxy are rotating much faster than expected if all the matter in the Galaxy is visible matter. Based on the rotation curve of the Milky Way, it appears that the Galaxy contains more dark matter than luminous matter. Beyond individual galaxies, though, there is also evidence for dark matter in clusters of galaxies. Just like the rotation curves of Galaxies, you can also study the velocities of galaxies inside massive galaxy clusters. The escape speed from an object (in this case a cluster) depends on the mass of that object. In many clusters, the velocities of the galaxies in that cluster suggest that the cluster could not remain bound if all it contains is normal matter. There must be additional dark matter in the cluster, or else many of the galaxies would escape.

Additional evidence for dark matter in galaxy clusters comes from images like the one below. When we observe some clusters, we see another effect predicted by Einstein, called strong gravitational lensing. Since Einstein predicted that massive objects can warp spacetime, he showed that the light from a background object will be bent if it passes by a massive object, like a galaxy cluster. Here is an image of a cluster lensing a background galaxy, just as predicted.

Hubble image of a cluster lensing a background galaxy explained in text
Figure 10.16: Hubble image of a cluster lensing a background galaxy

The arcs that you see in between the yellow galaxies are distorted images of the background galaxy. The details of the lensing effect depend on the mass of the lens (that is, the more massive the lens, the more distorted the background galaxy), and show that this particular cluster contains more mass than it appears based solely on the luminous galaxies. Like the case for individual galaxies, it appears that the amount of dark matter in clusters like this is significantly larger than the amount of luminous mass.

The evidence for dark energy comes from different sources. The first piece of evidence comes from the Hubble diagram as calibrated by Type Ia supernovae. These objects are so luminous that they allow us to measure their distances accurately out to redshifts of z>1 . When the first Hubble diagrams were constructed using distances obtained from Type Ia supernovae, though, astronomers found a significant deviation from expectations. The supernovae were systematically fainter than expected at large distances. Below is a Hubble Diagram using Type Ia supernovae studied by two different teams.

Plot of Hubble Diagram from Type la supernovae, explained in text
Figure 10.17: Plot of Hubble Diagram from Type Ia supernovae

You can see in both the top panel and the bottom panel that the points with redshifts greater than about 0.5 seem to deviate from the straight line. This suggested that our (at the time) accepted models for the expansion of the Universe were incorrect.

We know that there is some matter in the universe (we live on a giant ball of matter called the Earth, after all), but our measurements of the luminous and dark matter in the Universe have shown that there is not enough matter to close the universe, or even to make it flat (that is ρ ave < ρ crit ). In the mid-1990s, the data suggested that the universe is open and that the total amount of luminous matter plus dark matter in the universe was only about 30% of the critical amount necessary for a flat universe. Given that there is some matter in the Universe, though, we expected that for objects at large distances, their distances would deviate from Hubble's Law. The reason is that the combined gravitational pull of all of the objects on each other would oppose the expansion of the Universe, causing it to decelerate. Because of deceleration, at the largest distances, objects should appear closer to us than predicted by their redshift. So for many years, the question that many astronomers were pursuing using different research techniques was "How much is the universe decelerating?".

However, for supernovae, the exact opposite was found. These objects appear to be farther away from us than predicted by their redshifts and Hubble's Law. The only way for this to happen is if the expansion of the universe is accelerating, not decelerating. In order for the universe to accelerate, there must be some force pushing all of the galaxies away from each other, and this force must be strong enough to counteract the deceleration by gravity. Today, we do not know what is the exact cause of this force, just that it exists. Since we call the matter that we cannot observe directly "dark matter," we call this new mysterious force (or equivalently, the energy provided by this force) dark energy. If we add in the contribution of dark energy to the density of the universe, it appears that the combination of normal matter, dark matter, and dark energy is enough to make the universe flat ( Ω=1 , but here Ω= Ω matter  +  Ω darkenergy ). Remember, our measurements showed that matter makes up only about 30% of the critical density, so dark energy makes up the other 70%! It appears that the 30% matter is about 4% normal matter (people, planets, stars, galaxies) and about 26% is dark matter. So this means that at this time, astronomers can only directly observe about 4% of the universe, and the other 96% is divided up among this peculiar dark matter and dark energy, which we have still not identified.

You may think that this is a bold claim based solely upon the distances to a handful of Type Ia supernovae, but the fluctuations in the CMB seen by WMAP also predict that normal matter only makes up approximately 4% of the Universe. Thus, the results from WMAP appear to confirm the results from Type Ia supernovae. Below is an image from the WMAP team for their predictions for the contents of the Universe.

Pie charts showing the contents of the Universe
Figure 10.18: Pie charts showing the contents of the Universe
Click Here for text alternative for Figure 10.18.
Contents of the Universe Today
Type of Matter Percentage
Atoms 4.6%
Dark Matter 23%
Dark Energy 72%
Contents of the Universe 13.7 billion years ago
Type of Matter Percentage
Neutrinos 10%
Atoms 12%
Photons 15%
Dark Matter 63%
Credit: NASA / WMAP

At this point, let us reconsider the question of what will happen to the Universe over time. Right now, it is difficult to say, because we do not understand dark energy very well. However, it appears that, given the accelerating expansion of the Universe, the Universe will grow larger and larger and colder and colder. All of the luminous objects in the Universe will eventually die out, and the Universe will eventually end in a "Big Freeze," where it will be too cold to support any life.

Additional Resources

There are several resources related to Cosmology that you may find helpful:

  1. The NASA WMAP mission provides a website that they call "Universe 101," which is an excellent set of materials that elaborate more deeply on many of the topics from this lesson in more detail than I was able to do.
  2. As always, you can also refer to www.astronomynotes.com for an additional set of reference material.  Their cosmology chapter includes more sections than our lesson.
  3. Penn State Professor Niel Brandt has taught in past summers a week long workshop on Cosmology for science teachers, and he makes available all of his notes and overheads.
  4. WMAP also has an online activity for classroom use called "Measuring Accuracy."
  5. Another publication with cosmology background and related activities is the "Teacher's Guide to the Universe."
  6. At Crash Course Astronomy, Phil Plait has episodes on Dark Matter, the Big Bang, Dark Energy, A Brief History of the Universe, and Deep Time

Summary

Cosmology is a challenging topic. No single lesson can really do the topic justice, but you should have at least a foundation now that you can use if you do follow-up reading on your own. Discoveries related to dark energy may continue to happen in the next few years, so you may want to keep an eye out for those, in particular.

Activity 1 - Lesson 10 Quiz

Directions

First, please take the Web-based Lesson 10 quiz.

  1. Go to Canvas.
  2. Go to the "Lesson 10 Quiz" and complete the quiz.

Good luck!


Activity 2 - Discussion

Directions

For this activity, I want you to reflect on what we've covered in this lesson and to speculate about the Big Bang. Since this is a discussion activity, you will need to enter the discussion forum more than once in order to read and respond to others' postings.

Submitting your work

  1. Enter the "Big Bang" discussion forum in ANGEL.
  2. Post your ideas about teaching the topic of the Big Bang.
  3. Read postings by other ASTRO 801 students.
  4. Respond to at least one other posting by asking for clarification, asking a follow-up question, expanding on what has already been said, etc.

Grading criteria

You will be graded on the quality of your participation. See the grading rubric for specifics on how this assignment will be graded.


Activity 3 - Lab

Directions

During this week, you should complete the work you began on lab 3 last week.

Reminder - Complete all of the lesson tasks!

You have finished the reading for Lesson 10. Double-check the list of requirements on the Lesson 10 Overview page to make sure you have completed all of the activities listed there before beginning the next lesson.