Unit 17: Cosmology
 
 

OVERVIEW

The structure and evolution of the Universe as a whole is considered. Obler's paradox and what it implies is discussed. The Steady State Theory of the Universe is contrasted to Big Bang Theories of the Universe. Big Bang Theories win out, and the 3 models for the Universe's large scale structure (open, flat, closed) are reviewed along with the resulting consequences for the total mass, geometry, and fate of the Universe. The major triumphs of Big Bang Theories are reviewed, namely (1) the expansion of the Universe, and (2) the generation of the 3 K comic microwave background radiation.

LEARNING OBJECTIVES

At the end of this unit you should be able to:

1. Discuss what the study of cosmology means.

2. Summarize Obler's paradox and how it is resolved.

3. Summarize the Steady State Theory for the origin of the Universe in its simple form, along with what it can and cannot explain.

4. Summarize the Big Bang Theory for the origin of the Universe.

5. Explain, in a physical way, why Big Bang Theories successfully explain the expansion of the Universe and the 3 K cosmic microwave background radiation.

6. Describe the total mass, geometry, and fate of the Universe for Big Bang Models in which the Universe is open, flat, and closed.

 KEY WORDS cosmology

expansion of the Universe

rate of expansion

relativistic cosmology

Obler's Paradox

Steady State Theory

Big Bang Theories

primeval fireball

open Universe

saddle-like shape

flat Universe

flat shape

closed Universe

spherical shape

big crunch

3 K cosmic microwave background radiation

Cosmic Background Explorer (COBE)

total mass of the Universe

observable size of the Universe

age of the Universe

 WRITTEN NOTES Cosmology is the study of the Universe as a whole.

The earliest cosmologies (going back into ancient history) assumed that the Earth was at the center of the Universe (We covered that at the beginning of the course.), but this was  shown to be false in the later Middle Ages, when the Earth was found to orbit the Sun.

For a very long time, astronomers tended to assume that the Universe had always existed and had always looked about the same--that there had never been any large-scale changes in the history of the Universe.  However, with the discovery of Hubble's Law (1929) (which says that the farther away something is from us, the faster away from us it is moving), it soon became clear that any valid cosmology would have to account for the expansion of the Universe.

 The Earth, the Solar System, the Milky Way Galaxy, the Local Group, and the Local Supercluster occupy no special position in the Universe.

In modern cosmology we try to understand the origin of the Universe, its organization, its evolution, and its ultimate fate. Two specific questions of interest regarding its fate are:

1. How fast is the Universe expanding (rate of expansion)?

2. How fast is the expansion slowing down (deceleration)?

 Modern cosmology(sometimes called relativistic cosmology) relies on Einstein's Special and General Theories of Relativity, which relate measurements of length, time, velocity and mass.

Remember that, in contrast to Newton's view, Einstein saw the gravity of mass not as a force, but as a manifestation of the curvature of spacetime.

 Obler's Paradox and What it Implies As early as the 1700s one of the questions which astronomers puzzled over was why the night sky was dark. (Sometimes philosophers get to be famous by asking dumb-sounding questions!) When Obler considered the question in 1823 it became known as Obler's paradox. Obler was confused by the darkness of the night sky when observations showed that stars appeared to be evenly distributed throughout space.

Obler reasoned that if stars (or galaxies) were evenly distributed throughout space and were everywhere, then eventually an observer's line-of-sight should encounter the surface of a star. (That is, in any direction you look, you'd see a star, even if it's far away.) Therefore, the whole sky should be glowing like the surface of a star.

The resolution to Obler's paradox is that stars (or galaxies) are not everywhere in space. Eventually an observer's line-of-sight runs out of stars to encounter.   One reason for this is that the universe has a finite age.  Because the universe began at a certain time back in the past, light from the farthest parts of the universe has not had enough time to reach us yet.  The universe is about 13-15 billion years old, so we can not see farther away than 13-15 billion light years.  This ultimate limit on our vision is called the cosmic horizon.  With every passing year, we can see another light year farther away.  So the cosmic horizon is moving farther away as time goes on, letting us see farther.  In addition, the expansion of the Universe would also diminish the brightness of the night sky, because as light from distant galaxies is redshifted it loses energy.

 The resolution to Obler's paradox tells us about the nature of the Universe. The Steady State Theory of the Universe and What It Can't Explain According to the Steady State Theory (1940s), the Universe never had a beginning and will never have an end. Furthermore, the Universe should have about the same amount of matter everywhere and look about the same in every direction. These conditions are called the "perfect cosmological principle."

In the Steady State Theory, as the Universe expands matter must be created to fill the space left behind. Matter is created out of nothing. Thus, the properties of the matter in some large volume of the Universe should be constant with time.

The fact that matter is created, which violates the important conservation of energy law (remember energy and mass are equivalent), is not a real problem. After all, when the issue is the origin of the Universe, at some point matter must be created.

[Only one atom would have to be created in a cubic cm (cc or cm3) of space every million billion years (1015 years).] In its purest form, the Steady State Theory is not consistent with observations of the Universe. For example, we now know that the Universe has many more QSOs/AGN as we look out to larger and larger distances from the Milky Way (this corresponds to what the Universe was like in the past). Thus, the Universe is not constant. It evolves with time.

Attempts to modify the Steady State Theory to account for the observed evolution have been made. However, most scientists believe that the Steady State Theory is not a viable cosmological theory. A major reason for this is that Big Bang theories offer an explanation for some fundamental observations.

 Big Bang Theories of the Universe and What They Explain Lemaitre (a Catholic priest) proposed a specific Big Bang model for the Universe in the 1940s. In Big Bang theories, the Universe began some time ago (in the past) in a primeval fireball.  From that moment on the Universe has been expanding. The properties of the Universe change as it expands. For example, at some point in time (some redshift away from us) galaxies will begin to form. Summary of Big Bang Models In Big Bang theories, the large scale structure (shape) of the Universe has three possibilities. These are termed as follows: 1. Open (saddle-like shape). The Universe will expand forever with no limit to its size, because it has too little mass in it (and therefore too little gravity pulling back in on it) to stop the expansion.

2. Flat (flat shape). The situation in between an open and closed Universe.  The Universe will expand forever, but it will never get larger than a certain limiting size.  As it grows larger, it slows down its expansion gradually, approaching that limiting size more and more slowly.

3. Closed (spherical shape). The Universe will someday cease expanding because it has enough mass (and therefore gravity) to stop the expansion; it will then begin to collapse into a big crunch.

 Aside from the Universe's expansion ,Big Bang theories explain: 1. How the observed amounts of helium and some other elements are produced in the early Universe.

2. The existence of the 3 degree Kelvin "cosmic microwave background" radiation, which is the electromagnetic spectrum of a cold black body observed in every direction out into space.

 As summarized, Big Bang models for the origin of the Universe offer the most satisfactory explanation for what is observed. In the remainder of the course we will study the predictions and implications of Big Bang models. The Origin of the Observed 3 Degree Kelvin "Cosmic Background Radiation" As the Universe expanded, it cooled. Finally, after about 1 million years, it cooled to a temperature of about 3,000 degrees Kelvin (Note that in class, I mistakenly said the universe was several million degrees at that time.  3,000 deg. is correct.)

At this point in time the temperature of the free protons and electrons that made up the bulk of the matter in the Universe was low enough that the protons and electrons combined to form hydrogen atoms (a proton and electron bound together). This was a major event, because it meant that the Universe was now transparent to radiation. Before this time, it had been opaque.

Prior to becoming transparent to radiation, a photon could not travel very far in the Universe before being absorbed (like a photon in the interior of the Sun). However, once the Universe became transparent to radiation it could travel throughout the Universe without much chance of ever being absorbed (like a photon escaping the photosphere of the Sun).

Using a radio telescope equipped with a microwave receiver, the signal of radiation finally escaping from a 1 million year-old transparent Universe can be observed in every direction from Earth. The spectrum of this signal is that of a 3,000 degree Kelvin blackbody, but with a redshift that corresponds to a time when the Universe was only 1 million years old.

 The redshift is so high that the spectrum of this cosmic background radiation peaks at a wavelength where a blackbody with a temperature of 3 degrees Kelvin would peak.  This light was originally visible light, but it has been redshifted all the way out to microwaves.  (Another way of looking at this is that as the universe expanded, the wavelength of the light expanded with it.)

In 1989, NASA launched the Cosmic Background Explorer spacecraft on a Delta rocket. Observations from this mission have revealed the cosmic background radiation with great accuracy. The shape of the 3 degree Kelvin blackbody spectrum is amazingly constant in every direction they aimed the telescope.  The data show that the structure of the Universe was extremely smooth when it was 1 million years old (no evidence for clumping).

 The Total Mass of the Universe, the Cosmological Constant, the Observable Size of the Universe, & the Age of the Universe. The large scale structure (shape) of the Universe and its ultimate fate are determined by the Universe's total mass: 1. Open Universe. If the mass of the Universe is less than the critical mass, its large scale structure is saddle-like. Even after an infinite amount of time the Universe would still be expanding. The 2 dimensional analogy of space is the surface of a saddle.

2. Flat Universe. If the mass of the Universe equals the critical mass, its large scale structure is flat and its expansion will need an infinite amount of time to stop. The 2 dimensional analogy of space in this model is the surface of a plane (as in a flat sheet).

3. Closed Universe. If the mass of the Universe exceeds the critical mass, its large scale structure is spherical and ultimately its expansion will cease. The Universe will then collapse back in on itself in a "big crunch." Some speculate that after the big crunch another big bang would occur and that the Universe oscillates (i.e., . . ., big bang, then expansion, then collapse, then big crunch, then big bang, then expansion, . . .). The 2 dimensional analogy of space in this model is the surface of a sphere.
 

 Remember that the large scale structure of the Universe refers to its overall shape as determined by its total mass. According to General Relativity, within the Universe itself space will have many small scale curves caused by masses and their gravity. Observations currently indicate that the Universe is open, but this assumes that astronomers have correctly estimated the amount of non-luminous dark matter present in the Universe, and this is difficult to estimate. Philosophically, many prefer a flat Universe. A closed Universe also has philosophical appeal and would be likely if we have underestimated the amount of non-luminous dark matter.

The Cosmological Constant was a mathematical feature introduced by Albert Einstein into his theory of General Relativity.  It would appear as a weak "anti-gravity" force which would only appear at great distances.  He later retrtacted this part of the theory, although the math certainly allowed it to exist.  He considered it his "greatest blunder."  However, in 1998, there was eveidence found that the Cosmological Constant does exist.  If this is true, then it may be strong enough to keep the universe from ultimately collapsing--that is, it may make the universe open or at least flat.

Because distances to objects are measured in terms of look-back time or billions of light years, the observable size of the Universe is related to the age of the Universe. We clearly can not look back further in time than the age of the Universe. In fact, the 3 degree Kelvin cosmic background radiation creates an opaque wall in the Universe which we can not see beyond. Because of the cosmic background radiation, we can not see farther back in time than when the Universe was about 1 million years old.  (Remember that before that time, the universe was opaque.)

Because of look-back time effects, every observer in the Universe statistically sees about the same thing in every direction. There is no center to the expansion which exists within the Universe itself. (This is a modified form of the perfect cosmological principle in the Big Bang model.)

The age of the Universe depends on its total mass and its true expansion rate. Current observations tell us that the Universe must be between 13 and 15 billion years old.

 READING ASSIGNMENT

For this lesson, you are only responsible for the material I cover in these notes, but the following sections of the book may be helpful in explaining difficult parts:
    The following are found in Ch. 22:
    Big Bang: pp. 665-666.  Don't bother with too many details in 667-670.
              Part of section 22.3, pp.671-673.
    Olber's paradox:  Section 22.6 (682-684)
    Cosmological constant:  Read the "Thinking about" section on pp. 670-671.
 
    The Cosmic Horizon, the expansion of the universe, and related problems:  Read Ch. 19, sections 19.3 and 19.4.

HOMEWORK

No homework, just an in-class extra credit assignment.