This chapter was copied with permission from Nick Strobel’s Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

Cosmology

This chapter covers cosmology: the study of the nature, origin, and evolution of the universe as a whole. The distance-scale ladder topic is dealt with in the Steps to the Hubble Constant document. I discuss Olbers’ Paradox, the cosmic microwave background radiation, the fate of the universe (open or closed), dark matter, dark energy, inflation, and the cosmological constant. Update on determination of Hubble constant by Lemaître.

16.1 Introduction

This chapter gives you the Big Picture called cosmology. Cosmology is the study of the nature, origin, and evolution of the universe as a whole. The observational aspect of cosmology deals with finding distances to galaxies which is necessary for determining the geometry of the universe. This was covered in the last chapter. Vocabulary terms in the text are in boldface.

16.2 Observations and Some Implications

At first you might think that in order to understand the structure of something as large as the universe, which by definition contains everything there is, you would need some very powerful telescope to see to the farthest reaches of space and a complex theoretical model. Actually, there are some powerful conclusions you can draw from observations with the naked eye. You will explore that first and then move on to conclusions you can draw from extending your eyesight. You will explore the basic questions that human beings have been asking themselves ever since we have walked the Earth: where did we come from and where are we going?

16.2.1 Universe Contains Mass—Why has the Universe Not Collapsed?

The universe is not empty. There is matter with mass, so the attraction of gravity is present. Newton knew that if the universe has existed forever and is static, that is, it has no net pattern of motion, then there must be enough time for gravity to collapse the universe, but this has clearly not happened! He knew of three ways to resolve this paradox. Either the universe is infinite in volume and mass or it is expanding fast enough to overcome the gravitational attraction or the universe has a beginning and/or an end. The last two ways violate the assumptions of an eternal and static universe, of course. So Newton chose the infinite universe option. Notice that you are able to arrive at the conclusion of an infinite universe from just one observation: the universe is not empty. No telescopes are needed, just the ability to follow a train of logical thought to its conclusion.

16.2.2 Olbers’ Paradox and the Dark Night Sky

Another simple observation is that the visible night sky is dark. IF the universe is infinite, eternal, and static, then the sky should be as bright as the surface of the Sun all of the time! Heinrich Olbers (lived 1758–1840) popularized this paradox in 1826, but he was not the first to come up with this conclusion. Thomas Digges wrote about it in 1576, Kepler stated it in 1610, and Edmund Halley and Jean Philippe de Cheseaux talked about it in the 1720’s, but Olbers stated it very clearly, so he was given credit for it. This problem is called Olbers’ Paradox.

If the universe is uniformly filled with stars, then no matter which direction you look, your line of sight will eventually intersect a star (or other bright thing). Now it is known that stars are grouped into galaxies, but the paradox remains: your line of sight will eventually intersect a galaxy.

The brightnesses of stars does decrease with greater distance (remember the inverse square law) BUT there are more stars further out. The number of stars within a spherical shell around us will increase by the same amount as their brightness decreases. Therefore, each shell of stars will have the same overall luminosity and because there are a lot of ever bigger shells in an infinite universe, there is going to be a lot of light!

Any intervening material absorbing the starlight would eventually heat up and radiate as much energy as it absorbed, so the problem remains even if you try these “shields.” Of course, stars are not points. They do have a definite size, so they can block light from other stars. The total brightness of the universe will not be infinite, but only as bright as the surface of a star (!). You can substitute “galaxy” for “star” in the preceding paragraphs if you want to update Olbers’ Paradox for modern times. The way to resolve a paradox like this is to look at the assumptions that are used (the “if” statements) and determine whether or not they are valid.

16.2.3 Universe Is Expanding

Georges Lemaître and Albert Einstein

In 1915 Albert Einstein published his Theory of General Relativity that described gravity as a curvature of spacetime (see the Relativity chapter). In 1917 Einstein applied General Relativity to the universe as a whole and showed that the universe must either expand or contract. Since there was no evidence of such large-scale motion, he added a term to the equations called the “cosmological constant” to keep the universe static. Alexander Friedman (lived 1888 – 1925) in 1922 and then the Belgian priest/astrophysicist Georges Lemaître (lived 1894 – 1966) in 1927 (independent of Friedman) used General Relativity to show that the universe must be expanding. In his 1927 paper Lemaître suggested a relation between the galaxy speeds and distances like what Edwin Hubble would later observe. Einstein disagreed with Lemaître but Lemaître persevered. Einstein would later come to agree with Lemaître on the expansion of the universe arising from General Relativity after Edwin Hubble announced his observations in 1929 that the universe is not static—it is expanding. In later papers and conferences Lemaître argued for a beginning to the universe that would later become the Big Bang Theory described more fully later in this chapter. In 1933 Einstein agreed that Lemaître was correct. [There is now evidence that Lemaître actually derived a value for the Hubble constant using some early distance measurements of Hubble and Slipher’s redshifts in his 1927 paper but his work is less well-known than Hubble’s because the paper was published in an obscure journal (Annales de la Societe scientifique de Bruxelles) written in French while Hubble’s (with Milton Humason) paper in 1931 with better distance data laying out the case for the galaxy motions first announced in 1929 appeared in the more widely-read Astrophysical Journal and the English translation of Lemaître’s paper in a 1931 issue of Monthly Notices of the Royal Academy of Sciences did not have that derivation of the Hubble constant. It was probably the more convincing observational evidence laid out in the Hubble & Humason paper that led Einstein to admit that Lemaître was correct all along.]

The expansion is enough to resolve the paradox. As the universe expands, the light waves are stretched out and the energy is reduced. Also, the time to receive the light is also lengthened over the time it took to emit the photon. Because the luminosity = the energy/time, the apparent brightness will be reduced enough by the expansion to make the sky dark.

The stretching of the light waves makes the light from galaxies appear redshifted, mimicking a redshift from the Doppler effect as if the galaxies were moving through space away from us. However, the galaxies are simply being carried along with the expansion of the space between them—the whole coordinate system is expanding. The expansion of the universe means that galaxies were much closer together long ago. This implies that there is a finite age to the universe, it is not eternal. Even if the universe is infinite, the light from places very far away will not have had enough time to reach us. This will make the sky dark.

The Hubble law, speed = H_o × distance, says the expansion is uniform. The Hubble constant, H_o, is the slope of the line relating the speed of the galaxies away from each other and their distance apart from each other. It indicates the rate of the expansion. If the slope is steep (large H_o), then the expansion rate is large and the galaxies did not need much time to get to where they are now. If the slope is shallow (small H_o), then the galaxies need a lot of time to get to where they are now.

The age of the universe can be easily estimated from the simple relation of time = distance/speed. The Hubble Law can be rewritten 1/H_o = distance/speed. Notice that the expansion time interval = 1/H_o. The Hubble constant tells you the age of the universe, i.e., how long the galaxies have been expanding away from each other: Age = 1/H_o. This value for the age is an upper limit since the expansion has been slowing down due to gravity. That means that the Hubble “constant” actually was larger in the past. Taking the expansion slowdown into account, you get an age closer to 2/(3 H_o). Still, the age looks like a number × (1/H_o), so if the Hubble constant is large, the derived age of the universe will be small.

16.2.4 Universe is Uniform on Large Scales

On size scales of billions of light years, the universe is assumed to be uniform. This makes the universe models simpler and “more reasonable”—if we lived in an unusual part of the universe, then it would be almost impossible to understand the universe as a whole from observing our surroundings. The discovery of the long superclusters may seem to endanger this assumption. On large enough scales though, the universe has many superclusters in all directions. It is like a large bowl of tapioca pudding, one spoonful of pudding looks like any other spoonful, even though, there are the small tapioca pieces.

The idea of a uniform universe is called the cosmological principle. There are two aspects of the cosmological principle:

• The universe is homogeneous. This means there is no preferred observing position in the universe.
• The universe is also isotropic. This means you see no difference in the structure of the universe as you look in different directions.

The cosmological principle is a Copernican idea. It means we are not in a special place. Every observer at a given cosmological time will see the same thing, such as the same Hubble law. “Cosmological time” in this context means the time measured from some common event like the creation of the universe. Everyone at the same cosmological time will measure the same age of the universe. The cosmological principle allows the universe to change, or evolve, throughout time.

An extension of the cosmological principle called the perfect cosmological principle says that the universe also does not change with time; there is no evolution. Therefore, in an expanding universe, new matter must be continually created. This violates a central rule of nature known as the law of the conservation of mass. This law says that the total amount of mass does not change—mass is not created from nothing or destroyed. However, the amount of new matter that would need to be created for the perfect cosmological principle to be true is quite small—only one hydrogen atom per cubic centimeter every 10¹⁵ years. This is approximately one hydrogen atom/Houston Astrodome every year—a very small amount! As described in the last chapter, the increase in the number of quasars at large distances from us, is strong evidence of a universe that DOES change, or evolve. Other evidence for a changing universe is given later in this chapter.

16.2.5 No Center to the Expansion in 3-D Space

General Relativity describes gravity as a warping or distortion of space and time near a massive object. In General Relativity, four-dimensional spacetime is curved. You may want to refresh your memory of these concepts by reading the Relativity chapter.

To help you understand what curved spacetime means, let’s use the analogy of a two-dimensional world curving into the third dimension. Pretend you are confined to the surface of a balloon and you only know about “front,” “back,” “left,” and “right,” but not “up” and “down.” In your 2D universe you cannot see the third dimension. Your universe appears flat. Yet you know that your 2D universe must be curved because if you walk in a straight line, you eventually arrive back at where you started! The balloon universe has a finite size but no edge. You also know that the angles of large triangles add up to a number larger than 180°! For example, on the balloon the lines of longitude running north-south intercept the equator at a 90° angle and converge at the poles. So a triangle made of one point on the equator + the north pole + another point on the equator will have the angles add up to more than 180°. In a truly flat universe, the angles would add up to exactly 180°. You would be able to deduce that your universe is positively curved.

On sufficiently small scales the surface looks flat so the regular geometry rules apply. The angles in a small triangle add up to 180°. Here on the surface of the Earth, the Earth looks flat to us because the curvature of the Earth is so much larger than we are. The universe does not have to curve back on itself as shown in the illustrations above. This type of positively-curved universe is usually easier to picture, but the curvature could be the opposite. In a negatively-curved universe, the universe curves away from itself. A two-dimensional analogy would look like a saddle. The angles in large triangles would add up to less than 180°. Like the positively-curved universe, there would be no center on the surface and no edge.

Rather than setting up BIG triangles in the universe, astronomers can use how the number of galaxies increases with increasing distance. If the universe has zero curvature and the galaxies are spread roughly uniformly in the universe, then the number of galaxies should increase linearly with ever greater volume. Lines defining an angle spread out in straight lines. If the universe has positive curvature, then the number of galaxies increases with greater volume then decreases with very large volumes. Lines defining an angle spread out at first and then converge at great distances. If the universe has negative curvature, then the number of galaxies increases more rapidly with with ever greater volume than a flat universe. Lines defining an angle diverge at increasing angles as the lines curve away from each other.

The idea of a curved surface also explains why astronomers in every galaxy will see the other galaxies moving away from it and, therefore, derive the same Hubble Law. Go back to the balloon analogy, imagine that there are flat houses on it. As the balloon expands, the elastic material moves the houses apart from each other. A person sitting on their front porch see everybody else moving away from her and she appears to be the center of the expansion.

Now add another dimension and you have our situation. Just like there is not new balloon material being created in the 2D analogy, new three-dimensional space is not being created in the expansion. Like any analogy, though, the balloon analogy has its limits. In the analogy, the balloon expands into the region around it—there is space beyond the balloon. However, with the expanding universe, space itself is expanding in three dimensions—the whole coordinate system is expanding. Our universe is NOT expanding “into” anything “beyond.”

Sections Review

Vocabulary

• cosmological principle
• cosmology
• homogeneous
• Hubble constant
• Hubble law
• isotropic
• Olbers’ Paradox
• perfect cosmological principle

Review Questions 1

1. What are the assumptions that Olbers’ Paradox is based on?
2. Why is the night sky dark? What important conclusions can you draw from the simple observation that the night sky is dark?
3. Will an object with a large redshift be far away or close?
4. What can the Hubble constant constant (H_o) tell you about the age of the universe? How would the derived age of the universe change if H_o was 50 km/sec Mpc^-1 instead of 100 km/sec Mpc^-1?
5. Is the Hubble constant actually constant throughout time? Why or why not?
6. What would the relation between the radial velocity and distance be if there was no expansion? What would the relation be if the universe was contracting?
7. Is there a center to the expansion in normal three-dimensional space? Why or why not?
8. Why is an analogy like flat houses on an expanding balloon used to try to picture the expansion?
9. Is the space between stars inside a galaxy expanding? Why or why not? Is the space between the molecules in your body expanding with the universe? Why or why not?
10. How is looking at faraway objects equivalent to looking back in time?
11. What is the cosmological principle? What is the perfect cosmological principle? Which one can an evolving universe fit in?

16.2.6 Cosmic Microwave Background Radiation

George Gamov (lived 1904–1968) predicted in 1948 that there should be a faint glow left over from when the universe was much hotter and denser. Since the universe is observed to be expanding, it means that the galaxies were originally right on top of each other. Also, the energy of the universe was concentrated in a smaller volume. The entire universe would have glowed first in the gamma ray band, then the X-ray band, then to less energetic bands as the universe expanded. By now, about 14 billion years after the start of the expansion, the cold universe should glow in the radio band. The expansion rate has slowed down over time because of the force of gravity. This means that the early expansion was faster than it is now. At the start of the expansion, the expansion rate was extremely rapid.

The early large expansion rate and very hot temperatures made Fred Hoyle (lived 1915 – 2001) call this theory of the birth of the universe, the Big Bang. At the time he coined the term, Hoyle was advocating another theory that used the perfect cosmological principle called the Steady State theory. So at the time, Hoyle’s “Big Bang” term was made in joking disdain. However, the Big Bang proponents liked the term and used it from then on.

16.2.6.1 Observation

Arno Penzias and Robert Wilson observed in 1965 a radio background source that was spread all over the universe—the cosmic microwave background radiation. The radiation has the same intensity and spectral character as a thermal continuous source at 3 K (more precisely, 2.728 ± 0.004 K) as measured by the COBE satellite in every direction observed. To a high degree of precision the sky is uniformly bright in radio. The uniformity of the background radiation is evidence for the cosmological principle. The error bars in the figure below are too small to be seen.

16.2.6.2 Interpretation

This background radiation is interpreted to be the relic of the early universe. If this is correct, then the early universe was very uniform. Since the further out in space you look means the further back in time you look, the microwave radiation is coming from the universe as it was a few hundred thousand years after the Big Bang when the universe was much hotter. The glow from the early hot universe has been redshifted by 1000 times! Hoyle’s Steady State theory could not adequately explain the presence of the background radiation and so was abandoned by most astronomers.

Let’s take a closer look at what was happening in the universe when it produced the background radiation. The early universe (both the matter and the radiation) was much more compact. The radiation density was so great that it dominated the expansion rate and the conditions of the universe for the first 10,000 years. Remember Einstein’s equation relating energy and mass? The energy E=mc² so the radiation energy had a definite gravitational effect!

The early universe was hot and opaque (photons could not move very far before being absorbed). The freely-moving electrons, protons, and neutrons scattered the photons all about making the dense gas opaque. Dense hot gases will produce a continuous spectrum that depends only on the temperature (a thermal spectrum). The universe cooled off as it expanded. Eventually, the early universe cooled to where the electrons and protons could combine to form neutral hydrogen atoms and not be blown apart by energetic photons. The process of the electrons becoming bound to the protons to make atoms is called recombination. Okay, “recombination” is not really correct since this was the first time that the electrons combined with the protons, but the term also describes processes that occur today. Extrapolating the expansion rate and the temperature of the universe backward in time, one finds that at the temperature of 3000 K, the universe was about 380,000 years old.

At the time of recombination, the number of unit particles was cut at least in half (one electron + one proton become a single atom; the neutrons also were incorporated into the atoms). That meant the photons could travel further without hitting some kind of unit particle. Also, the expansion of the universe spread the matter out. In addition, the coolness of the universe (only 3000 K at the time of recombination) meant that longer wavelengths of light were present. Instead of the gamma rays and X-rays of earlier times, the predominant form of radiation was the longer wavelength visible light and infrared. Longer wavelengths of light are able to more easily to pass through gas. For all of these reasons the photons could then travel long distances without running into some particle. The universe became transparent when the universe was glowing at the temperature of the surface of a cool star. The photons from this time are now reaching our radio telescopes. They are by far the oldest radiation that can be detected.

The universe could not have been perfectly uniform, though. The universe must have been slightly lumpy to form galaxies and people later on from the internal gravity of the lumps. Gravity is symmetrical so it needed some initial density variations to provide some direction to where surrounding matter could be attracted. The COBE satellite found slight variations in the brightness of the background radiation of about 1 part in 100,000. The slight variations exist because some parts of the universe were slightly denser than other parts. The slightly denser regions had more gravity and attracted more material to them while the expansion occurred. Over time, the denser regions got even denser and eventually formed galaxies about 1 billion years after the Big Bang. The slightly less dense places got even emptier as gravity increased the contrast between the denser places and less dense places. See the figure at the end of the superclusters section for a simulation of this process.

Below is a sequence of false-color microwave all-sky maps from the Differential Microwave Radiometer (DMR) instrument on the COBE satellite. The galactic equator runs horizontally through the center of each map. The range of temperatures for each map is given in the caption.

The colors for the temperatures range from blue for 0 K to red for 4 K (yes, the color scheme is backward—blue should be hot and red should be cool). Notice that the background appears completely uniform at a temperature of 2.728 K.

The colors for the temperatures range from blue for 2.724 K to red for 2.732 K. The double-lobe pattern shows the doppler effect from the motion of the Sun with respect to the background radiation. The background appears about 1/1000 times hotter (redder in this false-color map) in the direction the Sun is moving toward and about 1/1000 times cooler (bluer here) in the direction the Sun is moving away from.

The colors for the temperatures range from blue for 2.7279 K to red for 2.7281 K. The effect of the Sun’s motion has been subtracted out leaving fluctuations that are thirty times smaller than the previous map. The faint microwave contribution of the Milky Way is clearly seen along the center. The Cygnus constellation is at left center, the Sagittarius constellation is at the center, and the Orion constellation is at right center.

Below is a picture of the fluctuations in the background radiation when the Milky Way’s contribution is subtracted out. It shows a comparison of the coarse resolution of COBE with the finer resolution of the Wilkinson Microwave Anisotropy Probe (WMAP). WMAP has over 30 times greater resolution than the COBE satellite. With that greater resolution WMAP is enabling us to learn the composition, geometry, and history of the universe, amount of matter in the universe, as well as, providing much tighter constraints on the models. Selecting the map will take you to the WMAP homepage in another window.

The time period between when the universe became transparent about 380,000 years after the Big Bang and formation of the first stars in the galaxies and the large black holes in the quasars begins flooding the universe with powerful ultraviolet is called the “Dark Ages” or “Dark Era” in cosmological models. The ultraviolet light re-ionized the gas, freeing a lot of electrons. The light from the cosmic background would scatter off these newly freed electrons and become “polarized” so that the light waves tend to oscillate in a particular direction. How the light is polarized can tell you when the electrons were being freed again, i.e., when the stars first began to shine.

WMAP has detected the polarization of the microwave background and derived a time of about 400 million years after the Big Bang for the first stars. The visible light from these first stars will now have been redshifted into the infrared. The Hubble Space Telescope has detected near-infrared light from galaxies shining about 750 million years after the Big Bang in the “Hubble Ultra Deep Field” (and even further back—600 million years after the Big Bang with the new WFPC3 camera) and the Spitzer Space Telescope may have spotted infrared light from early galaxies of about that time in other areas of the sky, but it will take the much larger light-gathering power and resolution of the proposed infrared James Webb Space Telescope to study these objects in detail.

16.2.7 Matter to Energy to Matter Conversion

Einstein’s equation E = mc² says that mass can be converted to energy and vice versa. If you extrapolate the expansion rate and temperature of the universe back to much closer to the Big Bang than when the cosmic microwave background was produced, you find that within the first few seconds, the energy of the photons was great enough to create particles like electrons and protons. But along with the ordinary particles, the photons also created the antimatter counterparts to the particles, e.g., anti-electrons (called positrons) and anti-protons. Antimatter is briefly discussed in the context of nuclear fusion and the neutrino sections of another chapter.

The antimatter counterpart of an ordinary particle has the same mass and opposite charge of the ordinary particle (if it is not neutral). When an ordinary particle and its antimatter counterpart collide, they completely annihilate each other to create photons. The process can be reversed if the photons have enough energy (i.e., are high-energy gamma ray photons). Within the first microsecond (10^-6 second), the universe was hot enough for the photon radiation to undergo this matter-antimatter particle transformation using massive particles like protons and neutrons. When the temperature dropped to about 10¹³ K at one microsecond after the Big Bang, this process stopped for the protons but it continued for the less massive particles like the electrons. Neutrons were not created in the energy-matter conversion process but some were created when protons and electrons fused together.

When the universe had expanded for another few seconds, it cooled to a temperature of “only” 6 × 10⁹ K and the electron-positron production and annihilation process ceased. This is also the time when the number of neutrons stopped increasing from the proton-electron fusion process. The number of neutrons was fixed at a ratio of 1 neutron for every 5 protons. For reasons not completely understood, there was a very slight excess of ordinary matter over antimatter (by about 1 part in 10⁹). This is why there was still some ordinary matter left over when all the antimatter had been annihilated. (This must be the case, otherwise you wouldn’t be here!) All of the protons, neutrons, and electrons in matter today were created in the first few seconds after the Big Bang.

The extreme conditions described above have been reproduced in high-energy particle accelerators on Earth and the experiments have confirmed this description. For times much closer to the moment of the Big Bang we need to extend the theory beyond direct experimental bounds to much higher energies and temperatures. At a time of 10^-38 to 10^-36 second after the Big Bang, most early universe models say there was an ultra-fast expansion called “inflation.”

16.2.8 Cosmic Abundance of Helium and Hydrogen

The Big Bang theory provides a natural way to explain the present abundance of the elements. At about 2 to 3 minutes after the Big Bang, the expanding universe had cooled to below about 10⁹ K so that protons and neutrons could fuse to make stable deuterium nuclei (a hydrogen isotope with one proton and one neutron) that would not be torn apart by energetic photons. Recall that deuterium is one part of the fusion chain process used by nature to fuse hydrogen nuclei to make a helium nucleus. The fusion chain process in the early universe was slightly different than what occurs in stars because of the abundant free neutrons in the early universe. However, the general process is the same: protons react to produce deuterium, deuterium nuclei react to make Helium-3 nuclei, and Helium-3 nuclei react to make the stable Helium-4 nucleus.

The deuterium nucleus is the weak link of the chain process, so the fusion chain reactions could not take place until the universe had cooled enough. The exact temperature depends sensitively on the density of the protons and neutrons at that time. Extremely small amounts of Lithium-7 were also produced during the early universe nucleosynthesis process. After about 15 minutes from the Big Bang, the universe had expanded and cooled so much that fusion was no longer possible. The composition of the universe was 10% helium and 90% hydrogen (or if you use the proportions by mass, then the proportions are 25% helium and 75% hydrogen).

Except for the extremely small amounts of the Lithium-7 produced in the early universe, the elements heavier than helium were produced in the cores of stars. Stars do produce some of the helium visible today, but not most of it. If all the helium present today was from stars, then the nuclear reaction rates would have to be extremely high and the galaxies should be much brighter than they are.

The deuterium nucleus is a nucleus of special importance because of the sensitivity of its production to the density of the protons and neutrons and temperature in the early universe. The number of deuterium nuclei that do not later undergo fusion reaction to make Helium-3 nuclei also depends sensitively on the temperature and density of the protons and neutrons. A denser universe would have had more deuterium fused to form helium. A less dense universe would have had more deuterium remaining. The amount of the final Helium-4 product is not as sensitive to the ordinary matter density of the early universe, so the amount of the remaining deuterium seen today is used as a probe of the early density. Therefore, measurement of the primordial deuterium can show if there is enough ordinary matter to make the universe positively-curved and eventually stop the expansion. Current measurements of the primordial deuterium show that the density of ordinary matter is about only 5% of the critical density—the boundary between having too little to stop the expansion and enough to eventually stop the expansion.

Measuring the abundances of the primordial material and comparing it with what is predicted in the Big Bang theory provides a crucial test of the theory. The Big Bang nucleosynthesis also turns out to place great constraints on the variation of G, the gravitational constant, because a different value of G in those first few minutes than what we see today would have significantly changed the expansion rate of the universe and that would have significantly (measurably) altered the relative abundances of the primordial elements. The gravitational constant G appears to truly be constant.

A nice interactive to get a handle on the stages of the Universe’s history and its future (in preparation for the next major section of this chapter) is History of the Universe interactive from NOVA’s Origins series that was broadcast on PBS (selecting the link will bring it up in a new window either in front of or behind this window).

16.2.9 Evidence Supporting the General Big Bang Scheme

The Big Bang Theory is a natural result of Einstein’s Theory of General Relativity as Lemaître showed back in the 1930s. What evidence is there for thinking the Big Bang theory is correct? The Big Bang theory may be nice but it has to pass the judgement of observation. Nature and experiments are the final judge of the correctness of scientific ideas. Though some details of the Big Bang still need to be perfected, the general scheme of a early hot universe with a definite beginning is accepted by most astronomers today. Even so, we have to be open to the possibility that future observations could show it to be wrong. The observations given below are sometimes said to be “proof” of the Big Bang theory. Actually, the observations are consistent with the Big Bang theory, but do not provide proof. Recall from the discussion in the chapter on the scientific method that scientific theories cannot be proven to be correct. As of now, the Big Bang theory is the only one that can explain all of these observations.

1. The galaxies (or galaxy clusters) are systematically moving away from us such that the farther away galaxies are moving faster away from us. As a result of General Relativity this means that space itself is expanding carrying the galaxies with it. Both the Big Bang Theory and its major competitor, the Steady State Theory, could explain it. Recall that the Steady State Theory used the perfect cosmological principle while the Big Bang uses the cosmological principle.
2. The cosmic microwave background radiation can be explained only by the Big Bang theory. The background radiation is the relic of an early hot universe. The Steady State theory could not explain the background radiation, and so fell into disfavor.
3. The amount of activity (active galaxies, quasars, collisions) was greater in the past than now. This shows that the universe does evolve (change) with time. The Steady State theory says that the universe should remain the same with time, so once again, it does not work.
4. The number of quasars drops off for very large redshifts(redshifts greater than about 50% of the speed of light). The Hubble Law says that these are for large look-back times. This observation is taken to mean that the universe was not old enough to produce quasars at those large redshifts. The universe did have a beginning.
5. The abundance of hydrogen, helium, deuterium, lithium agrees with that predicted by the Big Bang theory. The abundances are checked from the spectra of the the oldest stars and gas clouds which are made from unprocessed, primitive material. They have the predicted relative abundances.

The American Astronomical Society and the Astronomical Society of the Pacific published a beautifully-illustrated guide for teachers, students, and the public called An Ancient Universe: How Astronomers Know the Vast Scale of Cosmic Time. (PDF document: 800 kB in size!) This guide for Teachers, Students and the Public was written by a subcommittee of the American Astronomical Society’s Astronomy Education Board. This is a local copy from the AAS Education Board.

Sections Review

Vocabulary

• Big Bang
• cosmic microwave background radiation
• deuterium
• recombination

Review Questions 2

1. What is the cosmic microwave background radiation a relic of?
2. What is the type of spectrum of the background radiation? What is the temperature of the Universe now?
3. What can the photons do when recombination occurs and why is that?
4. About when did the Big Bang supposedly occur?
5. What was the universe like for the first few million years after the Big Bang? How was the early universe like the cores of stars shining today?
6. Where did most of the hydrogen and helium in the universe come from? How about the deuterium? Why did the early universe not continue the nucleosynthesis process to heavier nuclei?
7. How does the present abundance of deuterium provide a good constraint on the early density of the universe?
8. What is the evidence for a Big Bang type of model for the universe and for a universe that has evolved over time?

16.3 Fate of the Universe

Now that you have explored the beginnings of the universe and have an answer to the question “where did we come from?”, let’s address the other question, “where are we going?” This final section will cover the fate of the universe. We observe that the universe is expanding and that gravity is slowing it down. Which of them will win?

16.3.1 Depends on Mass (Curvature of Space)

The more mass there is, the more gravity there is to slow down the expansion. Is there enough gravity to halt the expansion and recollapse the universe or not? If there is enough matter (gravity) to recollapse the universe, the universe is “closed.” In the examples of curved space above, a closed universe would be shaped like a four-dimensional sphere (finite, but unbounded). Space curves back on itself and time has a beginning and an end. If there is not enough matter, the universe will keep expanding forever. Such a universe is “open.” In the examples of curved space, an open universe would be shaped like a four-dimensional saddle (infinite and unbounded). Space curves away from itself and time has no end.

Instead of trying to add up all of the mass in the universe, a more reasonable thing to do is to find the density of a representative region of the universe. The density = (mass in the region)/(volume of the region). If the region is truly representative, then the total mass of the universe = the density × the total volume of the universe. If the density is great enough, then the universe is closed. If the density is low enough, then the universe is open. In the popular astronomy magazines, you will probably see the mass density of the universe specified by the symbol “Ω.” It is the ratio of the current density to the “critical density” described in the next paragraph. If Ω < 1, the universe is open; if Ω > 1, the universe is closed.

16.3.2 Critical Density

The boundary density between the case where the universe has enough mass/volume to close universe and too little mass/volume to stop the expansion is called the critical density. The critical density = 3H²/(8pG), where H is the Hubble constant for a given cosmological time. Notice that the Hubble constant has appeared again! It measures the expansion rate, so it should be in the critical density relation. The current critical density is approximately 1.06 × 10^-29 g/cm³. This amounts to six hydrogen atoms per cubic meter on average overall.

A critical density universe has “flat” curvature. The W density parameter equals exactly 1 in a flat universe. The Hubble “constant” is not really a constant—it is different at different cosmological times. The greater the value of the Hubble constant at a given cosmological time, the faster the universe is expanding at that time. Gravity slows the expansion of the universe, so the early universe was expanding faster than it is now. That means that the critical density was greater at earlier times. It changes by the same factor that the actual density of the universe changes throughout the expansion. So if the universe starts out with a density greater than the critical density, then its density will always be greater than critical density. If the universe starts out with a density less than the critical density, then its density will always be less than the critical density.

16.3.3 Is the Universe Open or Closed?

The curvature of the universe is determined by the density of the universe. You can do a cosmic inventory of all of the mass from ordinary matter in a representative region of the universe to see if the region’s density is above the critical density. Such an inventory gives 10 to 20 times too little mass to close the universe. The primordial deuterium abundance provides a sensitive test of the density of ordinary matter in the early universe. Again, you get 15 to 20 times too little mass to close the universe. However, these measurements do not take into account all of the dark matter known to exist. Dark matter is all of the extra material that does not produce any light, but whose presence is detected by its significant gravitational effects.

16.3.4 Dark Matter

There maybe about 90 times more dark matter mass than visible, glowing matter. Some of the dark matter is regular sort of matter (atoms) that is too faint for us to detect such as dead burned out stars, planets, brown dwarfs, etc. The rest of the dark matter is made of material that is not made of atoms or their constituent parts. This strange material has a total mass about five times more than the total mass of the ordinary matter. Some evidence for the presence of dark matter has already been presented in the previous chapters. The list below summarizes the evidence for dark matter’s existence.

Orbital speeds of stars in galaxies

1. Flat rotation curves of spirals even though the amount of the light-producing matter falls off as the distance from the galaxy center increases. Remember the enclosed mass = (orbital speed)²× (orbit size)/G. Below is the rotation curve for our Milky Way Galaxy (a typical spiral galaxy).Also, the orbital speeds of stars in elliptical galaxies are too high to be explained by the gravitational force of just the luminous matter in the galaxies. The extra gravitational force is supplied by the dark matter in the ellipticals.
   

   Faint gas shells around ellipticals

2. Ellipticals have faint gas shells that need massive “dark” halos to contain them. The gas particles are moving too quickly (they are too hot) for the gravity of the visible matter to hang onto it. However, the number of ellipticals with these faint gas shells is too large to be only a temporary feature of ellipticals. The dark halos must extend out to 300,000 light years around each galaxy. The extent of this dark matter pushes Ω up to around 0.2. If the halos are larger than originally thought, Ω could approach 1.
   

   Motion of galaxies in a cluster

3. Galaxy cluster members are moving too fast to be gravitationally bound unless there is unseen mass. The reasonable assumption is that we do not live at a special time, so the galaxies in the cluster must have always been close to each other. The large velocities of the galaxies in the clusters are produced by more gravity force than can be explained with the gravity of the visible matter in the galaxies.
   

   Hot gas in clusters

4. The existence of HOT (i.e., fast moving) gas in galaxy clusters. To keep the gas bound to the cluster, there needs to be extra unseen mass.
   

   Quasar spectra

5. Absorption lines from hydrogen in quasar spectra tells us that there is a lot of material between us and the quasars.
   

   Gravitational Lensing

6. Gravitational lensing of the light from distant galaxies and quasars by closer galaxies or galaxy clusters enables us to calculate the amount of mass in the closer galaxy or galaxy cluster from the amount of bending of the light. The derived mass is greater than the amount of mass in the visible matter. Inventorying all of the ordinary matter in the lensing galaxy clusters (those that lens the light from distant galaxies) and comparing it to the total mass of the galaxy clusters gives a 5 to 1 ratio of dark matter to ordinary matter.
   

   Dark Matter separation from ordinary matter

7. The collision of the galaxy cluster 1E 0657-56, called the “bullet cluster”, with another galaxy cluster has produced a clear separation of the ordinary matter from the dark matter. The ordinary matter of one cluster is slowed by a drag force as it interacts with the gas (ordinary matter) of the other cluster. The dark matter is not slowed by the impact because it responds only to gravity and is not affected by gas pressure. In the picture below, the ordinary matter is colored pink—it is hot gas imaged by the Chandra X-ray Observatory. The blue areas are where most of the mass in the clusters is found (the dark matter). The dark matter locations were determined by gravitational lensing of light from background galaxies. Select the Chandra link to view animations of how the separation happened. The more recent observation of the MACS J0025.4-1222 cluster collisionhas shown the same sort of separation of dark matter from ordinary matter.

Current tallies of the total mass of the universe (visible and dark matter) indicate that there is only 28% of the matter needed to halt the expansion—we live in an open universe. Ordinary matter amounts to almost 5% and dark matter makes up the other 23%. Astronomers and physicists are exploring the possibility that perhaps there is an additional form of energy not associated with ordinary or dark matter, called “dark energy,” that would greatly affect the fate of the universe. This is discussed in the last section of this chapter.

One possible dark matter candidate was the neutrino. There are a lot of them, they have neutral charge and photons do not bump into them. Unfortunately, their mass is too small and they move much too fast to create the clumpy structure we see of the dark matter and ordinary matter. The universe would not have been able to make the galaxies and galaxy clusters if the dark matter was neutrinos. To create the lumpy universe, astronomers are looking at possible massive neutral particles that move relatively slowly. Various candidates fall under the heading of “WIMPs”—weakly interacting massive particles (sometimes, astronomers and physicists can be clever in their names).

16.3.5 Deriving the Geometry of the Universe from the Background Radiation

An independent way to measure the overall geometry of the universe is to look at the fluctuations in the cosmic microwave background radiation. If the universe is open (saddle-shaped), then lines starting out parallel will diverge (bend) away from each other. This will make distant objects look smaller than they would otherwise, so the ripples in the microwave background will appear largest on the half-degree scale. If the universe is flat, then lines starting out parallel will remain parallel. The ripples in the microwave background will appear largest on the 1-degree scale. If the universe is closed, the lines starting out parallel will eventually converge toward each other and meet. This focusing effect will make distant objects look larger than they would otherwise, so the ripples in the microwave background will appear largest on scales larger than 1-degree. Select the image below to go to the WMAP webpage from which the image came.

The resolution of the COBE satellite was about 7 degrees—not good enough to definitively measure the angular sizes of the fluctuations. After COBE, higher-resolution instruments were put up in high-altitude balloons and high mountains to observe the ripples in small patches of the sky. Those experiments indicated a flat geometry for the universe (to within 1% uncertainty). Cosmologists using the high resolution of the WMAP satellite to look at the distribution of sizes of the ripples confirmed that conclusion using its all-sky map of microwave background at a resolution over 30 times better than COBE. WMAP also gave a much improved measurement of the ripples. The distribution of the ripples peaks at the one-degree scale—the universe is flat. This result from the WMAP satellite and the too meager amount of matter in the universe to make the universe geometry flat is forcing astronomers to conclude that there is another form of energy that makes up 72.1% of the universe (called “dark energy” for lack of anything better). The “dark energy” is probably the “cosmological constant” discussed in the last section of this chapter. Furthermore, the distribution of the sizes of the ripples shows that some sizes are preferred and other sizes are damped out as would be the case if the dark matter was different from ordinary matter. The size distribution, the spectrum of sizes, gives the ratio of dark matter to ordinary matter. Dark matter not made of atoms makes up 23.3% of the critical density, leaving just 4.6% of the universe with what the rest of the previous chapters of this website have been about (ordinary matter). That ratio matches up very nicely with the ratios found using the other independent methods of Big Bang nucleosynthesis and the motions of galaxies.

Sections Review

Vocabulary

• closed universe
• critical density
• dark matter
• flat universe
• open universe

Review Questions 3

1. What is the overall curvature of space in a closed or open or flat universe? How does the expansion rate compare to the amount of gravity deceleration in each of these cases?
2. Why is the universe’s expansion rate slowing down?
3. Will it ever slow down completely? How can you find out?
4. What type of universe has a critical density? What would happen to the expansion if the current density < critical density? How about the case for the current density > critical density?
5. Would a universe starting out with a density > critical density ever expand enough so its density dropped below critical density? Explain why or why not!
6. What is all the fuss about dark matter? If it is not putting out any light for us to see, how is it known to exist? What are some examples of observations indicating its presence?
7. How can you use the cosmic microwave background (something from the far past) to determine the fate of the universe (something in the far future)?

16.4 Embellishments on the Big Bang

Flatness Problem

There are a couple of problems with the standard Big Bang model. The first is called the flatness problem—why is the universe density so nearly at the critical density or put another way, why is the universe so flat? Currently, the universe is so well-balanced between the positively-curved closed universe and the negatively-curved open universe that astronomers have a hard time figuring out which model to choose. Of all the possibilities from very positively-curved (very high density) to very negatively-curved (very low density), the current nearly flat condition is definitely a special case. The balance would need to have been even finer nearer the time of the Big Bang because any deviation from perfect balance gets magnified over time. For example, if the universe density was slightly greater than the critical density a billion years after the Big Bang, the universe would have recollapsed by now.

Consider the analogy of the difficulty of shooting an arrow at a small target from a distance away. If your angle of shooting is a little off, the arrow misses the target. The permitted range of deviation from the true direction gets narrower and narrower as you move farther and farther away from the target. The earlier in time the universe’s curvature became fixed, the more finely tuned the density must have been to make the universe’s current density be so near the critical density. If the curvature of the universe was just a few percent off from perfect flatness within a few seconds after the Big Bang, the universe would have either recollapsed before fusion ever began or the universe would expanded so much that it would seem to be devoid of matter. It appears that the density/curvature was very finely tuned.

Horizon Problem

The second problem with the standard Big Bang model is the horizon problem—why does the universe, particularly the microwave background, look the same in all directions? The only way for two regions to have the same conditions (e.g., temperature), is that they are close enough to each other for information to be exchanged between them so that they can equilibrate to a common state. The fastest speed that information can travel is the speed of light. If two regions are far enough apart that light has not had enough time to travel between the regions, the regions are isolated from each other. The regions are said to be beyond their horizons because the regions cannot be in contact with each other (recall the term event horizon in the discussion about black holes).

The photons from the microwave background have been traveling nearly the age of the universe to reach us right now. Those photons have certainly not had the time to travel across the entire universe to the regions in the opposite direction from which they came. Yet when astronomers look in the opposite directions, they see that the microwave background looks the same to very high precision. How can the regions be so precisely the same if they are beyond each other’s horizons? Running the expansion backward, astronomers find that regions even a degree apart in angular separation on our sky would have been beyond each other’s horizons at the time the microwave background was produced.

16.4.1 Inflation

On theoretical grounds, astronomers think that the very early universe experienced a time of ultra-fast expansion (called inflation). The inflation probably took place from about 10^-38 to 10^-36 seconds after the Big Bang, but astronomers are not sure of the cause of inflation so they cannot pinpoint the time it would have occurred. The size of the fluctuations in the cosmic microwave background indicate that the inflation could not have occurred before 10^-38 seconds after the Big Bang. The leading theory for the cause of the inflation says that it occurred when there was a break in the fundamental forces of nature. Before the time of 10^-38 seconds after the Big Bang, the fundamental forces of the strong nuclear force, the weak nuclear force, and electromagnetic force behaved in the same way under the extreme temperatures. They were part of the same fundamental unified force. Theories that describe the conditions when the forces were unified are called Grand Unified Theories (GUTs for short). At about 10^-38 seconds after the Big Bang, the universe had cooled down to “only” 10²⁹ K and the strong nuclear force broke away from the weak nuclear and electromagnetic forces. This breaking apart of the forces from each other somehow produced the huge expansion that expanded the universe by about 10⁵⁰ times in about 10^-36 seconds.

The inflation theory predicts that the ultra-fast inflation would have expanded away any large-scale curvature of the part of the universe we can detect. It is analogous to taking a small globe and expanding it to the size of the Earth. The globe is still curved but the local piece you would see would appear to be fairly flat. The small universe inflated by a large amount and the part of the universe you can observe appears to be nearly flat. That solves the flatness problem.

The horizon problem is solved by inflation because regions that appear to be isolated from each other were in contact with each other before the inflation period. They came into equilibrium before inflation expanded them far away from each other. Another bonus is that the GUTs that predict inflation also predict an asymmetry between matter and antimatter, so that there should be an excess of matter over antimatter.

The inflation theory might also explain where the ripples in the microwave background (the “galaxy seeds“) come from. Recall in an earlier section about the very early universe that matter-antimatter can change to energy and energy can change back to matter-antimatter. The laws of physics that deal with the very small scales of atoms, sub-atomic particles, etc. (quantum mechanics) predict that the matter-energy fluctuations should be going on even today at every point in space. It turns out that these quantum fluctuations can occur if they happen quickly enough to not be noticed (the greater the energy-matter fluctuation, the quicker the fluctuation must occur). Therefore, even in perfectly empty space (complete vacuum), there is a seething froth of fluctuations at very tiny scales, a vacuum energy—matter-antimatter virtual particles spontaneously appearing and then annihilating each other too quickly for us to detect. Although virtual particles-quantum foam might seem a bit too fanciful (to put it kindly), these virtual particles do produce measurable effects such as:

• In an atom, the appearance of electron-positron virtual particles will alter the orbit of the real electron orbiting the nucleus altering the energy levels which can be measured with very sensitive, precise equipment. The measured energy levels agree with those predicted by quantum if virtual particles are taken into account.
• Extra forces generated between close metal plates (the “Casimir Effect”) can be explained by the presence of more virtual particles on either side of the plates than in the gap between the plates.
• Collisions of real particles and real antiparticles in high-energy particle accelerators can supply energy to the vacuum and cause other particle-antiparticles to appear.

Now back to inflation. The quantum fluctuations in the very early universe could have been the galaxy seeds, but they would have been much too small to be the ripples we see in the cosmic microwave background. Before inflation that is! The super-rapid growth of the universe during inflation would have stretched the fluctuations to much larger sizes—large enough to create the ripples in the microwave background that eventually became enhanced to form galaxies under the action of gravity over billions of years. Although the current versions of inflation theory cannot answer all of the questions about the large-scale structures of our universe, they do predict a particular distribution of the ripple sizes in the microwave background that is consistent with the results from the high-altitude balloon experiments and WMAP. The distribution of the ripples peaks at an angular size of one degree on the sky and the temperature varies by about 1 part in 100,000 as predicted by inflation. As astronomers continue to gather data from WMAP and the PLANCK spacecraft, they will be looking at how the microwave background photons scattered off the electrons just before the universe became transparent. Scattering causes light to become preferentially oriented in a particular way (it is “polarized”). The simplest version of inflation predicts a particular polarization of the microwave background that appears to be seen in the WMAP data. WMAP and PLANCK will look for the imprint of gravitational waves predicted by the inflation theory.

History of the universe from the Big Bang to the present day

16.4.2 The Cosmological Constant

Albert Einstein completed his theory of General Relativity in 1915. When he applied his theory to the spacetime of the universe, he found that gravity would not permit the universe to be static. Over a decade before Hubble’s discovery of an expanding universe, Einstein made the reasonable assumption that the universe is static and unchanging (the perfect cosmological principle). He introduced a term called the cosmological constant that would act as a repulsive form of gravity to balance the attractive nature of gravity. The cosmological constant is an exotic form of energy filling empty space, the vacuum energy discussed above. The vacuum energy creates a repulsive gravitational force that does not depend on position or time; it truly is a constant. When Einstein learned of Hubble’s discovery, he realized that he should have had more faith in his original General Relativity. He discarded the cosmological constant as the “biggest blunder of his life.”

Recent observations are indicating that the cosmological constant should be brought back. Astronomers are finding that even when they include the maximum amount of dark matter allowed by the observations, there is not enough matter (luminous or dark) to flatten the universe—the universe is open with negative curvature if the cosmological constant is zero. The inflation theory predicts that the universe should be flat to very high precision. An extra energy called called dark energy is needed to make the universe curvature flat overall beyond what ordinary and dark matter can do. This dark energy is probably the cosmological constant (vacuum energy) described above. Recent observations of the cosmic microwave background show that the combined efforts of matter and dark energy flatten space as much as that predicted by inflation theory.

One major stumbling block in the theory of the cosmological constant is that quantum theory predicts that the total vacuum energy should be on the order of 10¹²⁰ times larger than what is observed. The cosmological constant predicted from quantum theory would cause the universe to expand so fast that you would not be able to see your hand in front of your face because the light would not be able to reach your eyes! In reality we can see to billions of light years. Physicists are trying to figure out why there is such a big discrepancy between the quantum theory’s prediction and observation. Some cosmologists are exploring the idea of a dark energy that varies with space and time called “quintessence”. Stay tuned for developments!

Another set of observations of very distant (“high-Z”) Type Ia supernovae show that the expansion rate is slower than expected from a flat universe. Type Ia supernovae are very luminous and can be used as standard candles to measure very large distances because they form from the collapse of a stellar core of a particular mass (1.4 solar masses). By measuring very large distances, astronomers can determine the geometry of the universe. The supernovae are fainter than expected. After exploring ordinary possibilities like intergalactic dust, gravitational lensing effects, and metallicity effects, astronomers are forced to conclude that either the universe has negative curvature (is open) or that the supernovae are farther away than the Hubble Law says they are—their redshifts are “too small” because the universe expanded more slowly in the past than expected. What is surprising about the supernova observations is that they may indicate that the expansion is accelerating!

Accelerating expansion is impossible without a repulsive cosmological constant to overcome the slowing down effect of gravity. An accelerating universe will increase the derived age of the universe because the expansion rate long ago was slower than the expansion rate is now. The galaxies needed more time to get to their large distances than the original decelerating universe model said. Long ago gravity was the dominant force affecting the universe’s expansion since everything was closer together. As the universe expanded the effect of gravity got diluted. Eventually, the strength of gravity dropped below the amount of the dark energy. Recent observations of how the expansion rate has changed over the history of the universe show that the dark energy began to dominate over gravity about 4 billion to 6 billion years ago but its presence being felt up to about 9 billion years ago.

The far future of the universe depends on the form that dark energy takes. If the dark energy is the cosmological constant, then the expansion of the universe will continue long after all of the stars have died out many trillions of years in the future. If the dark energy is one of the possible forms of “quintessence,” the acceleration rate increases and the galaxies, stars, even atoms are torn apart in a “big rip” on a time scale before all of the stars die out (but after our Sun dies). Other forms of the dark energy could cause the universe to re-collapse after its current period of acceleration.

Detailed studies of the microwave background and further observations of supernovae with better detectors and new larger space telescopes in the future will tell us if the dark energy is a cosmological constant or a quintessence form. Results from the WMAP mission lean toward the cosmological constant form, but it might take the PLANCK mission to settle the matter. However, we have learned enough from the past few years of surprising observations to say that Einstein’s greatest blunder was saying that he made a blunder!

Vocabulary

• cosmological constant
• dark energy
• inflation

Review Questions 4

1. What is the “flatness” problem in the standard Big Bang theory? How is it a fine-tuning problem?
2. What is the “horizon” problem in the standard Big Bang theory?
3. What is the inflation extension of the Big Bang theory and when is thought to have occurred in the universe’s history?
4. How does the inflation extension of the Big Bang theory explain the “flatness” and “horizon” problems that are part of the standard Big Bang theory?
5. How do we know that quantum fluctuations – virtual particles exist?
6. What is the “cosmological constant” and why did Einstein invent it? Why did Einstein say that was a mistake? Why do cosmologists now say it was not a mistake?
7. How does dark energy affect the expansion of the universe?

Is this page a copy of Strobel’s Astronomy Notes?