A.1 The Electromagnetic Spectrum
Figure A.1 shows the electromagnetic spectrum over a wide range of wavelengths. The units on the x-axis change from centimeters (cm) on the left to microns on the right to connect with the text. The scales merge at 0.1 cm = 1 mm = 1000 microns. Note that the wavelength gets smaller going to the right, which means that the energy of a photon increases going from left to the right.
Channel 83 on your TV, which is not in general use, has a wavelength of 34 cm. Microwave ovens operate at 12.2 cm. These are indicated as lines because most of the energy is concentrated near one wavelength. The cosmic microwave background (CMB) is a blackbody emitter that peaks near 0.1 cm but emits power over a large range of wavelengths. This is the same spectrum as shown in figure 2.1 but now in a broader context. The next vertical line shows the wavelength for the DIRBE image in plate 3. The spectrum labeled “Milky Way” corresponds to a blackbody at 30 K. The next spectrum is for a room temperature blackbody (300 K). IR cameras measure this thermal emission. The spectrum for the 6000 K Sun peaks around a wavelength of 0.5 microns. The gray scale corresponds to the colors of visible light our eyes detect and runs from red on the left to violet on the right. The UV spectrum is found at slightly shorter wavelengths. UV B radiation is at 0.3 microns. You can see that the Sun is still quite intense there, but we can’t see the UV light. Along the top of the plot are the designations for the “Microwave” wavelength band, “Far-infrared” band, and “Mid” and “Near” infrared bands. You can also see that the peaks of the four blackbody spectra follow the Wien displacement law.
FIGURE A.1.
A.2 Expanding Space
“Expanding space” is a controversial phrase. We use it simply as an intuitive description of the change in the scale of the universe with time. We take guidance from Einstein: “In that sense one can say, according to Friedmann,1 that the theory demands an expansion of space.” And “It is indeed an exacting requirement to have to ascribe physical reality to space in general, and especially to empty space.”
The coordinate system we use to measure the locations of objects in the universe is unambiguously expanding. At the same time, for most of the age of the universe, there is nothing that pushes galaxies apart that the phrase “expanding space” might bring to mind. Gravity is only attractive. The evolution of the universe during this time, over regions larger than shown in figures 1.3 and 1.4, can be described by giving the galaxies initial velocities and computing how they interact under the force of gravity.
However, for the past 4 billion years, since the cosmological constant has become the dominant form of energy density, a new force has come to dominate the universe that does indeed push galaxies apart. That force is quantified with the cosmological constant. Its action can be described as “expanding space” or “making space.” Similarly, if inflation is the correct model for the early universe, it too can be described as “expanding space,” but at an exponential rate over a very brief time. During inflation there is a force that pushes particles apart that is much stronger than gravity. The source of this force is an effective cosmological constant that is much larger than the one we currently observe.
There is another example of “making space.” If the universe were described by a closed geometry, corresponding to the righthand image in figure 4.1, the volume of the universe would be finite and would change with time. Space would indeed be created.
Understanding the nature of space—the nature of the vacuum—is at the forefront of physics. We do not understand the vacuum at a deep level. For some situations, we are almost forced to think of space as expanding, whereas for others the expansion of space may lull us into thinking there are forces that don’t exist. Nevertheless, we find the concept of an expanding space useful for envisioning many aspects of the universe.
A.3 Table of the Cosmic Time Line
|
Age |
Compactness or Scale Factor |
Event |
|
0 |
Minuscule! |
Our definition of the “Big Bang.” §1.2, §1.3 |
|
1.4 × 10−14 sec |
2.2 × 10−17 |
Typical energy of a photon equals the particle interaction energy at the Large Hadron Collider. §2.1 |
|
0.000025 sec |
1 × 10−12 |
Quark-gluon plasma as seen at RHIC. §2.1 |
|
3 min |
3 × 10−9 |
The nuclei of H, He, Li, and Be formed. The temperature was 1 billion K. §2.1, §2.4, §4.3 |
|
1 year |
1 × 10−6 |
Appendix A.4. |
|
51,000 yrs |
0.00029 |
“Matter-radiation equality.” The dominant form of energy density changes from radiation to matter and cosmic structure can start to grow. §2.4 |
|
400,000 yrs |
0.001 |
“Decoupling.” Hydrogen atoms form and the CMB is free to roam the universe. Some call this time “recombination.” §2.4, §3.2 |
|
1 million yrs |
0.0017 |
|
|
200 million yrs |
0.05 |
First objects form. §1.6, §2.4 |
|
370 million yrs |
0.078 |
Most distant object yet identified. §A.4 |
|
0.4–0.7 billion yrs |
0.08–0.12 |
Most distant objects in the Hubble Ultra Deep Field. §1.6, §2.4 |
|
0.5–1 billion yrs |
0.1–0.15 |
“Reionization.” The universe was reionized by the first stars and the free electrons scatter 5–8% of the CMB photons. §2.4, §4.3 |
|
5.9 billion yrs |
0.5 |
Universe is twice as compact. §1.3, §1.6 |
|
9.3 billion yrs |
0.71 |
Time when the Earth and Moon appeared. §1.3 |
|
10 billion yrs |
0.75 |
“Matter-Λ equality.” The dominant form of effective energy density changes from matter to dark energy. §2.4 |
|
13.7 billion yrs |
0.993 |
Dinosaurs roamed the Earth. §1.3 |
|
13.8 billion yrs |
1 |
We live in a ΛCDM universe. |
For the extremely small numbers, we have had to introduce scientific notation in which the exponent tells where to place the decimal point. For example, 1 × 102 = 100 and 1 × 10−2 = 0.01. The compactness is the number by which one should multiply the scale of the current universe to determine how much closer objects were in the past.
A.4 The Observable Universe versus Time
Figure A.4 shows the size of the observable universe versus its age. In going from left to right, the vertical dashed lines show when cosmic structure started to grow (section 2.1), when the CMB decoupled from the primordial plasma (section 2.4), and the “distance” to one of the farthest identifiable objects.
When we see a distant object, often the first question that jumps to mind is “how far away is it?” For the universe, we have to be especially careful in specifying when we want to know how far away it is. As light propagates to us from a distant object, the universe expands. By the time we receive the light, the universe has expanded. Although the “light travel distance” back to the Big Bang is 13.8 billion light-years, over that 13.8 billion years the universe has expanded a huge amount so its current “radius,” called the “comoving distance” in scientific literature, or more popularly the radius of the “observable universe,” is 46 billion light-years. This corresponds to 92 billion light-years in diameter, about three times the size we gave in section 1.4.
FIGURE A.4
The natural way to think about the universe is in terms of its compactness or “scale.” We ask its age and size with regard to when it was 10 or 100 or a billion times more compact. The reason for this is that the fundamental physical properties—the temperature, the densities, the rate of expansion, etc.—depend on the compactness. Then, from the history of compactness, we deduce the age and size. For example, from the lefthand side of the figure we read that when the universe was one million times more compact, it was one year old, and the size of the observable universe was a couple of million light-years. At this time the CMB was one million times hotter because temperature is directly proportional to compactness.
One of the farthest identifiable objects is a galaxy called EGSY8p7. The light from it started on its way to us when the universe was about ten times more compact. The light we now observe was emitted when the universe was 0.6 billion years old and so has been traveling to us for 13.8 − 0.6 = 13.2 billion years. In plate 5 this is in the purple band that the Hubble Ultra Deep Field can reach. The question of “how far away is it” isn’t really the right question to ask because the universe has expanded so much since it emitted the light we just now observe.
We could have extended the lefthand side of the plot much further. Some earlier times and associated events are given in appendix A.3.
1 Alexander Friedmann derived the equations that describe cosmology from the general theory of relativity as discussed in section 2.3. The quotes are from Relativity by Albert Einstein, Crown Publishers, 1961.