The Hot Big Bang Theory

The Discovery of the Cosmic Microwave Background

Gamow's 1948 prediction would have to wait until 1965 before it was verified and even then, the discovery was accidental. However, this accidental discovery would later earn its discoverers' (Penzias and Wilson) a Nobel prize. This is also an illustration of the important role of chance in science. Often times true advancement in any field arises from accidental discoveries. Penzias and Wilson were scientists working at Bell labs at the time, exploring the newly opened world of Microwave communication. In order to determine the signal strength that would be necessary for good communication, it was important to measure the ambient background noise that the signal would have to compete against. So a Microwave telescope was fashioned and Penzias and Wilson set out to map out this noise. They immediately noticed that no matter where the telescope was pointed, microwave flux was received. Originally, they thought the source was terrestrial in origin but further observations showed that there wasn't any 24 hour modulation of the signal. This lead to one only conclusion. Since the flux density of microwave photons arriving at their millimeter receiver was independent of position on the sky, the source had to be cosmological in origin. More precise observations were later made which showed that this background had a spectrum which was consistent with that of a blackbody, as predicted earlier by Gamow. This radiation is the Cosmic Microwave Background or CMB.

Figure 2.5 Blackbody fit to the 42 spectral data points obtained by the COBE satellite in 1990. The near perfect fit to the data indicates that the background radiation is like that of a blackbody, as predicted from simple thermodynamic arguments.

We thus have arrived at our second important cosmological observation - namely, the Universe is filled with a photon background whose energy today peaks in the Microwave part of the spectrum. In fact, the exact wavelength peak of this emission is directly related to the temperature, so if we can determine this peak we can determine the temperature (this is known as Wien's Law). In 1989 In 1989 NASA launched the Cosmic Background Explorer or COBE. COBE made very precise measurements of the background radiation. From the COBE spectrum (e.g. Figure 2.5) we know that the background temperature is 2.74 +/- 0.02 K. This is one of the most precise cosmological measurements ever made and any cosmological model must be able to predict the existence of this radiation and its nearly perfect blackbody character.

The Hot Big Bang Model

On the basis of two fundamental observations, 1) the Universe is currently in a state of uniform expansion and 2) the Universe is filled with photons, we can construct our general cosmological model, which is known as the Hot Big Bang model. While the details of this model will be elucidated in the coming chapters, its synopsis is simple. The Universe started, for reasons unknown to us, in a very hot and dense state and has been expanding and cooling ever since. While this model can explain several of the observed features of the Universe, we will come to learn that it can't explain everything and there may be serious challenges to it. However, the model is only 30 years old so we should not expect it to be a complete description of the Universe and in fact, should demand that its capable of being modified based on new data.

What the model can explain in overall terms is the following:

The Origin of the CMB: This is a simple consequence of the Universe being filled with energy (photons) in its past. The source of these photons is matter-anti-matter annihilation which is explored in the next Chapter. Once this energy/photon background is created, it cools with the expansion of the Universe and produces the background observed today. The intensity of the CMB corresponds to a space density of roughly 400 photons per cubic centimeter. When compared to the space density of particles, say, protons, one finds that for every particle of matter in the Universe, there are approximately 1-5 billion photons. This is known as the entropy of the Universe or the photon-to-baryon number. Thus, the number of photons in the Universe greatly exceeds the number of matter particles. This will have important implications on how the Universe evolves.
The Uniform Expansion of the Universe: By simple extrapolation to very small times, the currently observed expansion law, V=HD, must produce a situation where all the matter is concentrated into a small volume. At some point in this small volume, unknown physics initiated the expansion which caused the background radiation to continuously cool. Since the expansion has no preferred direction, the Universe is isotropic. This helps to explain the remarkable uniformity of the CMB - no matter where you look, you observe the same thing. This is a strong indication that the Universe is homogeneous as well.
The Abundance of Light Elements: This will be discussed in detail in the next Chapter. For now we just note the following generality: a hot dense early Universe would have gone through a period of nucleosynthesis that produced the light elements like Deuterium, helium, and Lithium. The overall cosmic abundance of these elements is related to the relative matter and energy densities and the temperature of the Universe at early times. From this, predictions can be made on what this abundance is. The observed helium abundance agrees with the prediction of the hot, dense Universe model.

As we will discuss later, the major unknown in the Big Bang model concerns the origin of galaxies and the development of the complex large scale structures that galaxies are embedded in. To understand this, we will have to appeal to the existence of dark matter. The presence of dark matter is not necessarily a general feature of Big Bang models and to account for it will require some modification known as the Inflationary paradigm.

The Geometry of the Universe

General relativity established the relation between mass and space. Mass causes a curvature in space time. The greater the mass, the greater the curvature. We can visualize this in the following figures which represent a 2D analog to the Universe. In the top row of Figure 2.6 we have a thin 2D rubber sheet. There is no mass embedded in the surface and the rubber sheet is therefore not distorted and remains flat. In the middle row we see the effects of placing a large mass on this rubber sheet. The large mass causes the surface to deform creating curvature in otherwise flat space. This curvature represents the gravitational potential well of that mass. Imagine rolling a ball bearing on this surface. If you gave the ball bearing insufficient energy and it found its way into a potential well, it would not come back out. It would stuck at the bottom of the well. This, in essence, is how gravity can capture material locally. Once mass is in a gravitational field (i.e. in a potential well), it has a tendency to stay there unless it can acquire enough energy to escape (climb out of the potential well)

In the bottom row we see the effects of varying masses placed on the sheet. Each mass causes an indentation which represents its own gravitational potential well. You can see that the depth of the indentation is larger the more mass there is, indicating a higher degree of curvature at this location in the Universe than is seen around the smaller masses. Correspondingly,it would take even more energy for a particle to climb out of that potential well. If you imagine that you are a particle moving on this surface you can imagine moving in and out of different size potential wells. Between the wells space is flat, but while inside a well, space is locally curved by an amount directly proportional to the mass. Thus, the overall mass distribution of the Universe determines its geometry. This geometery in turn specifies the allowable pathways that matter and energy can take as they travel through the Universe.

Since Mercury is so close to the sun it actually orbits in curves space which causes its orbit to precess this is one of the major observational tests of Einstein's theory.

5 Figure 2.6: Mass and Curved Spacetime (see text)

In addition, the presence of matter in the Universe means that the expansion is steadily slowing down as the combined gravitational attraction of the matter acts to slow down the expansion. In fact, if there is sufficient mass in the Universe, the expansion will eventually slow down and cease, and the matter in the Universe will then attract into what is colloquially known as The Big Crunch. This condition is known as a closed Universe. Conversely, if there is insufficient matter in the Universe then the expansion will never stop, but merely slow down and asymptotically approach zero. This condition is known as an open Universe. As discussed in Chapter 4, our current estimates of the total mass density in the Universe are uncertain by at least a factor of 10 and so we do not know if the Universe is open or closed. While this is of scientific interest, it also raises a philosophical question which many consider to be profound. A closed Universe offers us the possibility that the Universe can be reborn, expand and re-collapse in an infinite number of cycles. We are simply now in one of those cycles. The next cycle might produce a Universe with a different set of physics that might or might not allow for the development of intelligent life. In contrast, an open Universe has the dubious distinction of happening only once and then expanding forever, never to re-collapse and begin again. This naturally leads to the question "What happened before the Universe" - a question that can't be answered with our current knowledge.

Figure 2.7 Schematic representations of the possible geometries of space time. These are two-dimensional analogs of curved space. In positively curved space the sum of the angles of a projected triangle on that surface is greater than 180 degrees while in negatively curved space the sum is less than 180 degrees.

The large scale geometry of the Universe is different whether it's open or closed. The possible geometries are shown in Figure 2.7. In the case of the closed Universe, the curvature is positive, much like a basketball. If one draws a triangle on that surface the sum of the angles is greater than 180 degrees. In addition, two light rays which are initially emitted in parallel will eventually cross after they have traversed the curved surface. In the case of positive curvature, the surface is attached to itself and that is the sense of the term "closed". This closed surface will expand to some maximum radius before re-collapsing. An open Universe has negative curvature, which is represented by the saddle surface in Figure 2.7. In this case, parallel light rays will diverge, the sum of the angles of a triangle is less than 180 degrees and the surface does not "connect" to itself. Thus, the surface just keeps expanding and does not reach a maximum radius. The boundary between the open and closed Universes is a special case called a critical Universe in which space is perfectly flat on large scales. We will later see that flat space is one of the specific predictions of the inflationary theory for the origin of Universal expansion in which case the Universe has a very specific mass density.

Summary:

The development of the Cosmological Principle that asserts the Universe is homogeneous and isotropic. This means that any physics which acts locally acts the same way elsewhere in the Universe. The understanding of the motion of double stars in terms of Newtonian gravity served as empirical proof that the same physics that governed the orbital mechanics in the Solar System also worked millions of kilometers away.
Einstein was able to explain the positional discrepancy of Mercury by postulating that gravity was the manifestation of curved spacetime. The more mass that can be accumulated in one position in the Universe the greater the curvature of spacetime would be. The relation between mass and spacetime forms the precepts of General Relativity.
Einstein also showed, through the principle of equivalence, that mass and energy are the same thing. The relation E = mc² shows that photons have an energy related mass and thus are subject to gravitational forces. In addition, the conversion of mass into energy provides the explanation for the tremendous energy sources of the stars. The principle of equivalence was also the result of Einstein's demand that the speed of light, c is a universal constant that doesn't depend on the motion of the source emitting the light. This is a requirement if causality is to be present in the Universe.
Einstein thought the Universe was static but realized that some presence must exist to prevent it from collapsing. Out of this realization he formed the Cosmological Constant, a vacuum energy field that exactly balanced the gravitational attraction of all the mass in the Universe. When the Universe was later discovered to be expanding, Einstein called the development of the Cosmological Constant his "biggest blunder".
Over the period 1914 -- 1929, observations of galaxies revealed systematic redshifts. By 1929 Hubble used these observations to demonstrate that the Universe was expanding in a uniform fashion. This lead to the Hubble expansion law:
V_r = H_oD

H_o is the expansion rate of the Universe and H_o^-1 specifies the expansion age.
The discovery of the expansion of the Universe meant that in the past the Universe was a very dense place as all the matter must have been together. Equating the expanding Universe to an expanding bubble of gas, physicists postulated that the Universe could be filled with radiation, whose pattern was that of a blackbody radiator, whose average temperature was decreasing with the expansion.
The discovery of the Cosmic Microwave Background (CMB) in 1965 confirmed the existence of this radiation field. The ratio of observed CMB photons to matter was about one billion to one. This implies that the Universe was also a very hot place at early times.
These two observations lead to the development of the Hot Big Bang model. That model explains three crucial observations: 1) the existence of the CMB, 2) the uniform expansion of the Universe and 3) the abundance of light elements in the Universe (principally helium).
Under the assumption of large scale isotropy and homogeneity, a geometric model of the Universe can be specified. This model has three parameters: 1) the expansion rate H_o, 2) the matter density W, and 3) the vacuum energy field L. Under this model the universe is either open (expands forever) or closed (expands to some maximum radius and then collapses).