The Big Bang

The history of the universe following t=0, the time of the Big Bang, can be divided into two major eras: the radiation era and the matter era. Stars are made of matter and they form when particles gather together through their mutual gravitational attraction. The action of radiation (radiation in this context means photon, or light particles) is to try and blow apart such accumulations. During the radiation era, the pressure generated by photons impinging upon any particles overwhelms any mechanism such as gravitation which tries to pull them together to form structures. At temperatures > 3000 K the various materials that make up the universe are on the whole distributed uniformly throughout space, forming no complicated structures. In such an environment, many atoms are ionized. Hence, the radiation era in its latter stage consists predominantly of a plasma of electrons, protons, simple atomic nuclei and photons.

Again, the term radiation means --- light, or photons, of all forms. It comprises an entire spectrum from the most energetic gamma-rays to the weakest radio waves. The term, matter means anything that is made out of the fundamental particle building blocks, quarks and electrons. For example, hadrons (Latin meaning heavy particles) consist of either three quarks (which make up protons and neutrons among other things) or two quarks which make up somewhat lighter particles of an intermediate mass called mesons. Atoms and molecules consist of combinations of protons, neutrons and electrons. All matter is thus a combination of quarks and electrons.


All matter has a rest mass, m. This means that we can slow it down, stop it and "hold it in our hands", in a manner of speaking. It can never be made to travel faster than the speed of light, c=3 x 108 m/s. Light, or radiation, has no rest mass. If you stop it from moving, you "destroy" it, i.e., it gets absorbed by the matter that is used to stop it from moving. When it moves, it does so at the speed of light -- always.


Prof Einstein tells us that energy and mass are, in essence, equivalent. This equivalence is expressed by the famous equation

E = m c2

Thus, even though light has no rest mass, it does have an equivalent mass by virtue of its energy, as do all things. The energy of light is given by the expression

E = h f = h c / l

h = Planck's constant = 6.62 x 10-34 kgm2/s, f is the frequency of the light and l is its wavelength. A "bundle" of this light energy is a particle, called a photon. The effective mass of a photon is given by the expression

m = E / c2 = h f / c2 = h / l c

Now, right after the Big Bang went off, the Universe was filled mostly with pure energy in the form of light photons. The energy (or mass, since they are essentially equivalent) density was enormous and this light, or radiation, could interact with itself to produce matter and it did just that. This process in which real particles with a rest mass were produced is called pair production: two photons collide and merge; they disappear and their energy is directly converted into matter and anti-matter such as a quark anti-quark pair. As the number of such particles increased, the real particles and anti-particles could annihilate, creating two photons in the process. Eventually, the matter and radiation formed sort of a hot primordial soup filled with particles, anti-particles and photons almost in equilibrium in an on-going process of creation and destruction of matter. But mostly, the universe was filled with radiation and little matter. As the universe expanded and cooled, both matter and radiation were losing energy but radiation was losing it faster since its wavelength l was being stretched by the expansion of space. Both radiation density and the matter density were decreasing as the universe cooled and expanded, but the radiation density was dropping faster. The point where the two densities crossed over marks the transition from the radiation era to the matter era. This transition occurred about 3 x 1010 seconds or about 1000 years after the Big Bang. We now live in the matter era, or an era in which matter dominates the structures that are now emerging in our universe.











 

I. The Radiation Era (from age 0 to 1000 y)

Time (s):

Radius (m):

Density (kg / m 3):

Temperature(K):

< 10 -43

<10 -52

>10 95

>10 32


We cannot say what happened within the first 10-43 seconds of the Big Bang. We believe that the four known forces (gravitation, weak, electromagnetic and strong) that describe the behavior of all particles at this current epoch were completely indistinguishable from one another during those first fleeting moments of the early universe. In other words, there existed only one fundamental, unified force that described the behavior of everything that existed. The conditions of the universe of the universe were so bizarre that gravitation behaved in a way that could only be described in a quantum mechanical way. We have no idea how to formulate a quantum theory of gravity. Our knowledge of physics fails us here. Thus, we cannot intelligently discuss what went on during the first 10-43 seconds! We call this epoch --- the Planck epoch, after Max Planck, one of the founding fathers of the theory of quantum mechanics.


We do know, however, that when this epoch ended, the force of gravity "split off" apart from the remaining unified quantum force and from that point on could be described with great accuracy by Einstein's general theory of relativity. We also know that the universe was filled with a soup of photons and exotic particles created by the process of pair production.

 

Time (s):

Radius (m):

Density (kg / m 3):

Temperature(K):

10 -43 - 10 -35 s

10 -52 - 1 m

10 95 - 10 75 kg/m3

10 32 - 10 27K

 

During this time, the strong, electromagnetic and weak forces were unified. There was no discernible difference between them. The behavior of this unified force is described by a grand unified field theory, or GUT, for short. At this time, the temperature of the universe was so great that the process of pair production was generating all sorts of particle anti-particle pairs. Many of the pairs were the extremely massive grand unified x particles and their corresponding anti-particles, denoted here as x. The number of these particles grew to the point where as many were being created by radiation as were being destroyed by annihilation, converting back to radiation in the process. The amount of radiation and numbers of x, x pairs were in equilibrium. As the universe expanded, cooled and aged from 10 -43 to about 10 -35 s, these x, x pairs would mostly annihilate, but a number of them would remain as the end of the GUT epoch approached.


At around 10 -36 seconds, though, something incredibly interesting happened in the universe. It cooled to a temperature of about 10 29 K where it underwent a phase transition. It is analogous to the phase change that occurs when liquid water cools to ice at 273 K. There is no alignment of atoms that make up water when it is at a temperature higher than the freezing point. Imagine that you are submerged in a deep ocean of water. You have no sense of up, down --- front, back --- or left, right. Any direction looks the same as any other. The water thus exhibits a symmetry. This state of perfect symmetry of water is broken, however, when it freezes into ice. Ice has a crystalline structure with well defined x, y, z directions in space that line up along the crystalline axes. This is shown schematically in the accompanying figure. If you were embedded in a large cube of ice and you had the right sensors, you could tell which direction was up, down --- front, back --- or left, right. The state of "water" is not perfectly symmetrical at temperatures below the freezing point where it turns to ice. Liquid water has no such natural coordinate system.



This loss of symmetry that occurred in the universe when it cooled below 10 29 K manifested itself by a splitting of the grand unified force into two distinct forces: the strong force and a residual, unified electro-weak force. x and x particles could no longer be created by radiation interacting via the grand unified force. The grand unified force no longer existed and temperatures in the universe were now too low. Those x and x particles that remained then decayed into combinations of quarks, anti-quarks, electrons and positrons but the decay was now asymmetric: that is, the x and x decayed at different rates leaving a slight excess of quarks over anti-quarks. This decay rate asymmetry was the one of the discernible differences in behavior between the strong force and the electro-weak force. At the high temperatures that exist during the GUT epoch, x and x behave the same way; at the lower temperatures that occur following this epoch, they do not. The decays are mediated by the electro-weak force and this force acts differently on anti-particles than it does on real ones. It is this effect that ultimately led to our universe being constructed of matter and not anti-matter since matter is made from those quarks that did not annihilate with the slightly less abundant anti-quarks.


This "phase transition" had another enormous effect on the structure of the universe, beginning around 10 -36 seconds and continuing somewhat into the following epoch of the hadrons: the universe underwent a period of incredibly rapid expansion driven by the release of energy that occurred during the phase transition. Again, this phenomenon is akin to the energy that is released when water freezes into ice. As water freezes, the water molecules change from a state of random, dis-ordered motion into one where they are highly ordered and relatively fixed in position. The molecules thus go to a lower state of energy and heat energy is released in the process. Ask any fish in a lake about this phenomenon. If energy were not released as the top surface of the lake froze, the water underneath would not remain liquid and it would freeze, too. This energy release in the early universe maintained a constant energy density during its subsequent period of expansion which in turn generated an outward pressure that drove the expansion at an exponential rate. This incredibly rapid expansion that resulted from this process has been given the name inflation. The space between particles actually stretched out faster than the light travel time between them. Any gross inhomogeneities that existed in the universe as a whole would no longer be visible to us. Thus, our observable universe now consisted of a highly inflated region of smoothed out, relatively flat space that had once been extremely small.

 

Time (s):

Radius (m):

Density (kg / m 3):

Temperature(K):

10 -35 - 10 -4

1 - 2 x10 15

10 75 - 10 16

10 27 - 10 12

 

During this time, the temperature was hot enough for the radiation to produce all the currently known hadrons (except the x and x particles). The universe thus consisted of a soup of radiation, in equilibrium with the heavy particles, anti-particles and leptons (electrons, positrons, neutrinos and anti-neutrinos) that it produced. Mostly, though, it was a soup of photons, intermediate vector bosons (at these high temperatures, these particles behave like photons) quarks, anti-quarks, leptons and gluons. (Leptons are low mass or zero-mass particles like electrons and neutrinos. Gluons are particles that exert the strong force that binds quarks together in structures to form protons and neutrons.) However, at about 10-10 seconds, the temperature of the universe had cooled off to about 1013 degrees or so, too low to create intermediate vector bosons. This makes the weak force indistinguishable from the electromagnetic force. Thus, at 10-10 seconds, the final splitting of the unified force now occurred and the weak and electromagnetic force became distinguishable. From this point on, we have four completely separate forces in nature (strong, electromagnetic, weak and gravitational) and the future course of the universe would be determined by their characteristics.


Around 10 -5 - 10 -4 seconds, the universe cooled enough that all of our known hadrons (most prominently protons and neutrons) "condensed" out of this soup: that is, three quarks came together to form protons and neutrons, two quarks came together to form mesons and anti-quarks (those that had not yet annihilated) formed anti-protons, neutrons and mesons. Free quarks disappeared from the universe. From this point on, the only free, fairly stable particles in the universe were photons, leptons, protons and neutrons. These would form the building blocks of any subsequent structures.

 

Time (s):

Radius (m):

Density (kg / m 3):

Temperature(K):

10 -4 - 10 2 s

2x10 15 - 2x10 18

10 16 - 10 4

10 12 - 10 9

 

By this time, the temperature of the universe had fallen to the point where radiation could create only lepton pairs (electrons and their anti-particles, positrons) via the pair production process. Most of the protons and neutrons were annihilating with their corresponding anti-particles, but a small number would be left over at the end of this epoch. Thus, we now have a soup consisting mostly of photons in equilibrium with leptons with a small amount of heavy particles thrown in. Neutrinos completely decoupled from everything in the universe. The density of matter was now so low that these weakly interacting, neutral, zero rest mass leptons rarely interacted with any other form of radiation or matter. They were left to fly around through the universe --- ghost particles --- virtually unimpeded by anything in their path.

 

 

Time:

Radius:

Density:

Temperature:

10 2 - 3 x 10 10 s

10 19 - 10 22 m

10 4 - 10 -13 kg/m3

10 9 - 6 x 10 4K



The final significant event of the radiation era occurred during this epoch. Temperatures were now low enough that simple nuclear fusion reactions could occur between protons and neutrons to synthesize small amounts of deuterium (1H2 or D), Helium-3 (2He3), helium-4 (2He4) and lithium-7 (3Li7). This process is called primordial nucleosynthesis. An example of the fusion reactions that produce D, He3 and He4 are shown in the figure above. Nuclear species heavier than these were not created for two essential reasons: (1) free neutrons, i.e., those not bound up inside some nucleus, decay into a proton, electron and anti-neutrino with a half-life of about 10 minutes. Thus, they disappeared quickly in the early universe, (2) the universe was expanding rapidly and the temperature and density were dropping precipitously. Thus, subsequent fusion reactions that could create heavier nuclei had neither the fuel, nor the necessary energy required to initiate the fusion.



II. The Matter Era (from 3 x 10 10 s or 1000 y to Now)

Time (yr):

Radius (m):

Density (kg / m 3):

Temperature(K):

1000 - 10 6

4x10 22 - 10 24

10 -13- 10 -19

6 x 10 4 - 10 3

 

A critical change in the universe occurred at this time. The density of radiation dropped below the density of matter and at this point it failed to generate enough pressure to keep the negatively charged electrons from sticking to the positively charged nuclei that had been created during the nuclear epoch. Prior to that time the radiation was so intense that it broke apart any atoms that did momentarily form in the hot plasma that was then the universe. Furthermore, the kinetic energy of particles in this high temperature environment was still so great that atoms would get broken up into their constituent electrons and nuclei by the violence of any collisions among them. Thus, neutral atoms began to form, or "condense" out of the primordial soup.

Radiation does not interact easily with neutral atoms: it streams through a gas of neutral atoms rather easily. It does not do so in a gas of charged particles. Thus, as the neutral atoms formed, the universe suddenly became "transparent" -- as though a great fog had lifted and the radiation born in the Big Bang "decoupled" forever from the matter it had given birth to. From this point on, radiation would not provide much pressure to keep structures from beginning to out of this matter. This event was essentially complete when the temperature of the universe had fallen to about 3000 K at an age of about 300,000 years during the time that we now call the atomic epoch.

 

Time (yr):

Radius (m):

Density (kg / m 3):

Temperature(K):

10 6 - 10 9 y

10 24 - 4 x10 25

10 -19- 3 x 10 -25

10 3 - 10

 

With the removal of radiation pressure as a dominant force in the universe, gravity began to assert itself on the matter. We still do not understand the details of how galaxies, clusters and superclusters of galaxies actually formed. We do know that the matter in the universe must have been distributed in a way that was not completely smooth. There must have been large scale inhomogeneities in this distribution in order for matter to be pulled together by asymmetric gravitational forces. Evidence of such inhomogeneities is provided for us by measurements by COBE (COsmic Background Explorer) of inhomogeneities in the radiation left over from the Big Bang. This radiation was once strongly coupled to the matter it had produced and so any inhomogeneities it exhibits reflect any matter inhomogeneities that emerged as the universe entered the matter era. Be that as it may, large scale structures that turned into galaxies more or less as we see them now grew rapidly during this epoch.

Time (s):

Radius (m):

Density (kg / m 3):

Temperature(K):

10 9 - 15 x10 9 y

4 x10 25 -1.4 x10 26

3 x 10 -25 - 10 -26

10 - 3



By this time, galaxies, clusters and superclusters have pretty much formed. Stars are now the dominant structures being formed by gravitational collapse of the large clouds of gas and dust that make up galaxies. The collapse of matter into stars halts only when nuclear fusion starts in their cores which generate enough heat that the resulting pressure stabilizes the star against additional gravitational collapse. It is these nuclear fusion reactions in the cores of stars that generate all the elements in the universe from carbon-12 (6C12) up to iron-56 (26Fe56). Additional amounts of these elements as well as elements heavier than iron are formed via the process of explosive nucleosynthesis that occurs in the supernova explosions triggered by the catastrophic collapse of massive stars, which occurs after all energy generating fusion reactions in the star's core have been exhausted.



The universe itself has now expanded to a visible radius of about 3 x 1026 m and it has cooled to about 3 K. The CMBR (Cosmic Microwave Background Radiation) is the relic radiation left over from the Big Bang. Since it decoupled from matter at age about 500,000 years and temperature 3000 K, the universe has expanded about a factor of 1000 in size.







The significant events that we've just discussed are shown in the accompanying figure that depicts the expanding universe.

 

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