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The Observable Universe and Beyond

Big Bang Theory

cosmic expansion In 1922 Alexander Friedmann predicted the Big Bang cosmology, which portrays the universe as expanding space from a point where the matter-energy density was extremely high. The expansion can be visualized by a two dimensional analogy as shown in Figure 02-02. As the balloon expands, all the points on the surface recede from each other, and the wavelength on the surface is stretched. It is similar to the shift to longer wavelength when the source and receiver are moving away from each other. This phenomenon is called red shift of the spectrum because in visible light the shift to longer wavelength is toward the red colour. It plays a prominent role in discovering the cosmic expansion through the detection of the spectral line shift from distant galaxies.
Note that contrary to the balloon analogy, it is the space itself that is expanding. It needs neither a center to expand away from nor empty space on the ouside to expand into.

Figure 02-02 Cosmic Expansion
[view large image]

This simple picture of expanding universe with all the galaxies flying away from each other remained unchanged until the 1980s when the Inflation Theory was introduced to resolve a number of discrepancies. The rapid expansion occurred at the interval between 10-35 sec and 10-32 sec. It predicts a much smaller universe near the origin of the Big Bang such that the matter-energy within can be mixed evenly as reflected in the CMBR mapping. It also predicts that the geometry of the Universe is flat1. Events before the inflation is essentially unknown. It is subjected to a lot of speculations. For example, it is suggested that space-time may be created from vacuum fluctuation - the quantum foam; and that the four fundamental forces may be unified to just one kind (as envisioned by the grand unified theories). Baryongenesis (generation of quarks and anti-quarks which has a baryon number of 1/3 or -1/3) happened in an epoch before inflation, when a imbalance between matter and anti-matter was established by a quantum process called CP violation. Quarks and anti-quarks combined to form baryons and mesons at 10-5 sec. Nucleosynthesis started at about 3 min. During this epoch the light chemical elements were produced from protons and neutrons. The universe was still opaque up to 380,000 years when neutral atoms started to form and the radiation was able to escape as shown by the CMBR. This epoch is called decoupling to indicate that matter and radiation are separated. From then on matter had a chance to condense into stars and galaxies and evolved to the present-day universe. Figure 02-03a shows the history of the universe according to the Big Bang Theory. Table 02-01 summarizes the major events during the course of the cosmic history.

cosmology Supplement to the legend of Figure 02-03a:

The quark (q), electron (e), and neutrino (n) are the fundamental particles. The corresponding anti-particle is labeled with a bar on top. The gluon (g) is the boson mediating the strong interaction between quarks. The vector bosons W and Z mediate the weak interaction between electrons/neutrinos and the quarks. The photon (wavy line) mediates the electromagnetic interaction between charged particles. One quark and one anti-quark combine to form a meson. Three quarks combine to form a baryon (proton, neutron, etc.). Protons and neutrons combine to form nucleus (ion). Nucleus and electrons combine to form atom. The muon (m) and tau (t) are the 2nd and 3rd generation of the lepton family, the 1st generation is the electron. (See more about elementary particles in Topic-15.)

Figure 02-03a History of the Universe
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Cosmic Expansion There are scales for the time t (in second), temperature T (in oK) and energy
E (in Gev) of the photon gas at the bottom of Figure 02-03a. These variables are related by the simple mathematical formulas:
For the earlier relativistic matter dominated era: E(Gev) = 2.76x10-3 / t1/2(sec) --- (1) where the proportional constant is calibrated with the Planck scale of
E(Gev) = 1.2x1019 Gev at 5.4x10-44sec.

Figure 02-03b Cosmic Expansion
[view large image]

For the non-relativistic matter dominated era: E(Gev) = 156x10-3 / t2/3(sec) --- (2)
where the proportional constant is calibrated with the CMBR temperature of 2.73oK at the present age of 13.7x109years.

According to Eqs.(1) and (2), the energy of radiation and matter became equal at about 1000 years after the Big Bang.

The energy and temperature are related by the formula:    E(Gev) = 10-13 x T(oK) ----- (3)

There is no such simple formula for the size R of the early universe and time until 10-32 sec at the end of the inflation. Their relationship during the earlier epoch can be obtained from a graph (Figure 02-03b, the numerical values are not reliable as the precise numbers are highly uncertain caused by missing details in the Grand Unified Theories). For the later period, a mathematical formula for the size and time can be found from the standard model curve on the same graph:

log[R(cm)] = 0.5036 x log[t(sec)] + 19.12 ----- (4)

where the constants are estimated by fitting two points on the straight line - one with the size of 1000 cm for the end of the inflation at 10-32sec, the other with the size of about 1028cm for the present age of 13.7x109years. Eq.(4) implies a relativistic matter dominated cosmological model with R ~ 1019x t1/2; because in the logarithmic scale, more than 90% of the graph is related to the relativistic matter dominated era. It also equates the distance to the cosmic horizon (in the present) to be the size of the universe, which in general are not equal.

Table 02-01 depicts the sequence of events after the Big Bang in time order. The relics and observables are physical facts, while the interpretations of the events are mostly theories or conjectures.

Era Time Size Energy or
Relics & Observables Events
Planck era < 10-43 sec < 10-50 cm > 1019 Gev 4-dimensional spacetime;
cosmic expansion
Smallest unit of space-time started to expand; all forces united into one
GUT era < 10-35 sec < 10-47 cm > 1014 Gev Super-heavy particles; fundamental interactions Separation of spacetime and matter; gravitational, strong, and electroweak forces
Inflation < 10-32 sec < 1000 cm > 1013 Gev Observable universe;
large scale structures
Unstable vacuum;
quantum fluctuations
Electro-weak era < 10-10 sec < 1014 cm > 100 Gev Radiation; excess of matter over antimatter; separation of force and matter fields Radiation released in reheating; baryon-antibaryon asymmetry; separation of weak and electromagnetic forces, origin of mass
Strong era < 10-4 sec < 1017 cm > 200 Mev Exotic forms of dark matter Formation of hadrons from quarks including neutrons and protons
Weak decoupling < 1 sec < 1019 cm > 3 Mev Hydrogen nuclei domination Neutrinos decouple, neutron/proton ratio fixed
Nucleo-synthesis < 100 sec < 1020 cm > 200 Kev Light element abendances: D, He, Li Nuclear reactions freeze out, stable nuclei form
Spectral decoupling < 106 sec < 1022 cm > 3 Kev Blackbody background radiation End of efficient photon production
Matter ~ radiation < 104 yrs < 8x1024 cm > 3 ev Mass density fluctuations Matter density ~ radiation density
Recom-bination < 0.4 My < 5x1025 cm > 3000oK CMBR e- and p+ recombine into H atoms, universe transparent to light
Dark ages < 1 Gy < 3x1027 cm > 15oK First stars, heavy elements mass fluctuations grow, first small objects coalesce, reionization
Galaxy formation < 2 Gy < 4x1027 cm > 10oK Stars, quasars, galaxies Collapse to galactic systems
Bright ages < 13 Gy < 9.7x1027 cm > 2.8oK Milky Way and Solar System Gas consumed into stars, remnants, planets
Present era ~ 13.7 Gy ~ 1028 cm ~ 2.73oK Supercluster Large scale gravitational instability

Table 02-01 A History of Cosmic Expansion

In an effect to learn more about the processes occurred in the early universe, which was associated with very high energy as shown in Table 02-01. Particle Physicists have been simulating the condition in the laboratory with high energy particle accelerators (see the entries in top left of Figure 02-03a). In collaborating with the theory of elementary particles, experiments are developed to investigate the creation of fundamental particles, and their properties. A list major discoveries is shown in Table 15-01a. The cosmic history is shown with a lot of sight and sound in an animation called "The Big Bang Tour".

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