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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 [view large image]

Cosmic Expansion There is a scale with time t, temperature T, and energy E for the photon gas at the bottom of Figure 02-03a. A corresponding table below narrates the sequence of cosmic events in text. The running variable is the time t (in sec), which relates to size of the observable universe by L = c t (in cm), where c = 3x1010 cm/sec is the speed of light. The energy (E) from BB to the end of inflation are taken from scientific literatures (Figure 02-03b). Energy for the radiation era can be computed by E (in Gev) = 1.73x10-3/t1/2. See "Standard Cosmology".

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

In terms of the length scale L and time t, the formula for the unobservable expansion is :
log(L) = 21.2 + 0.6 log(t); while for the observable expansion, it is : log(L) = 10.5 + log(t), see Figure 02-03b.
The above formulas show that as the rate of expansion of the observable universe is greater than the unobservable one, the boundaries will merge in about 1010 Gy (a long long time comparing to the current age of 13.7 Gy). There will be no event horizon afterward.

BTW, the temperature T (in oK) is related to the energy E (in Gev) by the formula T = 1013xE.
Radiation Era : 10-32 sec - 0.24 My; Matter Era : 0.24 My - present; 1 year = 3.1557x107 sec.

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
@ end of era
Size (observable)
@ end of era
@ end of era
Relics & Observables Events (as re-constructed from theories)
Planck era < 5.4x10-44 sec < 1.6x10-33 cm > 1.2x1019 Gev (3+1)D space-time;
cosmic expansion
Expansion started from a point to Planck scale; all forces united into one
GUT era <10-35 sec < 3x10-25 cm > 1014 Gev High energy cosmic rays; fundamental interactions Separation of spacetime and matter; separation of gravitational, strong, and electroweak forces
Inflation (Rate of Expansion >>> c) < 10-32 sec < 3x10-22 cm = observable size
< 100 cm (unobs.)
> 1014 Gev Un-observable universe;
large scale structures
Reheating; Unstable vacuum;
quantum fluctuations
Electro-weak era < 10-11 sec < 0.3 cm
(see size scale)
> 300 Gev Radiation; excess of matter over antimatter; separation of force (bosons), and matter (fermions) fields Radiation released in reheating; baryon-antibaryon asymmetry; separation of weak and electromagnetic forces; origin of mass
Hadron era < 1 sec < 3x1010 cm > 1.7 Mev Formation of hadrons Axion as dark matter
Weak decoupling < 4 min < 7x1012 cm > 100 kev neutron/proton ratio fixed Neutrinos decouple
Nucleosynthesis < 1/2 hour < 5x1013 cm > 40 Kev Fraction of Light elements Nuclear reactions freeze out, stable nuclei form
Radiation era Matter era < 0.24 My < 2x1023 cm > 0.6 ev Mass density fluctuations Matter density finally exceeds radiation density
< 0.3 My < 3x1023 cm
> 3000oK CMBR e- and p+ recombine into H atoms,
universe became transparent to light
Dark ages
< 1 Gy < 1027 cm > 100oK 21 cm radio emission,
First stars, heavy elements
mass fluctuations grow, first small objects coalesce, reionization
Galaxy formation < 2 Gy < 2x1027 cm > 70oK Stars, quasars, galaxies Collapse to galactic systems
Bright age of Galactic Clusters < 12 Gy < 1028 cm > 3oK Solar system; decline of stellar formation from peak dark energy became dominant;
formation of clusters of galaxies
Present era ~ 13.7 Gy ~ 1.3x1028 cm ~ 2.73oK Supercluster Large scale gravitational instability

Table 02-01 A History of Cosmic Expansion (click image to enlarge)

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 also shown with a lot of sight and sound in an animation called "The Big Bang Tour". If pictures, table, and video all fail to convey some idea about the history of universe; there is a set of "Cosmic Scales", which relates the time, size, energy and simple description of events, by Fermilab to help easier visualization (hopefully).

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