Illustrations Courtesy of Alfred T. Kamajian Part-2 - Remote Sensing Application - Completely Remote Sensing, GPS, and GPS Tutorial
Illustrations Courtesy of Alfred T. Kamajian Part-2

On the left side is the model that equates the radius of the observable Universe with the age (rounded off here at 14 b.y.). This just assumes a "static" condition in which the age is determined by light speed alone. Light from the yellow spiral galaxy (which is the most distant from Earth) in the top panel left 14 b.y ago and arrives now in the bottom panel. But, in actuality, during that 14 billion years, the Universe has continued to expand. If one assumes a expansion factor of three during the 14 b.y. time interval, the situation is as pictured on the right. The light emitted from the galaxy has in 14 b.y. had to travel an ever enlarging space, so that today the galaxy is at least 42 billion years distant from Earth. Since we don't know where Earth really is in this finite Universe, it is currently impossible to determine the actual farthest points in opposing directions [on the sphere model, or on the flat model. But this diagram is important in indicating the Universe is really larger than the 28 billion light year dimensions cited above. How much larger is still speculative: Since we haven't any direct information about the extent of galaxies beyond the observable Horizon, we cannot specify a known size; several proposed models arrive at different dimensions including those greater than 42 billion light years.

Perchance at this point you may be confused a bit by these "heady" concepts. Some insight and a fresh look might result by checking these Expansion of Space, Gary Felder, Wikipedia and Prof. Seligman Internet sites.

Commenting further on the Universe's geometry: One view holds the present Universe to be finite but without boundaries. Its temporal character is such that it had a discrete beginning but will keep on existing and growing into the infinite future (unless there is sufficient [as yet undiscovered] mass to provide gravitational forces that slow the expansion and eventually cause contraction [collapse]). A much different model considers the Universe to be infinite in time and space - it always was and always will be (philosophically, these can be tied to concepts that equate God as an "intellectual presence" distributed throughout this naturalistic Universe)

Models for the Universe's shape hold it to be analogous to spherical, hyperbolic, or flat. A parameter called critical density (Ω) determines the shape (page 20-10). This diagram illustrates the three types:

The three general shapes of the Universe

In addition to specifying the Universe's shape, cosmologists seek to know whether it is open or closed, whether it is presently decelerating or accelerating, and whether it is infinite or finite in time and space - these topics are treated in detail on pages 20-8, 20-9, and 20-10. For now, lets preview these topics by saying that the prevailing view is that the Universe is flat, is open, and is accelerating its expansion.

Einstein, in particular, showed that any three-dimensional expansion must also consider the effects of the fourth dimension - time - to account for the behaviour of light traveling great distances in a vast "volume" (without known boundaries) making up what we conceive of as "space". He also deduced that space (within the Universe) must be curved (and light and other radiation will therefore follow curved paths as the shortest distance between widely separated points) and would, in his view, expand dynamically in a 4-dimensional spherical geometry (a spacetime dimensionality). (Einstein, at least in his early thinking, also considered the Universe to be finite and eternal; he did not take a firm stand on its overall shape.) As was considered in the Preface, the internal curvature of space was deduced by Einstein to be the consequence of the interaction between matter (responsible for gravity) and the "fabric" of space. These two diagrams depict this:
Interaction of Matter and Space geometry.
The warping of flat space (indicated as a 2-dimensional grid).

The next figure is a spacetime diagram that summarizes the history of the expanding and evolving Universe in terms of the general or Standard Big Bang (BB) model for its inception:

A model for the history (Era�s) of the Universe based on Big Bang expansion; time is the ordinate; the abscissa describes the growth of the dimensions of the Universe in light years; much of what happens in the first few minutes is generalized here (see text).

From J. Silk, The Big Bang, 2nd Ed., © 1989. Reproduced by permission of W.H. Freeman Co., New York

Each major step in this time history of the creation and development of the physical Universe will be reviewed in some detail later on this page. For now, the diagram lets us extract this sequence: 1) By the end of the first millionth of a second, hadrons (quarks that make up baryons [including protons and neutrons] and mesons) had formed; 2) in the next interval of time up to 1 second leptons (electrons, muons, and neutrinos) came into existence; 3) over the next 1000 or so seconds nucleosynthesis of mostly Hydrogen, some Deuterium, priordial Helium, and a tiny amount of Lithium occurred, that is, their nuclei started to form; 4) as expansion continued over the next several hundred thousand years, the particles in this young Universe would remain invisible to any backward-in-time-looking detector because of "opaqueness" imposed on the photons by the free electrons (not yet coupled with atomic nuclei) that interact with the photon "fog"; 5) thereafter, the nucleons consisting of H and He protons and neutrons began to combine with electrons in the process of decoupling; 6) during the post-decoupling stage in the first million years the now stable atoms of Hydrogen and Helium started to clump together into gaseous clouds and then stars to form the first galaxies.

A variation of this figure with additional information appears below:

Another diagram showing the history of the Universe.

The Big Bang as an expansion theory traces its roots to ideas proposed by A. Friedmann in 1922 to counter ideas attendant to Albert Einstein's Theory of General Relativity, from which that titan had (erroneously) derived a model of a static, non-expanding, eternal universe (he eventually abandoned this model as evidence for expansion was repeatedly verified and he realized his General Relativity proved very germane to the expansion models). This fundamental equation, which introduces the Scale Factor R (see page 20-8), can take several forms, one of which is (see caption for units):

One form of the Friedmann equation; R is a curvature of space factor; G is the Universal Gravitation constant; rho is density.

Multiplying each term by R2 yields this equation which expresses the rate of change of the cosmic Scale Factor R with time:

(dR/dt)2 = (8 Π G)/3 ρ R2 - kc2

The Abbe George Lemaitre (a Belgian Catholic priest - a Jesuit) in 1927, as an outgrowth of his Ph.D. thesis at MIT, set forth another expansion model that started with his proposed "Primeval (or Primordial) Atom", a hot, dense, very small object. (Lemaitre is credited with moving the idea of expansion into the mainstream of cosmology, but as indicated above, A. Friedmann had devised an expansion model 5 years earlier) The nature of a Big Bang was refined and embellished by the team of G. Gamow, R. Alpher, and R. Hermann and by others in the 1930s; their calculations showed that Hydrogen and some Helium are the dominant atomic species (with minor amounts of Lithium) that could form from their model of the Big Bang and its consequences. (The heavier elements up to Iron are produced by nucleosynthesis in the hot interiors of stars, as first demonstrated by Fred Hoyle and colleagues at the University of Cambridge.) Confirming evidence for expansion came from Edwin Hubble in the late 1920s. (Hubble's other major achievement was to prove the existence of galaxies outside of the Milky Way; he developed methods for determining distances to Andromeda and other nearby clusters of stars that were greater than the dimensions of the Milky Way.) The Big Bang can be mentally related to the above-mentioned singularity event by imagining that the expansion is run in reverse (like playing a film backwards): all materials that now appear as though moving outward (as space itself expands) would, if reversed in direction, then appear to ultimately converge on a "point of origin".

As described later in this Section (page 20-9), the BB concept drew its principal support from the observations by Edwin Hubble and others on radiation redshifts associated with the distribution of galaxy velocities. These redshifts (changes in the frequency [a decrease] of the EM radiation from excited atoms, resulting in relativistic increases in wavelengths owing to accelerations analogous to the Doppler effect [which causes a drop in pitch of a train whistle as it recedes from the listener; see page 20-9]) rise in value as light and other radiation from galaxies comes from ever farther positions in the expanding Universe. Those galaxies with higher redshifts are also ones that display as we see them now younger conditions - thus, we see them as they were in the earlier stages of cosmic time; being farther away it has taken longer for emitted light to get from the starting point to detectors at Earth.

The italicized segments below were taken from the University of Virginia's website on Cosmology:

The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. These effects, individually called the blueshift, and the redshift are together known as doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

so long as the velocity v is much less than the speed of light. A relativistic doppler formula is required when velocity is comparable to the speed of light.

The Cosmological Redshift is a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time.

The Gravitational Redshift is a shift in the frequency of a photon to lower energy as it climbs out of a gravitational field.

The general pattern of redshift change with distance (which in this diagram is given as the ages of the galaxies examined in terms of how long it has taken light from each to reach the Earth [thus those farthest away are shown as the youngest) follows this plot (shown for four values of the Hubble Constant H (see two paragraphs below), of which 72 is the current most favored value) is shown in this plot:

Redshift vs distance plot.

The exponential shape of this curve is carried over to the next plot which is a generalized representation of the cosmological redshift versus time since the Big Bang (set at 0 [13.7 b.y. ago], with the present age being 1). So far, the largest redshift actually measured is about 10, for a faint galaxy (observed by the Hubble Space Telescope) that may be as old as 13.4 billion years. /p>

Redshift versus cosmic age (as a fraction of 1, with 1 being the present and 0 being the time of the Big Bang.

The Universe has been enlarging ever since this first abrupt Big Bang, with space itself doing the expanding, and galaxies drawing apart, so that the size of the knowable part of this vast collection of galaxies, stars, gases, and dust is now measured in billions of light years (representing the distances reached by the fastest moving material [near the speed of light] since the moment of the Big Bang [~14 billion years ago]). This age or time since inception is determined from the Hubble Constant H (which may change its value) which is derived from the slope of a plot of distance (to stellar or galactic sources of light) versus the velocity of each source (see page 20-9).

The Hubble Constant H is a fundamental cosmological value that determines the rate of expansion of the Universe. It is a part of this key equation:

v = Hd

This, the Hubble equation, implies that the velocity of any point in expanding space (such as the location of a galaxy) has some current fixed value. Of greater import, the Hubble expansion directly leads to this conclusion: The galaxies are moving away from Earth at recessional velocities that increase systematically with distance from our planet (with corresponding increases in redshift). This is shown in this diagram, for galaxies up to a few billion light years away:

Velocity of receding galaxies versus their distance from Earth.

This plot shows that the speed of recession increases as one progresses outward (towards the outer limits of the observed Universe) by an amount derived from the value of H. This makes sense in that if all points began, at the Big Bang, from the same point at the moment of singularity and have now spread apart by expansion, the outermost points (earliest stars and galaxies) must have moved the fastest and those at the full range of distances along a line of sight going back to the point of observation are moving at progressively lesser velocities. In this way, one can say that everything is expanding, at a rate determined by the value of H. That value has now been determined to an accuracy of +/- 10% and is given as: 71 km/sec/Megaparsec or 21.5 km/sec/million light years. This diagram shows how H (given as H0) is determined as the slope of a straight line plot, using distances determined by different methods (page 20-9):

The plot from which H is determined.

The Hubble constant affords a measure of the age of the Universe, as will be developed on page 20-9. As a quick preview, consider this: Replace velocity in the above equation with d/t. The equation then becomes: d/t = Hd. Divide both sides by d and invert t, so that: t = 1/H0. An age of 13.7 billion years is the current best estimate.

The Hubble Constant also is applied to determining how fast galaxies at the observable Universe horizon are traveling. Starting with 71 km/sec/Megaparsec as the rate (and assuming this rate to be constant [it may have been slower in the past and is now faster], so this is an average) of expansion, the distance to a 13.7 billion light year object (if it could be seen) is about 4200 Megaparsecs (about 1.3 x 1023 km or 9 x 1022 miles). At 100 Megaparsecs, the velocity of a receding galaxy (as the observed object) is ~7000 km/sec (from a plot of velocity versus distance for an H of 71 km/sec/parsec). The velocity at that distance would then be 7000 x 42 = 294000 km sec - almost the speed of light

Aside from quantum speculation, nothing is really known about the state of the Universe-to-be just prior to the initiation of the Big Bang (a moment known as the Planck Epoch). The Laws and the 20 or so fundamental parameters or factors that control the observed behavior of all that is knowable in the Universe today become the prevailing reality at the instant of the Big Bang, but Science cannot as yet account for the "why" of their particular formulation and values, i.e., what controls their specifics and could they have come into existence spontaneously without any external originator, the "Creator" or "Designer". Among these conditions that had to be "fine-tuned" just right is this partial, but very significant list: homogeneity and isotropy of the Universe (the Cosmological Principle); relative amount of matter and anti-matter; the H/He and H/deuterium ratios; the neutron/proton ratio; the degree of chaos at the outset; the balance between nuclear attraction and electric repulsion; the optimal strength of gravity; the decay history of initial particles; the total number of neutrinos produced early on; the eventual mass density which affects the Critical Density; the specific (but varying) rates of expansion after the Big Bang; the delicate balance between Temperature and Pressure, both during the first moments, and much later during star formation; the ability within stars to produce carbon - essential to life; and much more. (See also another list at the bottom of page 20-11a.)

Some of these are interdependent but the important point is that if the observed values of these parameters/factors were to differ by small to moderate amounts, the Universe that we live in could almost certainly not have led to conditions that eventually fostered intelligent life capable of evolving during the history of the Universe as we know it. Also presumably necessary: beings that can attest to the Universe's existence and properties by making observations and deductions that lead to knowledge of the Universe. This requires the eventual appearance of "conscious reasoning" at least at the level conducted by humans on Earth, and perhaps also human-like creatures existing elsewhere in the Universe, - this concept is one of the tenets in what is referred to as the "Anthropic Principle" (page 20-11).

Moving on from the overview of the Universe afforded by the above paragraphs, we consider next the high temperature physics that pertains to what occurred in the vital first minute of the Big Bang.

Source: http://rst.gsfc.nasa.gov/