Illustrations Courtesy of Alfred T. Kamajian Part-1 - Remote Sensing Application - Completely Remote Sensing, GPS, and GPS Tutorial
Illustrations Courtesy of Alfred T. Kamajian Part-1

Intuition suggests that the dots in the above illustration would also be expanding (enlarging). These yellow dots represent galaxies. But in fact they remain roughly the same size during the expansion and move as a unit. The star distances within the galaxies stay about the same. This is due to the strong interstellar gravitation that holds a galaxy, once formed, to a near constant size. Over time as galaxies spread apart from expansion their mutual interactive gravitational attraction weakens and this may disturb their shapes and shift the stars; but the distances between stars in a galaxy remain more or less the same (i.e., are not affected by the general space expansion) owing to the countering effects of gravity.

Note that in the diagram, the expansion seems to start from a specific point. But for the Big Bang one cannot speak of a "there" in reference to the singularity point because the space that characterizes our Universe did not start to form until the moment of its beginning. It is difficult to think of any "there" since no dimensional frame of reference can be specified. At the outset of "creation" the singularity was made up of pure energy of some kind (in a "virtual" state within the false vacuum). What might have preceded this moment at which the Universe springs into being and how the singularity point came to be (become) remains speculative; theoreticians in the Sciences have proposed inventive, although somewhat abstract, solutions but the alternative and traditional views of philosophers (metaphysicians) are still taken seriously by many in the scientific community. This last idea is treated again near the bottom of Page 20-11.

Expansion is continuing through the present and into the future in part because the inertial effects (evident in the observed recessional motions of galaxies, etc.) imposed at the initial push still influence how space grows and, now it is believed, in part due to the continuing action of the above-mentioned repulsive energy. After the freeing of gravity from the other fundamental forces (see below), it has since been acting on all particles, from those grouped collectively into stars and intragalactic hydrogen/helium clouds making up the galaxies to individual nucleons, photons, etc. - thus at macro- to micro-scales. Gravity therefore exacts one controlling influence on the rate of expansion, serving to slow it down. But, this rate should be decreasing over time because gravity between the Universe's constituents weakens as expansion forces them further apart (Newtonian inverse square of distance r effect [1/r2]). As we shall elaborate later, recent evidence suggests that there are also anti-gravity forces (enabled by the repulsive energy of presently uncertain nature) that act to overcome the restraining effects of gravity; these forces seek to increase the expansion rate and over time push matter apart in a general dispersion. It is now believed that these forces are becoming greater than the countering force of gravity that eventually would have reversed expansion and caused a general collapse.

Gravity and the Kinetic Energy of outward expansion together constitute the total energy released from the Big Bang. By convention, the Kinetic Energy is taken as "positive" and Gravitational Energy as "negative". The two major energies comprise the Total Energy of Expansion. Thus; KE + GE = TE. Evidence favors a TE > 1, so that the Universe is likely to expand forever. The history of the expansion has been one of three successive stages: rapid deceleration, modest deceleration, and then exponential acceleration. This last step results from the increasing influence of Dark Energy (which maintains a constant density). Matter is thus said to be "falling outward" in the expanding sphere that comprises the observable Universe. This illustration generalizes the expansion history of the Universe:

The generalized history of the Universe's expansion since the Big Bang.

This diagram also has implicit reference to the above three major stages in the Universe's evolution: 1) initial acceleration accompanied by the dominance of radiation in the first few hundred thousand years of expansion; 2) the major role of matter as a factor in gravity over the next 7 billion or so years; and 3) the increasing importance of Dark Energy (or some other driving force) as the cause of re-acceleration since then.

Some readers may wish to acquire a broader insight into the topic of Universe expansion that describes a simplied Model, using an enlarging balloon as an analogy for the spacetime expansion of the Universe that has continued after the first eras of the Big Bang. This and related subjects are considered in more detail on pages 20-8, 20-9, and 20-10. But if you want to acquire a better understanding of the nature of Universe expansion before proceeding on this page, you can access a relevant review now on the separate page 20-1a. Check especially the paragraph in red at the bottom of page 20-1a, which alludes to models other than the Big Bang that could cause expansion and different sets of fundamental cosmological parameters.

This is an appropriate point to insert comments about the concept of the Instanton. This is an alternative version of the notion of the Singularity event described in previous paragraphs. It is a different version of what happens just prior to the Big Bang. The Instanton is a condition that derives from Yang-Mills Gauge theory which is a part of what is known as Quantum Chromodynamics (QCD). We will not delve further into Instantons (a rather difficult to follow summary is given at this Wikipedia website). Cosmologists such as Stephen Hawkings and Neil Turok have adapted Instanton theory to the conceptualizing of what was before and led up to the Big Bang, or any of the competing ideas for the Universe's inception. In a nutshell, they envision a process by which a quantum fluctuation in the vacuum or void prior to the initiation of the Big Bang led to the appearance of energy by a quantum tunneling process. Their "Pea Instanton", which had such high temperatures and pressures that it had to "explode", was created in this way. Rather than pursue this topic further here, we refer you to the Cambridge University link at the bottom of the Preface and to the links on this additional Web site: J.T. Wong.

Many scientists believe that what may have "existed" prior to the Universe was a quantum state (in a sense, analogous to the condition of "potency" in ancient Greek philosophy) which influenced a true vacuum (no matter whatsoever) that somehow possessed a high level of energy (of unknown nature but not, however, as photon radiation). As will become evident in this Section, astrophysicists now believe that no total vacuum exists anywhere -- all of space (the Cosmos) contains some form of energy having as yet an undetermined quantum nature. Countless quantum fluctuations (which in quantum theory are said not to depend on [obey] metaphysical cause/effect controls and are not subject to time ordering) in this vacuum energy density produced sets of virtual particles and anti-particles (analogs to positrons, the positively-charged equivalent of an electron; neutrons and anti-neutrons, etc) that could (according to quantum theory) into existence out if the Cosmos for very brief moments but then nearly all were annihilated. The nature of these particles is currently not well known but they may relate to the so-called Dark Energy that dominates the Universe.

Rarely, annihilation did not occur (as would be consistent with the probabilistic nature of Quantum Physics), so that a particle could grow and trigger a 'phase transition' that led to the Big Bang event from whence all that entails our Universe - with its internal matter, energy, space, and time - came into being. In this quantum model, particles could either be destroyed by interacting with antiparticles or could emerge from the vacuum from time to time and survive, leading to mulitple universes that, as far as we know theoretically, cannot have any direct contact. If so, the number of unconnected Universes may be very large, or very small if the success rate of a particle conversion to a Universe birth is near infinitely low frequency of occurrence. Though no one yet has offered any proof of a multiverse Cosmos, the likelihood is that the vast majority of virtual particles do not explode into individual Universes, but statistically some do; each Universe may have its own set of parameters and laws of physics and these conditions may never be "right enough" to foster life.

This non-contact status is one example of prohibition by relativistic limits, in which information travelling at the speed of light cannot reach us from beyond the horizon of our own observable universe. For our Universe, the concept of the Cosmological Horizon refers to the boundary or outer limits of the Universe that we can establish contact with, i.e., the farthest extent of the observable Universe that can be seen through the best telescopes. This is approximated by the currently observed farthest galaxies that formed in the first billion years of time in our Universe's history. This Horizon is also conceptualized as the surface dividing spacetime (which includes all locatable 4-dimensional points) into what we can see and measure from what is hidden and unobservable. The observable therefore must lie within our Light Cone, an imaginary surface that encloses all possible paths of light reaching us since the beginning of time. (The fifth illustration below is an example). Check page 20-10 for further discussion of these ideas.

If the Universe is about 14 billion years old, then light leaving just formed protogalaxies near the observable spatial limit (outer horizon) of the Universe departed some 13+ billion years ago but this radiation is only now reaching us, since it had to traverse across a Universe that was expanding (ever increasing the distances from Earth to the outer edges) and drawing the protogalaxies away from us. Scientists actually have detected cosmic background radiation (CBR), the "afterglow" (see below and page 20-9), which pervades the entire Universe. Its first confirmable appearance was only about 380,000 years after the BB, at the time when detectable radiation could penetrate ion clouds that blocked its escape. This appearance of CBR is the present limit to the farthest lookback time involved, i.e., the extent to which we can peer into the past to find the earliest discernible event; nothing that occurred between the BB and the 300,000 years following it up to the first detection of CBR can be directly detected or measured.

The Hubble Space Telescope has now seen faint galaxies that are close to the cosmological horizon. Light from these left them about 13 billion years ago. At that time all the earliest galaxies were much closer to each other. Over the next 13 billion years - to the present - the Universe has been expanding, so that the light initially emitted "way back then" has had to traverse an ever enlarging distance which we perceive as the observable Universe.

The ultimate size of the observable Universe - a term we have applied several times earlier on this page - is still an open question. It is also a very complicated question, as you would deduce if you read this Wikipedia website that contemplates the possibilities of Universes of different sizes, depending on the definitions and assumptions used.

Cosmologists are inclined to cite as one specifiable size some specific observable Universe which is the subset of a possibly much larger Universe that lies beyond the event horizon (limit of the spacetime distribution within which the earliest light has traveled to our planet); in this conception, what is being seen from Earth is just that part of a still larger assemblage of galaxies from which light has had enough time to reach our telescopes since the Big Bang 13.7 billion years ago. We see outward in all directions to those galaxies at the limit, as they were in their earliest appearances (they formed about 0.5 to 1 billion years after the Big Bang), and they appear much the same no matter what direction we look at them. Thus we can imagine a sphere of galaxies whose radius is at least that of the first galaxies, e.g., let us say 13 billion light years away (to the first recordable event horizon). The diameter of the sphere of the observable Universe is thus 27.4 billion light years. For this sphere, in our frame of reference, we perceive ourselves as being at the center. But someone observing from a planet in a galaxy elsewhere would see the same thing (the sphere thus seems centered at that planet). In this conception the presumption is that there are many billions of galaxies situated beyond the limit of detection that has been set by the time since the Big Bang over which light has traveled at its apparently constant speed. Perhaps these diagrams will help visualize this:
A superbig Universe
The observable Universe in a larger Universe.

In these diagrams the regions beyond the event horizon (which defines the observable Universe) were formed at the same time as those within. The extent of galaxies beyond the observable limit can be even much larger than shown in the diagrams but may(?) be finite (see two paragraphs down). Just how large is still unknown, is still conjectural, and is still dependent on which model or theory is being used. Two values show up in an Internet search of "the size of the Universe": a radius of 42 billion light years and a radius of 78 billion light years. Explanations of how these and other values have been reached are obtusely documented (as an example, see the 8th entry in Ned Wright's FAQs) and reasons for the mechanisms that lead to sizes beyond the observable Universe are glossed over. The most common argument states that the greater proposed radii are the consequence of Inflation (see next paragraph and again elsewhere on this page) which carried the earliest products of the Big Bang to distances much farther than the 13.7 billion light year limit imposed by observation.

Thus, there seems to be a paradox here. How can there be more galaxies outside the observable sphere? Inflation, which occurs almost at the beginning of the Big Bang, increases the rate (which has varied in the past) of expansion of the Universe by a very large factor (one proposed value = 1050; higher and lower rates have been proposed for various models). This is much greater than the speed of light (this does not violate the Einsteinian tenet that radiation within the Universe cannot go faster than light speed, which applies to movements of photons within space, whereas it can be argued that space itself can move faster the speed of light). Thus, there are a multitude of galaxies and other matter/energy outside of that spherical portion of space that can be observed that are part of the vast segment of megaspace (all space out to the farthest extent of the Universe) produced by the Big Bang + Inflation; we can't see them simply because they are too far for light from them to have had time to reach us since the beginning.

The concept of Inflation, coupled with the illustrations above, seems to be a straightforward and easily grasped clue to envisioning how there can be matter and energy - perhaps even as galaxies - beyond the 13.7 billion light year horizon. But there is a competing relativistic explanation that leads directly to the extension of the Universe's limits or size to values quoted above, to such numbers as 42 and 78 billion light years. The writer (NMS) first encountered this explanation in Lecture 8 of the Cosmology DVD, presented by Dr. Mark Whittle, that was cited at the beginning of this page. A search of all the main Internet references and several Cosmology textbooks failed to find anything comparable to his review.

Whittle begins that lecture by defining four terms: 1) demit = the distance light has traveled (to us) since it set out; 2) dnow = the distance that the galaxy actually is from us today; 3) dLT = the distance that a photon of light has traveled since it first left its source until now: and 4) the lookback time tLT = (tnow - temit, which is numerically equal to dLT but in units of years. These distances always have this interrelation: demit < dLT < dnow.

Two other terms are used in his calculations: 1) Scale factor S(t), which ranges from 0 (at the Big Bang) and 1 (now), and describes the extent of expansion at any stage; and 2) the so-called redshift of electromagnetic radiation (light) (defined as the displacement of spectral lines of elements such as H and Fe [whose wavelengths have reference values determined in their rest state in laboratories on Earth] towards longer wavelengths owing mainly to the outward expansion with progressively increasing velocities of the Universe; discussed below and on page 20-9) expressed as a variant known as the Redshift Stretch Factor (RSF). RSF = dnow/demit = λnow/λemit, which ranges from 1 to infinity. (The RSF has a value of 1000 associated with the Cosmic Background Radiation that is detectable about 400000 years after the Big Bang). (Note: redshifts took on large values during the first part of the Universe's expansion, especially during the first minute of the BB; this is quantified on page 20-9.)

It is not practical to try to reconstruct the details of his calculations as presented in the lecture. The specification of demit, which is just any time one chooses to start the journey of a photon (light) from a galaxy at any time between the beginning and now, and dLT, which is synonomous with the st(age) of the light source (a galaxy specified to be seen today as it was, say, 8 billion years ago is said to be 8 billion light years away), are readily understandable. But when dnow for this galaxy is stated as a number greater than 13.7 billion light years, the situation seems bewildering and counterintuitive.

Whittle gives two examples with concrete values that specify the various distances. In the first, he starts with a galaxy whose RSF = 3. This means that the Universe was 3 times smaller, so S(temit) was 1/3. Referring to the appropriate S(t) curve, temit is found to be 10.5 billion years ago, so that dLT is 10.5 billion light years. But since then, the Universe has been expanding so that the distance that light travels at a constant velocity keeps enlarging. This means that the present day (now) distance is greater than dLT. To determine this one must resort to calculus and integrate the distance of many small, ever changing increments over time. For a small interval, this distance = cΔt; over the full time of stretching (expansion) from then to now, the relevant S(t) must be used in the integration of the varying cΔt. The calculus formula for this is:


(Note: The html editor program used for this Tutorial has no character for the integral symbol, which was here extracted from the Internet, nor does it allow the formula to its right to be placed on the same line; so, in the above equation just mentally place the integral symbol next to the formula.)

For this set of parameters, the integrated dnow becomes 15 billion light years. Using the same approach, and specifying the Redshift Stretch Factor as RSF = 1000, dLT comes out as 13.7 billion light years, dnow is calculated to be 46 billion light years, and demit is found to be 26 million light years (a reasonable estimate for the very early Universe's limits).

These seem to be strange numbers, and the concept is hard to visualize. The writer (NMS) came up empty after seeking to find a dynamic illustration (or even a set of sequential static pictures) on the Internet. So, I have decided to make my own - which is only an approximation. Consider these:

At t(0)


At t(1)

O    <-- O

At t(2)

O      <-----       O

At t(3)

O     <---------              O

At t(4)

O<-------------                       O

At t(0), just after the Big Bang, two entities (let's make one O, on the right, what would later become a now distant galaxy and the other O being our galaxy containing what eventually becomes our planet Earth) are adjacent and light (represented by an arrow, whose length represents the distance traveled from the distant galaxy in the time interval t(n)) has just begun its travel. At t(1), the entities are expanded some distance apart at an amount governed by the Hubble expansion rate, but light has traveled (whose dLT is shown by the number of dashes in the <--) a lesser distance determined by its constant velocity and the time involved than this expansion distance. At t(2), the separation distance of the Os is now greater, but note that the light travel distance is itself now more but still increasingly less than the amount of O separation. This holds for t(3) and any other intervening intervals. At t(4), the light has now reached the left O, which is Earth, and its distance (d LT or 13.7 billion light years) is considerably less than the gap between the two Os. The increasing disparity between the O separations in successive times and the light travel distances is accounted for by the non-constant rate of expansion versus the constant rate of light propagation.

The question of the size of the Universe is not well covered on the Internet. One web site that proved informative is recommended: Distance Scale of the Universe. The figure below is taken from that site. Check the site for an explanation of the four distance parameters.

Four measures of cosmic distances; Gly = Giga light years (a giga is a billion).

The writer (NMS) has tried to find a description of what may lie beyond the 13.7 billion light year limit for the observable Universe. An Internet search found hundreds of citations - mostly blogs - which range from inconclusive to gibberish. I do not have an answer but this seems plausible: If there is organized matter (from nebulae to possible protogalaxies) beyond the observable Universe, then it should be similar to the earliest galaxies observed so far; or it might just be an extension of the Cosmic Background Radiation which can be traced to the "edge" of the observed Universe.

As is true for most earthbound illustrations that try to depict relativity and spacetime, this is an imperfect diagram. But it may give you some insight beyond what the exposition of the Whittle lecture calculations provided. Let's return to a consideration of plausible models for our, and perhaps other, Universe(s).

In one school of thought megaspace (the Cosmos - all possible space, not just that within the observable space of our limited Universe) is infinite. In another view, space is finite but much of it is beyond our detection. (What is outside of this megaspace is still conjectural). There is a variant of this (see page 20-10) embodied in the concept of Multiverses. In one model, each Universe can be likened to an expanding bubble and the bubbles may not be in contact (but in principle could interact) - the space between them itself also expands. Multiverses may be finite or infinite. Here is a pictorial example:

A myriad of Bubble Universes.

A corollary: In the Standard Model for the Big Bang, there have been and are parts of the Universe which cannot directly influence each other because there hasn't been enough time for light from any one part to have reached some others. Thus, the 'horizon' relative to Earth as the observing point (but any other position in the Universe is equally as valid an observing point) refers to the spatial or time limit that demarcates between what we can establish contact with in any part of the Universe and what lies beyond. This means that if an observer at one point in the observable Universe (as a sphere) sent a message shortly after the Big Bang to an observer at an antipodal point, there hasn't been enough time for the message to be received. This figure illustrates an extreme example of parts that cannot mutually communicate:

Simple cartoon showing distant galaxies viewed from Earth (center point labeled US) in opposite directions.

This gives rise to a seeming paradox that is implicit in the "Horizon problem". Simply stated: how can these isolated regions have very similar properties (such as similar densities of Dark Matter, Cosmic Background Radiation, and numbers of galaxies) if they are not in contact. This appears to violate the fundamental principle of universal causality, which holds that during expansion all parts of the Universe would need to have been in communication (by light transfer or other means of exchanging energy) so that the fundamental principles of physics would have ample causal opportunity to influence each other. This is seemingly necessary if at a gross scale the Universe is to maintain uniformity (the essence of the Cosmological Principle which postulates broad homogeneity and isotropism within the Universe as a whole). One explanation that accounts for the causality needed to obey this principle is given below in the subsection dealing with Inflation.

Nevertheless the isolation of regions of the Universe from one another is a real fact, as evident in the above illustration. And, specifically there were situations whereby some parts of the Universe were not in causal contact shortly after the Big Bang, and thus not visible to one another during early cosmic history, but will eventually, as expansion proceeds, become known to each other. Consider this next diagram based on spacetime light cones (see Preface):
Diagram illustrating the Horizon Problem.
From J. Silk, The Big Bang, 2nd Ed., © 1989. Reproduced by permission of W.H. Freeman Co., New York
Start with hypothetical observers at two points A and B not then in contact in early spacetime. Over expansion time, their light cones would eventually intersect, allowing each to see (at time t1) other parts of the Universe in common but not yet one another. At a later time, beyond t2 ("now") in the future, the horizons of A and B (boundaries of the two light cones) will finally intersect, allowing each to peer back into the past history of the other.

These intriguing ideas just discussed actually don't tell the full story. One model of Universe expansion arrives at a Universe whose farthest opposite points are now about 42 billion light years apart. Check this diagram:

A different way of extimating the Universe's spatial dimensions in light years.
From: Misconceptions about the Big Bang, by C.H. Lineweaver and T.M. Davis, Scientific American, March 2005