1
Historical Models of the Universe
The
following table outlines the significant historical models in
chronological order.
Notice that all the historic models possess one or more of the
attributes of expansion, contraction, and stability. Each universe can be
said to expand, oscillate between expansion and contraction, or do neither
and just sit there maintaining a static or equilibrium state. None can be
classified as cellularly structured. It seems that throughout history the
cellular universe was never seriously considered.
Table 1: Historical
Models of the Universe 
NAME 
Author & Date 
Classification 
REMARKS 
Brahmanda (Earliest known model) 
Ancient Hindu RigVeda treatise on cosmology 
Cyclical or oscillating.
Infinite in time. 
The universe is a cosmic egg that cycles
between expansion and total collapse. It expanded from a
concentrated form —a point called a Bindu. The universe, as a
living entity, is bound to the perpetual cycle of birth, death, and
rebirth ... 
Pythagorean cosmology 
Ancient Greek “Pythagoreans”
600400 B.C. 
Heliocentric 
The followers of Pythagoras believed that Earth (and
the planets) moved, along with the Sun, around a “central fire” at the
center of the universe, a central fire which was visible only
indirectly from its reflected light. The Earth rotated daily on its
own axis. The motions of the
planets were supposedly related to numerical harmonics like those of
musical notes. 
Atomist universe 
Anaxagoras (500428 B.C.) & later Epicurus 
Infinite in extent 
The universe contains only two things: an
infinite number of tiny seeds, or atoms, and the void of infinite
extent. All atoms are made of the same substance, but differ in size
and shape. Objects are formed from atom aggregations and decay back
into atoms. Incorporates Leucippus’ principle of causality: ”nothing
happens at random; everything happens out of reason and necessity.”
The universe was not ruled by gods. 
Stoic universe 
Stoics 3rd^{ }& 4th c. B.C. 
Island universe 
The cosmos is finite and surrounded by an
infinite void. It is in a state of flux, as it pulsates in
size and periodically passes through upheavals and conflagrations
reminiscent of some 20^{th}
century big bang models. 
Aristotelian universe
(based on the model of Plato’s student Eudoxus) 
Aristotle (384322 B.C.) 
Geocentric
Static, steady state, finite 
A
spherical and spatiallyinfinite cosmos. Spherical earth is surrounded by concentric
celestial spheres. Universe exists unchanged throughout
eternity. Emphasis on Plato’s geometric ideal of perfectly circular
orbits. Motions are caused and controlled by intelligent agents
("souls"). Contains a 5th element called
ether (also known as
quintessence).
The ideas of a beginning of the cosmos and of a beginning of time are
rejected. Aristotle’s cosmology is considered to be the first
“steadystate” universe. 
Aristarchean universe 
Aristarchus of Samos (circa 280 B.C.) 
Heliocentric 
Earth rotates daily on its axis and revolves
annually about the sun in a circular orbit. Sphere of fixed stars is
centered about the sun. Aristarchus beat Copernicus to this
realization by 1800 years. 
Ptolemaic model (based on the Aristotelian
universe) 
Claudius Ptolemaeus
(2nd century A.D.) 
Geocentric 
Universe orbits about a stationary Earth. Planets move in circular
epicycles, each having a center that moved in a larger circular orbit
(called an eccentric or a deferent) around a centerpoint near the
Earth. The use of equants added another level of complexity.
The most successful universe model of all time, using the criterion of
longevity. Almagest (the Great System). The System
allowed astronomers to predict the positions of the planets reasonably
well.
Its fatal flaw was its inability to account for the observable
changes in the phases of Venus, revealed after the invention of the
optical telescope just prior to 1608. 
Copernican universe 
Nicolaus Copernicus 1543 
Heliocentric 
The ancient Aristarchean universe rediscovered. The
Copernican universe was essentially a remapping of the Ptolemaic
scheme to make the Sun the center of the system rather than the
Earth. It retained ideal circular orbits and still needed epicycles.
But it captured the revolutionary idea that the Earth moves!
"Revolutions of the Celestial Spheres."
Condemned by the Catholic Church in 1616. 
Static Newtonian 
Sir Isaac Newton (16421727) 
Static (evolving), steady state, infinite 
Every particle in the universe attracts every
other particle. Matter on the large scale is uniformly distributed.
Gravitationally balanced but UNSTABLE. 
Hierarchical universe
(Fractal universe) 
Immanuel Kant, Johann Lambert 1700s 
Static (evolving), steady state, infinite 
Matter is clustered on ever larger scales of
hierarchy; forming a fractal universe. Matter is endlessly being
recycled.
Fatal flaw: It has a cosmic center. 
' ' 
Carl Charlier, early 20th century Swedish astronomer 

Charlier pointed out that "In a hierarchical universe the density of
matter becomes progressively less when averaged over larger and larger
regions." In theory, the hierarchy may be arranged so that in the
limit, on the cosmic scale, the average density of the universe
approaches zero. The larger the scale the weaker gravity becomes. On
the largest scale gravity vanishes. 
Einstein 'Equilibrium' universe 
Albert Einstein 1917 
Static (nominally). Bounded (finite) 
“Matter without motion.” Contains uniformly
distributed matter. Has a constant radius of R_{E}= 1/Λ^{2}.
Has uniformly curved spherical space; space is said to curve in on
itself. It is based on
Riemann’s hypersphere. Curvature is set equal to Λ.
In effect Λ is equivalent to a repulsive force
which counteracts gravity. UNSTABLE. 
MacMillan 
William MacMillan 1920s 
Static &
steady state 
New matter is created from radiation. Starlight
is perpetually recycled into new matter particles. 
Dirac universe 
Paul Dirac 1930s 
Expanding 
Demands a large variation in G, which decreases
with time. Gravity weakens as universe evolves. 
Note: the term “static” simply means not
expanding and not contracting. Symbol G represents Newton’s
gravitational constant; Λ (Lambda) is the cosmological
constant. 
The Ptolemaic model was the Western world’s most
popular and successful cosmology of all time, and represented the orthodox
view for more than 1500 years. It was so firmly established that only a
revolution could lead to dethronement. And as it happened the Copernican
revolution took hold. An Ancient idea gained new life as Copernicus
revived Aristarchus’ Heliocentric model and became
widespread throughout Europe and beyond. The Ptolemaic cosmology was doomed. Nothing could
save the established theory of the heavens: Not the vast power of the
Church; not the Papal edicts; not the threats of the Inquisitors; not the
torture of heretics; and not the burning of books.
If the succession of the Ptolemaic universe by the Copernican universe
represents the third cosmology revolution; then the overthrow of the
Copernican world by the Big Bang (BB) universe represents the fourth
cosmology revolution. Now let us draw a critical parallel between the most
popular model of the past with the most popular model of the present.
The Ptolemaic model placed the Earth at its center and used geometric
elaborations involving circles within circles. It was a mechanically
intricate complexity that actually managed to replicate the apparent
orbital motions of the planets and make reasonably accurate positional
predictions. The Ptolemaic model, however, seems almost simple when
compared to the BB model. The BB uses geometric curvature, hot and cold
dark matter, dark energy (expansion), inflation (hyperexpansion), acceleration (when not using
deceleration), reinflation (more expansion), and something called "open inflation." [Scientific
American Jan 1999 p66]. In the Archaic system, eccentrics,
epicycles, and equants, served as the model’s mechanical adjustments that permitted its
defenders to say, with a straight face, "See, the celestial objects are
precisely where they should be." In the modern BB system we have a similar
situation. Such unreal things as spacecurvature, dark matter, virtual
particles, inflation, acceleration, and even 9dimensional strings, have all
been proposed to justify the similar claim, "See, the universe evolves
precisely as our revised model says that it should."
Ptolemy’s "eccentrics,
epicycles, and equants" were found to have no basis in reality and were
cast aside. Curvature, dark matter, virtualparticle energy, inflation, acceleration, and
strings, (as used in BB cosmology) are equally devoid of reality and, in
the fifth cosmological revolution, will suffer the same fate.
Another popular historic model was the Hierarchical universe. With its
endless progression of systems of increasing size filling infinite space,
it seemed an elegant and simple construction. Unfortunately it could not
survive an important finding of modern cosmology.
Although the organization of matter into spherical and near
spherical systems is the rule over virtually the entire astronomical
hierarchy, the rule breaks down suddenly and dramatically when we reach
the top level —the largest structures in the astronomical Universe.
Witness the size progression: Gravitating bodies are spherical; planetary
and binary systems are spherical; solar systems are spherical; star
systems (globular clusters) are spherical; galaxies are, to varying
degrees, spherical; and finally rich galaxy clusters are spherical. But
there the rule ends. The clusters of galaxies are not grouped into
anything resembling spheres. “Instead, they are strung out in filaments,
which lie on the surfaces of huge bubblelike regions within which there are no
clusters and few or no bright galaxies.” Instead, the clusters surround
giant voids of empty space. [David Layzer, 1991. Cosmogenesis, the
Growth of Order in the Universe, p166]
2
Expanding Universe Models
The 20th century was the golden age of the expanding
type of universe. The philosophical and religious motivation for birthandrebirth
cosmology had, throughout the ages, favored universes that grow and
expand. But in the early years of the last century it was discovered
(thanks to Vesto Slipher’s surprising redshift measurements) that the distant galaxies
all appeared to be receding. Two interpretations emerged. The obvious idea
was that the galaxies are actually in Doppler motion and moving away
radially in all directions. The other view posited that space in general
and the space between us and the “receding” galaxy in particular was
somehow expanding. (Needless to say there was also a minority view
in which the apparent recession was believed to be just that an
apparent recession.)
Then, from the dominant views, a simple but fateful extrapolation
was made: If galaxies appear to be receding then the whole universe is
probably expanding. If the evidence shows that space expands then the
whole universe must be expanding. Cosmology took a major turn. What had
for the most part been a stable universe was deemed, by the scientific
community, henceforth to be an expanding universe. The fourth revolution in
cosmology was a swift one. With the opposing sides coming to the same
conclusion, in spite of their differences over the interpretation of the
cosmic redshift, it is small wonder the revolution towards the
expandinguniverse concept became unstoppable.
And so the 20th century became the age of discovery of the
seemingly endless ways in which the universe could expand at least
mathematically. Table 2 describes the most
popular constructions and those with some special significance. Notice that Big
Bang cosmology is the main subclass of expandinguniverse cosmology.
Table
2: Expanding Universe Models 
NAME 
Author & Date 
Classification 
REMARKS 
Brahmanda 
Ancient Hindu RigVeda
treatise on cosmology 
Expanding and contracting
in cycles.
Infinite in time. 
Models the Hindu belief
that the Universe has no absolute beginning or end, but follows a
perpetual cosmic creation and dissolution. See Table 1 for more
details. 
DeSitter universe 
Willem de Sitter 1917
(Dutch astronomer) 
Expanding flat space.
Steady state.
Λ > 0 
“Motion without matter.” Only apparently
static. Based on Einstein’s General Relativity. Scaling factor
(radius of a region of infinite universe) increases exponentially. 
Friedmann universe of spherical space 
Alexander Friedmann 1922 (Russian
mathematician) 
Spherical expanding space.
k = +1; no Λ 
Space geometry is similar to Einstein’s
Equilibrium model, but in addition to the positive curvature of space
there is also a curvature of time. In Friedmann’s version of the
closed universe there is a beginning and an end to time when material
expands from and recollapses to infinite densities. Curvature constant k = +1.
Expands then recollapses. Matter dominated. Spatially closed (finite).

Friedmann universe of hyperbolic space 
Alexander Friedmann 1924 
Hyperbolic expanding space.
k = −1; no Λ 
Negative curvature. Said to be spatially
and materially infinite
(but ambiguous). Unbounded. Begins with expansion from a big bang of
infinite density. Expands forever (The question you’re not supposed to
ask is, What does it expand into?). 
Friedmann zerocurvature,
aka the EinsteinDeSitter universe 
Einstein & DeSitter 1932 
Expanding flat space.
k = 0; Λ = 0
Critical density 
Spacecurvature constant k is zero; space
pressure is zero; cosmological constant Λ is zero.
Said to be infinite (but ambiguous). "Unbounded cosmos of limited extent."
Begins with a big bang and expands forever.
Specifically, the expanding distance between widely separated
galaxies varies as time to the 2/3 power. "Simplest"
of all known universes. Named after but not considered by Friedmann.
Has a deceleration term q =½, which means that its expansion
rate slows down.
(Einstein published his new model in a paper,
coauthored with Willem de Sitter, entitled “On the relation between
the expansion and the mean density of the universe” and presented at
the 1932 proceedings of the National Academy of Sciences.) 
Georges Lemaître
the original Big Bang
aka
FriedmannLemaître Model 
Georges Lemaître (Belgian priest &
mathematician) 1927 & 1929 & 1933 
Expansion
Λ > 0
Λ > Gravity 
In 1927 Lemaître rediscovered the
Friedmann 1922 model; and in subsequent years he added a positive
Λ with a magnitude greater than Gravity. Universe has initial high density
state ("primeval atom"). Followed by a twostage expansion. Λ
is used to destabilize the universe.
(Lemaître is
considered to be the father of the bigbang model.) 
Oscillating universe
(aka FriedmannEinstein; was latter’s 1st choice after rejecting his
1917 model) 
Favored by Friedmann
1920s & 1930s 
Expanding and contracting in cycles 
Time is endless and beginningless; thus
avoids the beginningoftime paradox. Perpetual cycles of big
explosion followed by big implosion. Each cycle is slightly larger and
longer than the preceding cycle owing to the growth of entropy.
However, back extrapolation revealed that the beginning paradox
could not in fact be resolved.
Philosophically and religiously motivated forms of the Oscillating, or more picturesquely, the “Phoenix” universe are among the oldest
known cosmologies. In Greek and Roman antiquity, for instance, each
eternally repeating cycle was called “a Great Year.” 
Eddington eternal universe 
Arthur Eddington 1930 
first Static
then Expands 
Static Einstein 1917 universe with its
instability disturbed into expansion mode; with relentless matter
dilution becomes a DeSitter universe. Λ dominates
gravity. 
Milne universe of
kinematic relativity 
Edward A. Milne,1933,
1935.
William H. McCrea
1930s 
Kinematic
expansion with NO space expansion 
Rejects general
relativity and the expanding space paradigm. Gravity not
included as initial assumption. Obeys cosmological principle & rules
of special relativity. The Milne expanding universe consists of a
finite spherical cloud of particles (or galaxies) that expands WITHIN
flat space which is infinite and otherwise empty. It has a center and
a cosmic edge (the surface of the particle cloud) which expands at
light speed. His explanation of gravity was elaborate and
unconvincing. For instance, his universe has an infinite number of
particles, with a nonconstant G, hence infinite mass, within a finite cosmic volume!!
It also has two separate time scales! 
Dirac universe 
Paul Dirac 1930s 
Expanding 
Demands a large variation in G, which decreases
with time. Gravity weakens as universe evolves. 
BransDicke 
Carl H. Brans Robert H. Dicke 
Expanding 
Based on Mach’s principle and general relativity. G varies with time
(G falls as the universe ages; G is proportional to 1/t),
and therefore mass also varies with time, as universe expands. “But
nobody is quite sure what Mach’s principle actually means.” 
RobertsonWalker
universe 
Howard Robertson,
Arthur Walker, 1935 
Uniformly
expanding 
Uses the most
general form of the general relativity metric for a spacetime
satisfying the cosmological principle (homogeneity and isotropy).
Spacetime separates into uniformly curved space and cosmic time common
to all comoving observers. The formulation system is now known as the
RobertsonWalker metrics of cosmic time and curved space. 
Steadystate expanding (Bondi &
Gold) 
Herman Bondi, Thomas Gold 1948 
Expanding, steady state, infinite 
Matter creation rate maintains constant
density. Continuous creation out of nothing from nowhere. (Presumably,
like the Hoyle model below, the energy released by space expansion is
used in the process of matter creation.) Exponential
expansion. Deceleration term q = −1.
No mechanism for terminating matter; and therefore, arguably, violates
conservation of matter. 
Steadystate expanding (Hoyle) 
Fred Hoyle 1948 
Expanding, steady state; but unstable 
Matter creation rate maintains constant
density. Energy released by space expansion is used in the process of
matter creation. But critics have argued that since matter
creation rate must be exactly balanced with the space expansion rate,
the system is unstable.
No mechanism for terminating matter; and therefore, arguably, violates
conservation of matter. 
Negative pressure universe 
William McCrea 1951
(British cosmologist) 
Expanding, steady state 
A universe in tension: McCrea
proposed that a negative pressure (equivalent to a state of cosmic
tension) may be present in the universe. It can be detected only in
the way it affects the dynamics of the universe. As the universe
expands energy is released, and this energy
could take the form of newly created matter. 
Steadystate (Shrinking atom model) 
Fred Hoyle,
Narlikar 1975 
Static. Expansion is only apparent 
Instead of an expanding universe with
atoms of constant mass this model has a STATIC universe of SHRINKING
atoms making the universe appear to be expanding. When atoms grow in
size, universe appears to collapse. Avoids creation mystery. 
Cyclic Model 
Paul Steinhardt (Princeton); Neil Turok (Cambridge) 2002 
Expanding and contracting in cycles 
A controversial revival of Oscillating
universe (above) based on brane and string theories.
Two parallel planes known as Mbranes, one of which represents
our visible universe, collide periodically in a higher dimensional
space (up to 10dimensional space in some versions). Each collision corresponds to a reversal from contraction to
expansion. Fails largely because the collision mechanism is highly
speculative and poorly understood. Details on Cyclic universe can be
found on
arxiv.org 
Symbol G represents Newton’s
gravitational constant; Λ (Lambda) is the cosmological
constant.
A table similar to this one appears in Wikipedia, the online encyclopedia,
as
Models of the Universe and was originally created by the author. 
SOME CLASSIFICATION NOTES
LAMBDA.
Lambda, Λ, when positive, is a force or effect that opposes
gravity. Lambda is an intrinsic property of space, or the space medium, itself.
AMBIGUITY OF INFINITY.
There is a certain ambiguity of the "infinite" designation
with respect to some models: If a universe has a
pointlike beginning and then progressively expands as it ages, how can it
be infinite? Arguably, not in age! and certainly not in size!
A universe that is said to have a true beginning precludes
infinity of age. A universe that is said to expand precludes
infinity of size. The reason is simply that only finite entities can
logically be said to expand. To say that something of infinite size is
itself expanding is unnecessary as well as meaningless, for that which is
infinite is already fully expanded. That which is infinite in its spatial
dimensions cannot become more infinite. To say the universe becomes more
infinite in extent is to deny that it was infinite in the first place.
Furthermore, whatever is finite, no matter how much it grows, will always
remain finite; it can never become infinite.
TYPES OF EXPANSION.
Physicists have several methods for driving the expansion.
(1)
Expansion may be caused by curvature of space. This is the
mathematical method. The great advantage is that it allows the confinement
of that which is infinite.
(2)
Expansion caused by the physical growth of the space medium.
This is a plainandsimple method. It allows theorist to give the space
medium various essential or fundamental properties —theoryspecific
properties.
(3)
Expansion caused by something called inflation. This
is the
‘savetheappearancebyanymeans’ method.
(4)
Expansion caused by something called dark energy. This
is the
‘darkandmysterious’ method.
(5) There
are other methods such as Kinematic expansion, Quintessence,
Space tension, etc.
TYPES OF UNIVERSE THAT MAINTAIN EQUILIBRIUM:
Static Universe:
No expansion, no contraction —motionless.
A static universe is one that is constant in size.
Any contained objects can have peculiar motions
and can evolve.
Therefore, its appearance may change.
Steady State Universe: May have expansion or contraction, or a
harmonious balance of both.
Any activity that occurs must be
perpetual and unalterable.
Static Steady State: No expansion or contraction.
Its appearance, on average, must never
change.
Later we will see that a cellular universe is another type that has the
ability to maintain equilibrium.
COMMENTARY ON CRUCIAL ASPECTS OF
THE EXPANSION PARADIGM
THE GRAVITY PROBLEM. Einstein, during his
early years, denied the existence of absolute
space, but this did not stop him from giving nonexistent space some
suspiciously real properties such as geometric curvature and the dynamic
ability to expand and contract. His unreal space even acquired the
ability to order the very real motions of the planets, the stars
and the galaxies.
Edward Milne, at least, was more consistent. (See
Table 2 entry.) He
denied, just as Einstein had, the existence of absolute space, but then
went further. Having made it clear that space “by itself has no existence”
he refused to attribute to space any properties whatsoever
—no curvature, no
expansion, no contraction, no spacevacuum energy (no Λ). He rejected
general relativity and the expandingspace paradigm of which he said,

This concept though
mathematically significant has by itself no physical content; it is
merely the choice of a particular mathematical apparatus for
describing and analyzing phenomena. An alternate procedure is to
choose a static space, as in ordinary physics, and analyze the
expansion phenomena as actual motions in this space.
–Milne, E. A. A Newtonian Expanding Universe, Quarterly Journal of
Mathematics, Oxford Ser., 5, 64 (1934). 

Unfortunately Milne’s purist rejection of all properties of space,
in favor of a Euclidean space, leads to the conclusion that his universe
possesses a center and a cosmic edge —attributes which no
realistic model may have. The other models in
Table 2 do not fare any better. It turns out that almost all of
them share this problem.
Cosmic center and cosmic edge are imperfect features
a modelmaker strives to expunge from his creation. And yet ... they
persist ... they demand inclusion. If gravity is to be a part of the grand
construction, which is almost always the case, then they demand some kind
of inclusion.
David Layzer at Harvard in 1954 updated the notion that gravity is
impotent in a universe without center and edge. [Layzer, D. On the
Significance of Newtonian Cosmology, Astronomical Journal 59, p268270
(1954 Aug)] The finding has profound significance for conventional
cosmology. Categorically, the gravitational effect in expansion models is
definitively not impotent (the DeSitter model is an
exception). Gravity is actually one of the two most powerful and potent
grandscale effects in, and of, the Cosmos (Λ is the other). The
conclusion is unavoidable. Concordant with Layzer’s research, all such
models do have a center and a cosmic edge! And why is this so bad?
... It is nothing less than a gross violation of a fundamental principle
of cosmology.
The gravity problem may be stated this way:
For gravity to be potent
there must be some sort of cosmic center and some kind of cosmic boundary, but at the same time,
while affirming gravity’s potency, there must be absolutely no violation
of the cosmological principle! While gravity requires some
sort of preferred location(s), the cosmological principle prohibits
preferred locations for the Universe!
There is only one class of models with the potential of solving the
Layzer gravity problem. Only one class. It is the cellular class, and will
be described later.
THE FAILURE OF EXPANSION MODELS. All the expanding universe
models above (and others not listed) have one common flaw. They all
violate an important axiom of cosmology —known as the containment
principle (as well as the related cosmological principle). It demands that the universe includes or contains
everything that is physical (everything measurable) and nothing else. In
practical terms it means a universe can have no boundary that separates
itself from some outer region that is not a part of itself.
Any hypothesis that does not comply is burdened with a fatal flaw and
is precluded from rising to the status of a viable theory. A noncompliant model
carries a red flag; it labels itself as an implausible model.
Astrophysicist Henning Genz sums up the situation:

Let me stress that all these
models of the development of the universe from nothing ... from some
point
[like the primordial atom of the Big Bang models]...
have to be seen for what they are: models, devoid of compelling
experimental verification. The scenarios we develop from them are
possible, and they illustrate various features we can follow up on,
but none is ultimately persuasive. –Nothingness: The Science of
Empty Space p296 

As David Layzer argued, if gravity is to be a dominant
force/effect then a limiting boundary or cosmic edge must exist. We know
that gravity is the dominant player in our Universe. So let us ask the
question, the one the experts tell us we are not supposed to ask: As the Big Bang universe (or any expanding universe) expands,
what in the world (or whatever) is it expanding into? Furthermore, if it
is expanding into a nothingnessvoid (or whatever), why isn’t that
considered part of our universe? The "whatever" region is a forbidden
region beyond the cosmic edge.
Conversely we might ask, in the case of the contracting phase of the
oscillating models, what happens to the volume that the fullyexpanded
universe had previously occupied? Is it still there ready to be revisited
during the next expansion phase? The answer: Unless we are willing to use
the magic of mathematics as our guide to reality, the only rational answer
is to admit that expanding models are but subuniverses of a fullstatus
Universe —one
that is infinite in extent and nonexpanding.
MATHEMATICAL MAGIC. True enough, mathematical hyperdimensional space
can conform to the above principles. Here, one should try to
understand that (mathematically speaking) curved cosmic space can form a
fourdimensional sphere called a hypersphere. If your
imagination is good, think of ordinary threedimensional space being
analogous to the twodimensional surface of an ordinary sphere: Such a
universe is said to be finite and unbounded. Inside a
fourdimensional sphere (hypersphere) one can travel indefinitely in any
direction without reaching an edge; just as on the surface of a
threedimensional sphere. A universe hypothesized as a geometric
hypersphere is a marvelous thing. It has no exterior to which we can point
and say, "Hey, this outer region is not contained in your universe!" No
exterior to which light can ever escape! Yes, there are equations that,
almost like magic, prove that light never leaves the confines of the hypersphere
universe, but instead, curves in its path to reemerge from the opposite direction
(having circumnavigated the hypersphere). This means that
in a universe of positively curved space if you could see far
enough and wait long enough you would glimpse the back of your head
—the light beam having circled the universe to arrive at the front of your telescope
[Timothy Ferris, The Whole Shebang p320]. The equations dictate that
over the course of many billions of years light circumnavigates the
universe.
Welcome to the wonderful world of curved space. If you think the
foregoing defies all common sense, you are not alone. Something doesn’t
seem right; yet it would be pointless to argue with the logic of the
formulation. Mathematically the Friedmann universe of positively
curved space (and the Einstein 1917 universe,
Table 1), which is based on the
hypersphere, does not have a cosmic edge and does not violate
containment. The ‘something’ that does not seem right is the
connection with objective reality. We base our principles on reality
—and a real universe cannot have a cosmic edge. The question
is, “Is the hypersphere based on reality?"
I present the reader with a choice: Accept the truth of the statement:
If something is real (has a physical reality) then it can be
represented mathematically. Or accept the truth of the converse: If
something can be represented mathematically then it is real (has a
physical reality).
The validity of the first statement should immediately be
selfevident. Anything that is physically real can be measured (length,
width, height, time, speed, temperature, pressure, mass, force, energy,
... ). Measurements, of course, can be converted into numbers and numbers
can be manipulated with mathematics. Now what about the converse
statement, is it also true? ... It is not. It does not follow that if
something can be represented mathematically then it must possess a
physical reality. To make such a claim constitutes an error in logic
known as the fallacy of the converse. The choices I offered are not
logically equivalent.
Reality is the master that restrains the applicability of
mathematics. Mathematics does not dictate reality. It is physical
law that determines the mathematical constructions; mathematical
constructions do not necessarily determine the laws of physics.

All mathematics ... can be
interpreted as mapmaking. Pure mathematics constructs maps of abstract
space. A mathematician can map the contours of a fourdimensional
sphere or a tendimensional cube without worrying about whether any
such thing actually exists.
–Timothy Ferris, The Whole Shebang p70
[Some theories]
substitute mathematical symbols as the basis of science and deny that
any concrete experience underlies these symbols, thus replacing an
objective [universe] by a subjective universe.
–Louis Trenchard More, as in Revolution in Science, I. Bernard Cohen p414 

That the latter choice can lead to a deadend is easily revealed. If
mathematics ruled reality then the various string theories that have
occupied theorists for decades would long ago have been verified. String
theory involves several branches of mathematics, elegant equations,
kaleidoscopic symmetries, unfathomable complexity, and little else.
Research into strings and membranes have so far shown that any and all
hypotheses that require more than the basic four dimensions (3 spatial and
1 temporal) do not represent anything that is real in a physical sense.
We must conclude that a 4dimensional sphere is not something real. A
universe based on the 4dimensional sphere —whether the
hypersphere of positively curved space or of negatively
curved space—
is not a real universe. Furthermore, we must recognize that higher
dimensional geometry (and topology) when misapplied turns into a
mathematical trick to circumvent the cosmic edge and cosmological
principle.
UNIVERSAL EXPANSION AND INFINITE SIZE ARE MUTUALLY EXCLUSIVE. All the
expansion models (Table 2), although
meticulously crafted, are speculative. Each uses its own mathematical
construction in an attempt to dictate reality. Each fails a crucial
reality check. The models of Table 2 all
represent universes that expand and are, explicitly or implicitly, of
finite size. These two properties are not coincidental. One cannot
construct a universe predicated on universewide expansion, then expect to
have unrestricted freedom of choice with respect to size —finite or
infinite. If one claims that an entire universe expands, then it must
necessarily be a finite universe. By that very activity of growing, it
defines itself as a universe of limited extent.
And what is so faulty with finite constructions? ... Well,
there‘s that cosmicedgeandforbiddenregion problem once again. A
universe of finite size has an uncontained exterior into which it is
expanding. Each expansion model fails because it neglects the reality that the
Universe we live in has always been fully expanded. This universe is
infinite and cannot expand!
However, this does not mean that no expansion takes place
in our universe. Let me state categorically: The space
medium (the vacuum) is expanding in the universe.
The vacuum expands as part of a “harmony of opposites” as the
Ancient Greeks would say. The vacuum expands in a patterned
equilibrium with opposing contraction. Note the distinction: Expansion is
in the universe, not of the universe.
The historic Steady State models are classified as
"infinite" (Table 2); but as we have just seen this
cannot be. One cannot claim that a universe is infinite in extent and
simultaneously expanding (no matter how good one's imagination). The two
concepts are mutually exclusive.
FEAR OF INFINITY. If it is so easy to expose the failings of the
expansion models, how then does one explain their persistent popularity?
Think, for a moment, of mankind’s fallible ways of selecting and promoting ideas. Everything else being
equal, which hypothesis will grab more headlines, generate more
excitement, motivate more recruits, elicit more government and corporate
funding: on the one hand, a scenario of universal expansion with a fireandbrimstone genesis, or on the other hand, a scenario in which
nothing extraordinary happened (there was no beginning and the
universe simply exists in some state of steady processes)? ... Exactly. The flashy
awardwinning BlockBuster theory will upstage the staid and steady
presentation. Throw in the support, during the 20^{th} century, of
the Western World’s dominant religion with its affinity for cataclysmic
events and, behold, the Expansion model becomes enshrined in reverence. It
becomes a popular religiocultural icon. And to suggest that the sanctioned
viewoftheworld is wrong is risky. Any alternate view becomes ungodly.
If we wanted to proffer a deeper reason
for the popularity of expansion models then the fear of the infinite would be
a likely choice. All the models, arguably, avoid the dreaded concept of
infinite size. Although the BondiGold steadystate model claims to
be infinite, the argument that was used above reveals otherwise. If one is
willing to delve deeper, the fear of infinity can be found in
diverse fields and throughout
history in philosophy, in religion (let us not forget why Giordano Bruno
was tortured to death), in mathematics, in science, and in modern
cosmology.
THE MOST CRITICAL DEFECT. The most critical defect of all Expansion
models is their inability, utterly hopeless inability, to account for
what is known as the Abell 85 anomaly —a major inexplicable
configuration of galaxy clusters in the direction of the A85 rich cluster.
THE LAWS OF PHYSICS ALLOW BOTH
SPACEEXPANSION AND SPACECONTRACTION. So far, the
discussion has focused on expansion —expansion of space, expansion of the
universe. There is, however, another side to the story. Einstein wrote,

Cosmic expansion may be simply a temporary condition which will be
followed at some future epoch of cosmic time by a period of
contraction. The universe in this picture is a pulsating balloon in
which cycles of expansion and contraction succeed each other through
eternity. 

The significance of the dual expanding and contracting models is that
astrophysicists acknowledge that if space can expand then it can also
contract. The postulating of oscillating and cyclic models
represents tacit admission that if space can expand then it can also
contract. This is important to the DSSU model which takes the unique and
perfectly legitimate step of using both expansion and contraction. Moreover,
it uses them simultaneously.
3
Cellular Universe Models
In this section we
deal with that class of model neglected by mainstream cosmology: The class
of the Cellular Universe.
It is rather surprising that the cellular concept has never
been seriously applied to the universe. Consider that so much of the
natural world divides itself into repetitive subunits. Prominent in this
tendency is the organic realm; all organisms are structurally divided into
living cells. Entities such as viruses, classified as somewhere between
living and nonliving, are structured as cells. The inorganic realm as
well, structures itself as cells: Ice under certain natural conditions
becomes cellular and is referred to as candled ice; crystalline
minerals are composed of unit cells of the fourteen Bravis Lattices. One
of the most remarkable examples of molecularscale formation of cells is
the buckyball structure of molecular carbon C60
found in the rare coallike mineral known as shungite. In their
geometric perfection they are indeed remarkable. On a larger scale:
sunbaked and dehydrated mudflats crack into polygonal cells; the tundra
of the Canadian north, in response to the expansionandcontraction effect
of the freezethaw cycle, is shaped into large flat cells. Even the sun’s
surface is divided into cells (called thermal convection cells). If one
considers individual atoms and molecules as being celllike, then all
solids, liquids and gases are likewise cellular. ... Then why not the
entire universe?
It seems a reasonable proposal, being as it is nature's
preferred arrangement. The only necessary ingredients for cellularizing
the universe are the processes of spacemedium expansion and
contraction —known processes, known to take place. Matter itself is
ancillary. In this simplification, matter in the form of luminous stars
and galaxies serves only to highlight the boundaries of the cells formed
by the dynamics of space itself.
Yet the concept, as applied to the universe, has been almost
totally neglected (as the brevity of Table 3
reveals)! The table has only three entries: an antiquated one, an
observational one, and a theoretical one.
A search of the literature will find no true cellular models
—only
quasicellular ones. The construction of René Descartes (the Cartesian
Vortex universe Table 3) is more of a
historical model than anything else; it is probably the first attempt at a
cellular design. The Descartes model uses a vortex hypothesis in an effort
to explain the formation of astronomical structures such as stars,
planets, comets, and planetary systems.
With its aetherlike space in dynamic motion it was definitely on the
right track.
Table
3: Cellular Universe Models 
NAME
(or Type) 
Author & Date 
Classification 
REMARKS 
Cartesian Vortex universe 
René Descartes
17th century 
QuasiCellular
INFINITE 
A system of huge swirling whirlpools of aethereal or
fine matter produces what we would call gravitational effects. His
vacuum was not empty. All space was filled with matter that swirled
around in large and small vortices. The universe was a system of
interlocking vortices called “tourbillons.” 
Observational 
Jaan Einasto 1977 
Quasicellular 
Structure of the universe has a preferred cellular
scale of 100Mega parsec. However, this structure exists within a
universe believed to be
expanding. 
Dynamic Steady State Universe
(D S S U)
(consisting of cosmic cells) 
Conrad Ranzan 2002 
Cellular,
quasistatic in structure;
steady state in terms of processes;
infinite 
The DSSU infinite universe is a stable latticelike
structure of cosmic cells. Categorically a nonexpanding
universe.
Spatially distinct regions of expanding and contracting aether are
maintained by the equilibrium expressed in: contractile gravity =
expansionary Λ.
Cosmic cells are selfregulating in size and are in a perpetual steady
state of simultaneous mediumexpansion and mediumcontraction. In
other words, the "space" constituting a cell is continuously dynamic.
The cell boundaries constitute a stable (almost static) Euclidean
structure that exists within the nonexpanding universe.
DSSU complies with both the Copernican principle and the
perfect cosmological principle (timeindependent homogeneity and
isotropy on the large scale). 
The cellular class is defined by the
compartmentation of the oneandonly real Universe. The cellular type of universe should not be confused with
what are popularly known as bubble universes. Bubble
universes belong to the class of multiverses (a speculative class which also
includes parallel worlds and multiple domains); some of
the better known are described in Table 4
Miscellaneous Universe Models, which appears in the Appendix.
The Bubble model of Alan Guth and the
ChaoticInflation (bubble) model of Andreï Linde, as
Table 4 makes obvious, are highly
speculative. With names suggestive of instability (think bursting bubbles)
and chaotic randomness, they are far removed from stable cellular
organization and it comes as no surprise that they make no meaningful
predictions. Their ability to explain the Universe and its phenomena are
severely limited.
There are many additional bubble models; practically all are based
on the concept of inflationary space. The list includes extended inflation,
natural inflation,
hybrid inflation and many others. The description Andreï Linde applies to
one of his favorite, the selfreproducing inflationary universe,
gives the impression that his universe is diseased with a chronic cosmic
cancer: There are scalar fields that evolve to produce arrays of inflating
bubbles, some of which mature to make more bubbles, and so on ... ad infinitum. “In
essence, one inflationary universe sprouts other inflationary bubbles,
which in turn produce other inflationary bubbles.” [The
SelfReproducing Inflationary Universe, Scientific American Nov 1994,
p38] Models of this nature never achieve equilibrium, and cannot be
truly cellular.
Coming back to
Table 3, the quasicellular universe
attributed to Jaan Einasto is strictly an
observational entry. By Einasto’s own admission it has no theoretical
backing.
The Dynamic Steady State Universe (DSSU) stands alone
and professes to be the first true cellular universe. It is
supported by the observations of veteran astronomer, Jaan Einasto. As a
comprehensive model it incorporates the very cause, as well as the effect,
of gravitation. No other model in mainstream cosmology makes such a claim.
The
Dynamic Steady State Universe has the distinction of being the first
universe model in the history of cosmology to incorporate the concept of a
fully dynamic aetherspace, which means, first and foremost, that
the space medium expands and contracts. In the DSSU model,
spacemedium expansion is a primary dynamic activity. But note carefully,
aether expands regionally. Simultaneously, aether contracts elsewhere —again,
regionally. Hence, there is cellular order inherent in this universe.
The space medium expands as part of a “harmony of opposites” as the Ancient Greeks would say. The space
medium expands in a patterned equilibrium with opposing contraction.
The patterned equilibrium is shown in the schematic of
Fig. 1.
The model represents dynamic stability: Expansion is in
the universe, not of the universe.
The DSSU, being infinite, has no cosmic center and no cosmic edge
(and no forbidden external regions). And yet,
remarkably, gravity retains its potency!
Gravity asserts its power regionally.
This cellular model of the universe solves the Layzer gravity problem.
It manages to maintain gravity’s potency by ordering the Universe into
gravity regions (cells) each with its own cosmic center and
boundaries. See the popular article
Gravity and Lambda a Story of Opposite.
The details of the
gravity resolution and other aspects of DSSU theory are explored in
several research papers by the author. For
The following section continues with the overview of World models.
4 Two
Conflicting World Views
WORLD VIEWS. It is
possible to argue that the major world views, past and present, can be
grouped into the perpetual, unchanging, universe on the one hand and the
dynamic, tumultuous, even cyclical and plural, on the other —or simply,
the steadystate view and the dynamicstate view.
The early Chinese believed in a steady state "celestial sphere" theory
which was later (3^{rd} century AD) displaced by a weak dynamic
system, conceived as an infinite emptyspace universe in which
astronomical bodies floated freely subjected only to a mysterious "hard
wind" force.
The dynamic system (the Brahmanda, Table 1 & 2)
of the Buddhists, in addition to having a plurality of universes, used
lengthy time cycles of destruction and rebirth of the universe. The
Cartesians (Table 3), in contrast, had
their steady state universe which was filled with matter and in which the
same amount of matter and motion is always conserved. Since we cannot
think of any limit to the extent of space, it was argued, the Cartesian
universe must be infinite.
WORLD VIEWS IN CONFLICT. The scientific debate (using a rather
broad meaning) between proponents of the unchanging universe and the
defenders of a dynamic universe has existed for the most part of three
millennia. Aristotle and Eudoxus’ crystalline celestial spheres were in
opposition to Heraclitus and Anaximander’s perpetual change where nothing
ever stays still and all things are processes. "All things are in
flux," the dynamic side claimed. The ancient steadystaters came out on top, the
dynamicmovers had to bide their time.
In another age, Copernicus (14731543) still believed in a rigid sphere
of stars when he shifted the center of the universe. Thomas Digges
(154395) probably felt that the system was too unchanging and opted for a
theory in which stars extended infinitely into space, not fixed to a celestial
sphere as Copernicus had believed. However, the church decreed that the
heavens, once created, embody unchanging perfection; Giordano Bruno
(15481600) did not entirely agree and suffered the Christian consequences
of heresy.
In the last century, Einstein’s delicately crafted steady state
universe of 1917 (Table 1) was overturned
by Lemaître’s violent primordial bomb (Table 2).
In 1939, in the United States, George Gamow, Ralph Alpher and Hans Bethe
developed a version of the Big Bang that involved cataclysmic creation a ‘hot’ nuclear explosion.
Within a
decade it was countered by the BondiGold continuous creation, constant
density,
steady state (SS) universe (Table 2);
and by the very similar steady state model of Fred Hoyle (Table
2). Then in 1952 the world’s dominant Church decided to proclaim
the revised infallible truth. The universe was no longer in a perpetual steady state
of perfection, but rather a dynamic state of perfection; in
the new version the universe had a primeval fireball genesis and has
undergone explosive expansion ever since. It may expand forever; yes, even to infinity —Giordano,
your sin, your insight into infinity, has been forgiven. The sad and
tragic irony: Given enough time, heresy becomes orthodoxy.
With the discovery of the cosmic background radiation (CBR) and
its misinterpretation as the creationists’ smoking gun, the Lemaître side
claimed victory over the Steady State. Thereafter, the SS
model declined in popularity as Mainstream researchers turned their
attention to the development of a bewildering variety of dynamic
expansion models (overwhelmingly, variations of the bigbang theme).
... Although greatly weakened, the
steadystate side never accepted defeat. The steady state
concept was too beautiful to discard; it had the ingredients most
desirable in any fundamental and valid theory: simplicity and
inevitability. Work continued on the model. Hoyle, Burbidge and Narlikar
introduced the QuasiSteady State Cosmology in an attempt to allow
for the evolution of the CBR temperature in a universe that is always the
same over the very long term. A sinusoidal cycle is superimposed over the
exponential growth of the scaling factor (a measure of expansion analogous
to the radius of the universe). It is a universe with alternating cosmic
periods of expansion and contraction. See Edward Wright's
summary. (Just think, if they had used
simultaneous expansion and contraction they could have called it the
Dynamic Steady State.)
Sometimes one side or the other runs out of scientific arguments. The
English physicist C. J. Isham argued in favor of the BB by questioning the
atheism and psychological motivation of the advocates of the opposing Steady State.
While on the opposing side, John Maddox, the editor of Nature, in 1989 argued against the BB
and judged its cosmogony “philosophically unacceptable.” [Adolf Grünbaum.
Creation in Cosmology, Encyclopedia of Cosmology p126]
The massmedia and massculture of today interpret and present
"space
science" in the frame of the BB model. Any unexpected observations or
inconsistencies that arise bring another adjustment to the BB model. This
involves a Ptolemaiclike modification designed to “save appearances” and
retain the model. The official establishment model is not allowed
to fail. The formal scientific community feeds the media the
establishment model, and the media then amplify the message, while the
Steady State is largely ignored. And worse, it is sometimes treated as
though it had never existed. “It is telling that when Allan Guth, the
young elementary particle physicist who first proposed the inflationary
universe model in 1980, was asked about its relationship to the steady
state model, his answer was ‘What is the steady state theory?’ ” [Helge Kragh.
Steady State Theory, Encyclopedia of Cosmology p635 ]
The BB model gives all appearance of a solid and secure theory. Writers
and spokespeople are relentless in emphasizing just how indubitably secure
it seems with its observational successes and scientifically sound
hypotheses. The 2006 Nobel Prize in physics was awarded for research into
CBR, the phenomenon that is still interpreted as the remnant flash of a
genesis event, affirming the establishment’s patronization of the
dynamic world view —the
BB model. It seems unassailable. And yet ...

One of
the obvious lessons to be learned from the history of scientific
achievement is that no theory survives forever, and that often when things
seem most settled new observations and fresh ideas replace them with new
concepts. But, then, this is part of the adventure that is science, part
of the slow conquest of the puzzle that is the natural world, part of what
Alfred Noyes so elegantly termed the ‘long battle for the light’ in which
man has engaged since the first days of his earliest civilization.
–Colin Ronan, Science: its History and Development Among the World Cultures p527 

Attacks on the BB
model can be found in popular books such as: The Big Bang Never
Happened, by Eric J. Lerner, which advocates Hannes Alfvén's Plasma
Cosmology instead of the Big Bang theory; Astronomy On Trial: A
Devastating and Complete Repudiation of the Big Bang Fiasco (1999) by
Roy C. Martin. Another book, Seeing Red: Redshifts, Cosmology and
Academic Science, by the legendary astronomer Halton Arp, is described
as “a frontal assault on the standard model of the universe.”
But the main arena in which the conflict of the world views
takes place is that of science journals and magazine. There, one may find
a wealth of articles critical of the Big Bang and many more published in
its defense.
5
The Cellular DSSU Combines the Two Conflicting World Views
The DSSU theory manages to
accomplish the seemingly impossible: it combines the world view of
perpetual change with the other world view embracing the absence of
change. It brings together both sides of the contentious issue that
has divided cosmologists and philosophers for millennia. The cellular DSSU
is both dynamic and static. It is static in the sense
that the universe neither expands nor contracts. And it is dynamic
in the sense that the universe is permeated by an immaterial medium that
is dynamic (it induces motion). And most importantly, this universe is
both dynamic and static simultaneously and perpetually —not
sequentially. [C. Ranzan, "The Dynamic Steady State Universe"
Physics Essays Vol.27, No.2, p286315 (2014)]
The dynamic flow pattern of the space medium sustains
cosmicscale cells, as shown in Fig. 1.




Fig. 1.
Flow pattern of the dynamic space medium sustains cosmicscale cells.
The hexagon is a highlyschematic 2dimensional representation of a
single cell of the DSSU. The red arrows represent the effect of
Lambda. The blue arrows represent the
effect of Gravity. 

The Universe, on the
grandest scale, is mainly static. See Fig. 2.




Fig. 2.
Static Cellular Universe. Each hexagon represents a
dodecahedral cell (about 300 million lightyears across) within an
infinite and static (nonexpanding, noncontracting) universe. (Again, highly schematic) 

UNIFICATION OF MODELS. It is rather ironic but all the
evidence indicates that the kinematic and dynamic expansion of the big
bang and contraction of the big crunch and the perpetual
uniformity of the steady state, when brought together, comprise a
comprehensive cosmic theory. The research conducted over many years in the
preparation of numerous DSSU articles found no evidence to the contrary.
Our world is both an everchanging dynamic universe and an unchanging
steadystate universe. The DSSU is the triple amalgam of dynamic
"space", steady state processes, and static structure. And like
the structure of a living organism there is an ongoing renewal and
cellscaffolding replacement.
It has happened before. In the history of science there are
found two notable
rival theories that claimed to describe the nature of light.
One was known as the wave theory, the other the corpuscular theory (or
streamofparticles theory). After several contentious centuries there
emerged a waveparticle duality theory of electromagnetic radiation. In other words, the explanation of light
required both wave and particle theories. Remarkably, conflicting
explanations became united to form a superior single theory.
A functionally superior theory of the Universe requires features from
the two conflicting world views. The explanation of our Universe
requires dynamic vacuum, steady state processes, and quasistatic structure.
THE DSSU IN THE COMPETITION OF SCIENTIFIC THEORIES. The system for the
selection of scientific truth involves lots of random scattered ideas and
theories competing for survival. There follows the selection of the idea
that seems to work best. One idea dominates, and this is followed by its
amplification. [Heinz Pagels, The Dreams of Reason p138] ...
But no theory, no matter how orthodox, is ever safe from competition.

Scientific
knowledge, like the evolution of life, is a selective system. Theories
of the natural world evolve... –Heinz Pagels, Ibid., p168 

Now if a superior idea is omitted from the initial selection system,
then an inferior idea may take hold —then reasonable people may be led
astray. The superior idea —the cellularuniverse idea with
its dual nature (or triple nature)— has never been put forward. It has
never been in the competition (and therefore has never been rejected).
While the standard Steady State and others were rightfully
rejected, the BB became dominant (by default), became amplified, and now
rules under the sponsorship of the Academic Establishment. The only "debate"
has been among different versions of the BB model. None of these versions
is persuasive.
The DSSU is now in the competition.
The future of cosmology may very well lie not with a simplistic
singlecell Big Bang but with a multicell, dynamic,
Steady State.
Appendix
Table 4: Miscellaneous Universe Model 
NAME
(Type) 
Author & Date 
Classification 
REMARKS 
Plasma Universe 
Hannes Alfvén (Nobel Laureate); 1965 
not classified 
Infinite in time; the universe has always
existed. Infinite in size. The "big bang" is merely a local
explosion. Not based on general relativity. Galaxies and clusters of
galaxies are shaped not only by gravity, but by vast electrical and
magnetic fields. Based on the observed fact that the matter of the
universe is 99% plasma —ionized
gas that can conduct electricity. The universe is sculpted by
titanic electric currents and associated magnetic fields that flow
through the plasma. (Eric J. Lerner, The Big Bang Never Happened,
Discover 1988, June)
No space expansion. Cosmic RS is caused
by energy loss when light interacts with atoms in the intergalactic
medium.
Utilizes matterantimatter symmetry in that the universe may be
composed of separate cosmic bubbles of each type of matter. 
Multiverse (or metauniverse) 
Hugh Everett (originator)
Max Tegmark (main proponent) 
multiverse
(Generally an
infinite universe with fractal structure at all scales.) 
A multiverse (or metauniverse) is the hypothetical
set of multiple possible universes (including our universe). The
different universes within a multiverse are called parallel universes
or "parallel worlds."
The narrow meaning of "multiverse" applies to a set of
disconnected spacetimes. The broad meaning includes virtually any
kind of multipledomain and multipleparallel universes.
Multiverse models in general lack the empirical connection with
reality that comes with hard physical evidence; they arguably fall
outside the methodology of scientific investigation. They cannot be
confirmed or disproved; and therefore are more mathematically
theoretical and metaphysical than scientific in nature.
The multiverse represents more of a classification than it does a
theory. As a theory it is weak since it allows for far too many
possibilities  evident in the 4 heirarchical levels of
classification of possible metauniverses. 
Bubble Universe 
see below 
complex expanding universe 
Bubble Universe theory posits an infinite
number of "bubbles" or open multiverses; each may have different
effective physical constants, dimensionality and particle content.
Both large and small bubbles are created from the quantum foam energy
fluctuations of a "parent universe." A small energy fluctuation leads
to the formation of a tiny bubble universe which may experience some
expansion like an inflating balloon, and then contract and disappear
from existence. However, an energy fluctuation greater than a
particular critical value, leads to the formation of a bubble universe
which experiences longterm expansion, and the possible formation of
matter and largescale galactic structures. This Bubble universe
theory fits well with the widely accepted hypothesis of cosmic
inflation as well as chaotic inflation. 
Inflation (Bubbles) model 
Alan Guth
1981 
complex expanding universe 
An evolving universe based on the concept of
hot inflation. (In the original model the bubbles were way
too small, while in a later version they were too big.) As the early
hot universe cooled, a supercooled vacuumstate developed which
eventually led to a process of bubble nucleation bubbles of
true vacuum spontaneously form in the sea of false vacuum
and begin a rapid lightspeed expansion. While bubbles are expanding
at the speed of light, the bubbles themselves are spaced far enough
apart so that the expansion of interbubble space made any bubble
interaction exceedingly rare. The problem: there was a
knifeedge balance involving the rate of bubble formation. If the
rate is not finely tuned, the scenario fails.
Since each bubble represents a separate universe, Guth’s model
should also be classified as a multiverse. 
Inflation (Bubbles) models 
Andreï Linde,
Andreas Albrecht, Paul Steinhardt
1982 
complex expanding universes 
Inflation models (there are more than a few) represent
evolving universes of the multiverse type. They are based on the
concept of cold inflation (in contrast with Guth’s hot
inflation). And again, bubbles nucleate in a spacetime foam. Inflation
models violate the cosmological principle. Inflation theory, in
Linde’s words, “predicts that on the extremely large scale the
Universe becomes entirely inhomgeneous ...”
In Andreï Linde’s 1983 version, called Chaotic Inflation,
we have "little bangs" inflating themselves, at random, all over the
place. Each with independent initial conditions; some expand into
bubble universes supposedly like our entire cosmos. 
The QSSU 
Fred Hoyle, Geoffrey Burbidge, Jayant V. Narlikar
1993 
cyclical expansion and contraction 
The whole universe steadily expands and contracts (yet does not
restrict itself to being a finite universe). The universe
undergoes cyclic oscillations between periods of compression and
rarefaction involving enormous time scales. A notable characteristic
is that new matter formation takes place in regions of intense
gravitation, primarily in active galactic nuclei. Uses a Machian
theory of gravity. Space and time are geometrized (as in general
relativity theory). 




The Plasma Universe has a serious down side;
it does not make
sufficiently concrete predictions that would allow one to test and to
judge the validity of the theory. A point of interest is that it
postulates the existence of vast magnetic vortices which are reminiscent
of René Descartes' 17thcentury Vortex universe with its system of huge
swirling whirlpools of fine matter.
The originator of the multiverse concept
is generally considered to be Hugh Everett whose 1957 Princeton doctoral
thesis first presented what has come to be called the "many worlds"
interpretation of quantum mechanics.
But the concept is more a flight of fantasy than science
—a
mathematical fantasy spawned in “the century of mathematical universes.”
Cosmologist Edward Harrison sums up this category nicely: "When
postulating other universes [multiverses] we quit the solid ground of
empirical knowledge for the airy heights of unfalsifiable speculation." [E. R.
Harrison, Masks of the Universe, p288]
The QuasiSteadyState Universe (QSSU)
is an infinite universe that is steadily expanding and contracting on a
time scale of about 10^{12} years. In a later version the time scale of the
expanding and contracting cycles is 4050 Gigayears. The cyclic oscillations
"involve maximum and minimum periods of compression and rarefaction" with
creation activity in galactic nuclei being greatest in the periods of
compression. It is a universe based on a modified version of Einstein's
geometrized space and time.
New matter formation takes place at active galactic nuclei where
astronomers observe energy in the form of hot gas, relativistic particles,
and coherent objects being ejected (comparable to H. Arp’s view) but nothing falling in. The traditional
view of the black hole as representing the crushing collapse of matter is
rejected. Ejection, not mass inflow, is the dominant mode of a black hole;
and this is how new matter and energy, sometimes in the form of compact
objects such as galaxies and quasistellar objects, is born. This is the
cosmogony of small "big bangs" in which energy is created in regions of
very strong gravitational fields in already existing systems. [G. Burbidge,
An Alternative Approach to Cosmogony and Cosmology, J. Astrophys. Astr.
(1997) 18, p349351] Continuous matter creation events occur in regions of
very strong gravitational fields in the centers of galaxies in a process
supported by the HoyleNarlikar Cfield theory ("C" for creation) which contains a
modification of Einstein’s theory. Matter creation is balanced by negative
kinetic energy (whatever that is!). Unlike Einstein's cosmological
constant, which has a positive value, the QSSU Λ is negative; and
"does not represent the [vacuum] energy density of the quantum fields."
The model uses a Machian theory of gravity in which mass and
inertia arise from the interaction of a body or particle with all the
other bodies in the universe. But like all Machian models it lacks a
causal mechanism for gravitation.
The QSSU can explain the abundances of the light elements and their
isotopes. All elements are the product of stellarbased nuclear processes.
Microwave background radiation is a local effect caused by space
borne iron whiskers having favorable characteristics.
Like all other theories of the universe, except the cellular class,
the QSSU does not give a cause for the rotation of galaxies.
Although it claims to be an alternative to the discredited BB
model, the QSSU, amazingly, supports the expanding universe paradigm. The
QSSU embraces the very same pillar that makes the BB model untenable! As
we have seen so often in the comparative study of universe models, the
unscientific extrapolation of the fundamental process of the Universe
—space expansion— always leads to irresolvable problems.
* * *
2005 rev20148
Copyright © by Conrad Ranzan Email: Ranzan@CellularUniverse.org
SELECTED SOURCES OF HISTORICAL DETAILS:
Encyclopedia of Cosmology, Norriss S. Hetherington, Editor
(Garland Publishing, Inc. NY & London, 1993)
Cosmology, the Science of the Universe,
E. R. Harrison (Cambridge University Press, 1981)
The Atlas of
Scientific Discovery, Colin
Ronan(Crescent Books,
1983)
Science: its
History and Development Among the World Cultures,
Colin Ronan (The Hamlyn Publishing
Group Ltd, New York, 1982)
Lonely Hearts of the Cosmos,
Dennis Overbye (1999 ed.; Little, Brown and Company)
Partial Bibliography:
Arp, Halton. 1998. Seeing Red: Redshifts, Cosmology
and Academic Science
Cohen, I. Bernard. 1985. Revolution in Science (The
Belknap Press of Harvard University Press, Cambridge, Massachusetts)
Ferris, T. 1997. The Whole Shebang, A StateoftheUniverse(s) Report
(Simon & Schuster, New York)
Genz, Henning. 1998. Nothingness: The Science of Empty Space (Perseus
Books)
Harrison, E. R. 2003. Masks of the Universe (2nd ed. Cambridge
University Press)
Pagels, Heinz R. 1988. The Dreams of Reason (Bantam Books)
Ranzan, C. 2014. The Dynamic Steady State Universe, in Physics
Essays, Vol.27, No.2, p286315
Weinberg, Steven. 1992. Dreams of a Final Theory (Pantheon Books,
NY)

2005 rev20148 Copyright © by Conrad Ranzan Email: Ranzan@CellularUniverse.org
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