The big bang theory postulates that the entire universe
originated in a cosmic explosion about 15 billion years ago. Such an idea
had no serious constituency until Edwin Hubble discovered the redshift of
galaxy light in the 1920s, which seemed to imply an expanding universe.
However, our ability to test cosmological theories has vastly improved with
modern telescopes covering all wavelengths, some of them in orbit. Despite
the widespread acceptance of the big bang theory as a working model for
interpreting new findings, not a single important prediction of the theory
has yet been confirmed, and substantial evidence has accumulated against it.
Here, we examine the evidence for the most fundamental postulate of the big
bang, the expansion of the universe. We conclude that the evidence does not
support the theory; and that it is time to stop patching up the theory to
keep it viable, and to consider fundamentally new working models for the
origin and nature of the universe in better agreement with the observations.
For most of the existence of our species on this planet, mankind has
believed that our home, the Earth, was located at the center of the
universe. Copernicus's theory and the Scientific Method finally displaced
this strongly held geocentric view with the humbler but more realistic
perspective that we are no place special in the universe.
Because this basic perspective change was so difficult to achieve, modern
science has since always insisted that any theory seeming to put humans in a
special place in the universe was thereby automatically suspect. So when
modern cosmologies were first formulated, they were required to obey the
"cosmological principle", that the universe should have a uniform matter
distribution on the largest scales ("homogeneity"), and look essentially the
same for all observers viewing in all directions ("isotropy").
With this background, it therefore came as a surprise in the 1920s when
Edwin Hubble found that the light from galaxies appeared redshifted; and
that the fainter (and therefore farther away, on average) a galaxy was, the
more its light was redshifted. Here was an observable property of the
universe that seemed centered on us, and changed uniformly with distance
away from us, as if we were at the center of the universe.
The timing of this discovery was critical to further evolution of the
theories. At just that time, Einstein's general theory of relativity had
received observational support and was gaining in favor with physicists.
But there was a serious problem in incorporating general relativity into
cosmology. It appeared that gravity made the universe unstable, inducing it
to collapse. Wherever galaxies or large assemblies of matter existed, other
distant galaxies or assemblies would be attracted toward them; and these
mutual attractions would cause all galaxies or large assemblies to be pulled
toward one another, since they had insufficient velocity to resist the
attraction. Simply put, all sufficiently large structures, including the
universe as a whole, must collapse under the weight of mutual gravitation.
Yet observations showed this did not happen.
To get around this difficulty, Einstein invented the "cosmological
constant" -- a hypothetical repulsive force operating on large scales that
prevented the collapse of the universe. This was the unsatisfactory state
of affairs when Hubble made his redshift discovery. Physicists of the day
immediately knew that, if the redshift of galaxy light was caused by
galaxies moving away from us, the implied expansion of the universe would
serve to solve the "problem" with the stability of the universe in a far
more elegant way.
Friedmann described three possible models in which the universe would
appear homogeneous and isotropic, yet be seen as expanding, by all observers
in it at the present time:
(1) The open universe, in which the rate of expansion everywhere exceeds the
velocity of escape from the rest of the matter in the universe. Such an
expansion would continue forever; and space in such a universe can be
described as negatively curved.
(2) The closed universe, in which the expansion is eventually halted by
gravity and becomes a collapse back to the origin. Such a universe has a
finite lifetime unless it bounces and continues expanding and recollapsing
forever. Space in this type of universe has positive curvature. As on a
sphere, a straight line in any direction eventually returns to its starting
(3) The flat universe, in which the expansion is critically balanced at the
threshold between open and closed. The expansion goes on forever,
asymptotically approaching zero velocity after infinite time has elapsed and
the universe has become infinitely large. Space therein has no curvature.
In principle, observations should allow us to determine which type of
Friedmann expanding universe we inhabit. We simply measure the cosmic
deceleration parameter, q. In a flat universe, the total matter in the
universe is just enough to halt the expansion after an infinite time. This
corresponds to a cosmic deceleration q0 = 0.5. If the observed value of q0
is larger than 0.5, the universe is closed. If q0 is less than 0.5, the
universe is open. If there were no cosmic deceleration, q0 = 0; or if the
expansion accelerates due to some hypothetical force of repulsion, q0 < 0.
The most widely accepted form of the big bang theory predicts that q0 = 0.5.
Thus, the big bang theory was born from the adoption of Friedmann's
premises as the explanation for Einstein's quandary about the collapse of
galaxies and Hubble's redshift data. However, in their eagerness to solve
these dilemmas, astronomers and physicists were induced to accept a new, if
less distressing, way of accepting that the observer was special. It is
true that the Earth would occupy no special place in a Friedmann-type
universe, and everything would look basically the same in all directions as
seen by anyone anywhere. However, everything in the universe would always
be at a special time, a finite number of years from the beginning or end of
the universe, and evolving accordingly. The universe looked rather
different at any two widely spaced moments of time. The Friedmann models
still obeyed the original cosmological principle; but they violated the new
"perfect" cosmological principle, in which the universe should look
essentially the same to any observer at any time as well.
This development was ironic, because one of the accomplishments of the
theory of relativity was to show the large extent to which space and time
were similar and interchangeable. That symmetry had to be abandoned by the
big bang when the perfect cosmological principle was abandoned. As we will
discuss, this pragmatic decision to once again allow the observer to be
special (observing at a special time) was probably a wrong turn for science.
WHAT DOES EXPANSION MEAN?
The essence of the big bang cosmology is an expanding universe. The
redshift of the light from galaxies is proportional to their distance (as
inferred from brightness). No cause of galaxy redshift other than a
velocity away from the observer was considered plausible, so Hubble's result
was taken to mean that, the farther away from us a galaxy is, the faster it
moves away from us. Hence, the overall universe had to be expanding.
Of course, the redshift still might be caused by something other than
velocity. The only way to be sure is to perform observational tests. When
considering tests for expansion, it is important to know what expansion
really means in the big bang theory. The three Friedmann models described
ways in which the expansion would appear the same from everywhere within the
universe. But if this expansion meant that all matter in the universe was
at one time located at a point in space, then the universe would have a
center and an edge. That would make every point in it "special" with
respect to the origin point and with respect to the void beyond the edge.
The view would not be the same from everywhere.
To understand expansion in the big bang theory, we are asked to visualize
an expanding balloon as a 2-dimensional analogy of our 3-dimensional
universe. Every point on the surface of the balloon gets farther away from
every other point as the balloon expands. Yet no point on the surface
serves as the center, and there is no edge. The expansion is slowed by
gravity and may eventually halt and begin to contract back to its origin
point; or the expansion rate may be too high to ever halt the expansion. It
is up to observations to tell us which kind of Friedmann universe we inhabit
by allowing us to measure the cosmic deceleration parameter, q.
But all these Friedmann universes are very different from the kind of
expansion one would get if the universe originated in an explosion into
pre-existing empty space. This is because the big bang is an explosion of
space and time, not an explosion into space and time. A recent paper by
Harrison explains: "From a purist point of view one cannot help but deplore
the expression 'big bang', loaded with inappropriate connotations ..., which
conjures up a false picture of a bounded universe expanding from a center in
space. In modern cosmology, the universe does not expand in space, but
consists of expanding space. And this correct picture leads naturally to a
distinction between the redshift-distance and velocity-distance
Odenwald and Fienberg state the point in more
detail:3 "This [cosmological]
redshift, which again is not a Doppler shift, arises from the expansion of
space-time itself. Light waves literally stretch as the universe expands
between the time the light was emitted and today, when it finally reaches
us." ... "Now galaxies are located at fixed positions in space. They
might perform small dances about these positions in accordance with special
relativity and local gravitational fields, but the real 'motion' is in the
literal expansion of the space between them." ... "This is not a form of
motion that any human being has ever experienced, in that it does not
involve travel through space. So it is not surprising that our intuition
reels at its implications and seeks less radical interpretations."
So the big bang postulates that the cosmological expansion occurs, not
because galaxies move apart through space, but because more space is being
continually added between them. This continual creation of space ex
is an integral part of the theory. Without it, the cosmological principle
would be violated.
"And in the beginning there was nothing. And God said 'Let there be light.'
And there was still nothing, but now you could SEE it!" -- Anonymous
DOES THE UNIVERSE REALLY EXPAND?
One might be inclined to think, given the popularity of the big bang theory
today, that we must by now have solid evidence that the universe is indeed
expanding. But in truth, that most fundamental premise to the big bang
cosmology remains an assumption. Attempts to show its truth observationally
have frustrated astronomers for decades. Moles recently summarized the four
classical tests for
These involve the relationships between the
redshift of galaxies on the one hand, and apparent magnitude, surface
brightness, number counts, or angular size of galaxies on the other hand.
The redshift of galaxy light is assumed to be caused by the velocity of the
galaxy away from us. We are here examining tests of the correctness of that
assumption. In the next section we will mention some alternative
interpretations of redshift for galaxies. To be clear on this point, it is
well established that the redshift of ordinary galaxies (although not radio
galaxies, Seyfert galaxies, "active galactic nuclei", or quasars) is closely
correlated with the distance of those galaxies. But is not well established
that the redshift is caused by an increase in that distance.
These classical tests are somewhat complicated with respect to proving or
disproving the expansion hypothesis by the influence of unknown evolutionary
effects. But these galactic evolutionary effects themselves, and also
supernova lightcurves and the ages of globular clusters and galaxy
superclusters, each offer the possibility of specialized tests of the
expansion hypothesis. We can also easily test non-expanding (static)
models, since these generally have no evolutionary effects.
One great difficulty in applying observational tests to galaxy samples is
the influence of Malmquist bias. Galaxy sizes do not seem to have any
definite maximum, but very large galaxies are rare compared to those of
average size. So if we take a small sample of galaxies, it probably will
not contain any galaxies very much larger than normal. But the larger our
sample becomes, the more extreme the largest galaxy in it is likely to be.
So as we look farther out into the universe, two things happen
simultaneously: We start to lose the smaller galaxies from our samples
because they are too faint to be seen; and the total number of galaxies
increases with roughly the cube of distance. The first fact tends to push
the average galaxy in our samples toward the brighter, and therefore larger,
galaxies. The second fact implies that the brightest galaxies in our
samples will tend to get brighter with distance simply because a larger
sample will tend to find more abnormally large galaxies than a smaller
sample would. Both effects bias our samples toward larger, brighter
galaxies as distance increases. Astronomers must make the effort to
compensate for this using appropriate sampling techniques, or the
observational test results may become misleading.
For the equations underlying these tests and more details of the analyses,
see Moles (1991).5
Test #1: Apparent magnitude versus redshift for galaxies
Applications of this test potentially suffer not only from Malmquist bias,
but also because of extinction due to the intergalactic medium, making
distant galaxies appear fainter than they otherwise would. But when these
biases are compensated to the best of our ability, the observed relationship
seems to agree well with expansion models that have a cosmic deceleration
parameter q0 = 1 or slightly larger (closed universe). Of course, given
that q0 is a free parameter, some form of the expansion hypothesis was sure
to agree with observations. It is interesting to note that the static
universe model, with no free parameters, also agrees with these
observations. Taken in isolation, this test would therefore favor static
universe models because they are simpler theories in the sense of Occam's
Razor ("Invent no unnecessary hypotheses") or in the sense of Beysian
analysis -- models with fewer free parameters are preferred, other things
Test #2: Galaxy number counts versus redshift
Results of this test6,
taken at face value, do not agree with expansion
models unless ad hoc evolutionary corrections are applied, and the universe
is open. q0 <= 0 is implied for the cosmic deceleration parameter.
These results do, however, agree with static models. As before, the static models
are without benefit of extra parameters. In expansion models, the
evolutionary corrections must already be important at a redshift of 0.4,
where galaxies were thought to be only very mildly different from those in
the present universe, according to the big bang model. So this test, too,
favors static models over expanding ones.
Test #3: Surface brightness versus redshift for galaxies
The surface brightness versus redshift test is the most difficult to
correct for observational bias effects such as Malmquist bias. It therefore
is the least conclusive test. The best available results are broadly
consistent with both expansion and static models, but give better agreement
with expanding models.
Test #4: Angular size versus redshift for galaxies and radio sources
This test predicts the most drastic difference between expanding and static
models, since expansion requires a minimum angular size near roughly
redshift z = 1.2, whereas static models usually predict no minimum in the
observable range. The test is also the most observational-bias-free among
the four classical tests. Results from observations of galaxy cluster
radii, and (independently) from the sizes of brightest cluster
both disagree strongly with predictions of any form of the Friedmann
expanding universe models since no such minimum angular size is seen, but
agree reasonably well with static universe models. Results from the largest
angular sizes of double radio sources are less consistent with static
models, but still disagree strongly with all expansion models. Results
showing a lack of small radio sources give cosmological parameters
inconsistent with any of the preceding, but may themselves be explained by
interplanetary scintillation effects.8
To defend expanding models it is necessary to postulate strong evolutionary
effects, sometimes counter-intuitive ones. For example, the most powerful
radio sources must also be the intrinsically smallest ones. It is also
necessary to have little or no deceleration of the universe, or even an
acceleration of the expansion; i.e., the universe must be strongly open;
except for the small radio source observations, which seem to imply the
universe must be strongly closed unless the lack of small sources is a
scintillation effect. In most static models, redshift is not a distance
indicator for radio sources such as quasars and most radio galaxies, so only
the galaxy results (which agree) should be considered significant.
Therefore three of four independent applications of this test, two of them
strongly, favor static universe models over expanding models; and the fourth
test is inapplicable to most static models.
Test #5: Supernova lightcurves
Type Ia supernova lightcurves have a characteristic shape and rate of
decline. If the universe were expanding, supernova lightcurves in high
redshift galaxies would be stretched out in time due to the rapid recession
of the parent galaxy. In a static universe, no such stretching would occur.
The best case so far is for a supernova in a redshift z = 0.31 galaxy seen
only after the explosion reached its maximum brightness and begun its
decline. Model-dependent assumptions about the time and intensity of the
maximum brightness must be made. The observations can then be fit with an
But expansion is not required for a good fit to
the observations because the light maximum was not seen, so static models
work too. The results of this test are therefore presently ambiguous. In
1993, another supernova was seen in a galaxy at redshift z = 0.43. Details
of an analysis of those observations are eagerly awaited.
Test #6: The ages of globular clusters and of superclusters of galaxies
If the universe originated 10-15 billion years ago, then no objects within
it can be older than that. Yet the deduced ages of globular clusters of
stars in our own galaxy do appear somewhat older than that, perhaps 16-18
billion years old. It is usually assumed that either something is wrong
with stellar evolution theory, making the calculations come out too large;
or that the universe is actually more like 20 billion years old, as
astronomer Sandage has argued. So the age of globular clusters is not
presently a strong argument for any model of the universe.
The age problem is a bit more severe in the case of superclusters of
galaxies. These huge structures would take perhaps 100 billion years to
form, given the typical relative speed of
galaxies10. The same problem
applies to "great walls" of galaxies, which are even vaster structures.
There is no clear way to form structures on such large scales in the time
available unless relative velocities were much higher in the past. But
higher past velocities would require a dissipation mechanism which would
have released tremendous energy. There is no credible evidence at present
for the operation of such an enormous energy sink as would be required to
resolve this dilemma. Therefore, this test presently favors static universe
models, which have essentially unlimited time to form the observed
structures through normal processes.
Test #7: Galaxy evolution
If the universe originated just 10-15 billion years ago, galaxies are a
recent phenomenon, and galaxy evolution would be a strong feature of the
early universe. If the universe is not expanding, then presumably galaxies
today are of the same character as those of 10-15 billion years ago. It is
argued that, in a non-expanding universe, the radio galaxy 3C 65 at a
redshift of 1.2 would be larger and fainter than any known galaxy in the
local universe at the present
which seemingly implies the need for
evolutionary effects. However, as already noted, in many static universe
cosmologies, redshift is not a distance indicator for quasars and most types
of radio galaxies. So inferences about the true size and intrinsic
brightness of the radio galaxy would not be applicable. Indeed, the entire
progression from quasars to ordinary galaxies, postulated in the big bang,
is interpreted quite differently in static models, so that no clear
distinguishing test of models appears possible using these exotic objects.
In recent years it has been popular to point to the so-called
"Butcher-Oemler effect" as evidence that galaxies do evolve with time. This
is an observation that faint blue galaxies are far more abundant at
redshifts of 0.4 and up than they appear to be in the local universe.
However, in the most recent findings it now appears that
low-surface-brightness (LSB) galaxies may be the local counterpart of these
faint blue distant
LSB galaxies are difficult to discover
locally because we tend to look right through them. But in a recent survey
specially designed to detect such objects, they appeared to be as abundant
as normal spiral galaxies. However, like their possible distant cousins,
they are much bluer than spiral galaxies, making them good candidates to be
the local counterparts of the Butcher-Oemler faint blue galaxies. If that
identification is correct, this strongest remaining argument for the
evolution of galaxies as a class with time would be invalidated.
||Consistent with Friedmann models?
||Consistent with Static universe models?
||mag. vs z
||if q0 >= 1
||# vs z
||if q0 <= 0
||SB vs z
||ang. size vs z
||if q0 <= 0
A summary of the seven tests is shown in the table. For an expanding
universe model to be consistent with the observations, a solution must be
found to the unexpected existence of extremely large structures in the
universe, such as superclusters of galaxies and great walls, which have had
insufficient time to form since the origin of the universe; ad hoc
evolutionary effects must be postulated to explain some test results,
especially the absence of the predicted minimum angular size for
large-redshift objects; and a solution must be found to the apparent
contradiction between the results of test #1 and those of tests #2 & #4 for
the implied value of the cosmic deceleration parameter q0.
These difficulties for the Friedmann models cannot be rescued by Einstein's
cosmological constant because incompatible values would be required by
different tests, and because the scarcity of observed gravitational lenses
severely limits any non-zero value for this parameter to be too small to
help the big bang theory.13
Also, big bang models now use an ever increasing variety of free parameters
to maintain consistency with various observational constraints. Related to
origin and expansion conditions alone, we now have the Hubble constant h (=
expansion rate); the cosmological constant
(= pressure resisting gravity);
the cosmic deceleration parameter q0 (= expansion deceleration); the density
(= ratio of actual matter density to density needed for flat
universe), subdivided into the density for ordinary matter and that for
invisible dark matter; and the bias parameter b (= measures lumpiness of
matter distribution). The hypothetical dark matter is itself a fudge factor
required to obtain agreement with observations that were not in accord with
big bang expectations, and it comes in three flavors: hot, cold, or mixed.
So even if the difficulties shown in the table were solved elegantly,
Occam's Razor (a part of Scientific Method) tells us that we should still
prefer the model with fewer free parameters.
If the field of astronomy were not presently over-invested in the expanding
universe paradigm, it is clear that modern observations would now compel us
to adopt a static universe model as the basis of any sound cosmological theory.
WHAT ELSE CAN CAUSE REDSHIFT?
If the redshift of galaxies is not due to expansion velocity, then what
might cause the redshift? Over the years, a surprising number of proposals
have been made. A recent summary article lists 20 non-velocity redshift
Basically, anything that causes light to lose energy will
cause it to redshift. The trick is to have an energy loss mechanism that
doesn't scatter the light. The absence of observed scattering is the main
objection to the so-called "tired light" theory, in which intergalactic
matter is supposed to be responsible for the energy loss of light.
One of many possibilities (the one favored by this author) is that one day
we will discover the particle or wave serving as the carrier of the
gravitational force. If such entities, dubbed "gravitons", exist, they must
necessarily be of a much finer scale than current quantum particles. It
therefore seems likely that they would have negligible scattering effects on
light over cosmological distances, although light traveling through such a
resisting medium of gravitons would necessarily lose energy and be
redshifted. In such a case, we would expect to see light from galaxies
redshifted in proportion to their distances from us, just as observed; yet
there would be no expansion of the universe. The perfect cosmological
principle would be obeyed.
This particular notion of gravitons also answers the dilemma for general
relativity faced by Einstein -- Why doesn't the universe collapse from its
own gravity? If these hypothetical gravitons have a finite cross-sectional
area, then they can only travel a finite distance, however great, before
colliding with another graviton. So the range of the force of gravity would
necessarily be limited in this way. Curiously, if the mean flight distance
between collisions for gravitons was about 2 kiloparsecs (about the diameter
of the core of many galaxies), then the limited range of the force of
gravity would give rise to a change in the inverse square force law over
distances larger than 2 kiloparsecs. The predicted form of this change
happens to imitate just what we observe in the behavior of galaxies that has
led big bang astronomers to hypothesize the existence of "dark matter" in
ever greater quantities to account for the rotation and clustering of
galaxies on these large scales. In other words, if this graviton conjecture
is correct, there would be no need of invisible dark matter to explain
large-scale behavior of dynamical systems. More details of this alternative
model are published elsewhere by this
What of the cosmic microwave radiation and the light element abundance
predictions, often touted as successful predictions of the big bang model?
These points have been critiqued in detail
elsewhere10,15,16, and that
discussion is beyond the scope of this paper. To make a one-sentence
summary about each point: The big bang made no quantitative prediction that
the "background" radiation would have a temperature of 3 degrees Kelvin (in
fact its initial prediction was 30 degrees Kelvin); whereas Eddington in
had already calculated that the "temperature of space" produced by the
radiation of starlight would be found to be 3 degrees Kelvin. And no
element abundance prediction of the big bang was successful without some ad
hoc parameterization to "adjust" predictions that otherwise would have been
judged as failures.
As a final note on the question of the universe's expansion, it should not
be forgotten that it is not even certain that the universe is presently
expanding (as opposed to contracting) even within the context of the big
bang theory. Sumner has recently argued that the new space introduced by
the expansion must dilute the permittivity of the vacuum, which in turn must
alter the frequency of electrons around atoms. This affects observed
redshifts twice as strongly as the speed of expansion. When this
consideration is factored into the equations, it turns out that the present
universe is actually collapsing, not expanding, under big bang
So we see that, despite the widespread popularity of the big bang model,
even its most basic premise, the expansion of the universe, is of dubious
validity, both observationally and theoretically.
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