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Did the Universe Have a Beginning?

by Tom Van Flandern, [13]Meta Research

[14]Abstract

[15]Introduction

[16]What Does Expansion Mean?

[17]Does the Universe Really Expand?
* [18]Test #1: Apparent magnitude versus redshift for galaxies
* [19]Test #2: Galaxy number counts versus redshift
* [20]Test #3: Surface brightness versus redshift for galaxies
* [21]Test #4: Angular size versus redshift for galaxies and radio
sources
* [22]Test #5: Supernova lightcurves
* [23]Test #6: The ages of globular clusters and of superclusters of
galaxies
* [24]Test #7: Galaxy evolution

[25]Conclusions

[26]What Else Can Cause Redshift?

[27]Footnotes

_CAPTION:_ _ABSTRACT_

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.

INTRODUCTION

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 point.

(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 laws."
[28]2 Odenwald and Fienberg state the point in more detail:[29]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 nihilo_[30]4 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
expansion.[31]5 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).[32]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 being equal.

Test #2: Galaxy number counts versus redshift

Results of this test
[33]6, 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 members
[34]7, 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.[35]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 expanding universe model.
[36]9 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 galaxies
[37]10. 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 epoch
[38]11, 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 galaxies.[39]12 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.

CONCLUSIONS

Test Description Consistent with Friedmann models? Consistent with
Static universe models?
1 mag. vs z if q0 >= 1 yes
2 # vs z if q0 <= 0 yes
3 SB vs z yes yes?
4 ang. size vs z if q0 <= 0 yes
5 supernovas yes yes
6 ages no? yes
7 evolution yes yes

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.
[40]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
_[MATH:_ &Lambda; _:MATH]_
(= pressure resisting gravity); the cosmic deceleration parameter q0
(= expansion deceleration); the density parameter
_[MATH:_ &Omega; _:MATH]_
(= 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 mechanisms.
[41]14 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 author. [42]15

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
elsewhere[43]10,15,16, 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 1926[44]17 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 premises![45]18

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.
_________________________________________________________________

FOOTNOTES:

1. Meta Research, Inc. / 6327 Western Ave, NW / Washington, DC
20015-2456 / USA.
2. Harrison, E. (1993), "The redshift-distance and velocity-distance
laws", _ApJ 403_, 28-31.
3. Odenwald, S. & Fienberg, R.T. (1993), "Galaxy redshifts
reconsidered", _Sky & Telescope_ February, 31-35.
4. from nothing.
5. Moles, M. (1991), Proc. XII Autumn School of Physics: _"The
physical universe: the interface between cosmology, astrophysics
and partical physics"_, ed J.D. Barrow et al., Springer, Berlin,
197-226.
6. LaViolette, P.A. (1986), "Is the universe really expanding?", _ApJ
301_, 544-553.
7. Djorgovski, S. and Spinrad, H. (1981), "Toward the application of
a metric size function in galactic evolution and cosmology", _ApJ
251_, 417-423.
8. Hajivassiliou, C.A. (1991), "On the cosmological significance of
the apparent deficit of small interplanetary scintillation
sources", _ApJ 381_, 3-5.
9. Norgaard-Nielsen, H.U. et al. (1989), "The discovery of a type Ia
supernova at a redshift of 0.31", _Nature 339_, 523-525.
10. Lerner, E. (1991), _"The big bang never happened"_, Times Books,
New York, pp. 23-24 & 28.
11. Rigler, M.A. & Lilly, S.J. (1994), "Infrared surface photometry of
3C 65: stellar evolution and the Tolman signal", _ApJ 427_,
L79-L82.
12. McGaugh, S.S. (1994), "A possible local counterpart to the excess
population of faint blue galaxies", _Nature 367_, 538-541.
13. Maoz, D. and Rix, H.W. (1993), "Early-type galaxies, dark halos,
and gravitational lensing statistics", _ApJ 416_, 425-443.
14. Ghosh, A. (1991), "Velocity-dependent inertial induction: a
possible tired-light mechanism", _Apeiron_ 9-10, 35-44.
15. Van Flandern, T. (1993), [46]"Dark Matter, Missing Planets and New
Comets", North Atlantic Books, Berkeley. Also available from Meta
Research.
16. Van Flandern, T. (1993), "Is the microwave radiation really from
the big bang 'fireball'?", _Reflector_ (The Astronomical League
Newsletter) _XLV_, 4.
17. Eddington, A.E. (1926), _"Internal constitution of the stars"_,
Cambridge University Press, reprinted 1988. See chapter 13, "The
temperature of space".
18. Sumner, W.Q. (1994), "On the variation of vacuum permittivity in
Friedmann universes", _ApJ 429_, 491-498.

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