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WHAT DOES EXPANSION MEAN?

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."² 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 nihilo⁴ 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?

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

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

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 members⁷, 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 expanding universe model.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

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 epoch¹¹, 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.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

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 $\Lambda$ (= pressure resisting gravity); the cosmic deceleration parameter q0 (= expansion deceleration); the density parameter $\Omega$ (= 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.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. 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^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 1926¹⁷ 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!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.

1. Meta Research, Inc. / 994 Woolsey Ct / Sequim WA 98382-5058 / USA.
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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.
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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.
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17. Eddington, A.E. (1926), "Internal constitution of the stars", Cambridge University Press, reprinted 1988. See chapter 13, "The temperature of space".
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