The Big Bang Model and the Cosmological Principle

In spite of the foregoing difficulties it might still be argued that Big Bang model must be correct because it predicts a universe in accord with the Cosmological Principle, viz., that the universe appears the same irrespective of the location of the observer in the universe. The problem with this argument is that we really do not know the Cosmological Principle is true. In fact, all that we know is that the large scale structure of the universe appears to be approximately isotropic (i.e., the same in all directions) from our present point of observation. Modern cosmology justifies the Cosmological Principle by coupling the observation of isotropy about our position with the assumption that our galaxy does not occupy a special position in the universe. That is, if our galaxy occupies a non-specific or arbitrary position in the universe, then it follows the universe must be isotropic everywhere and hence homogeneous as well.

But what if our galaxy does occupy a privileged position in the universe? First, it would no longer be logical to extrapolate the isotropy which we observe to the other parts of the universe, which means it would no longer be possible to justify either the condition of homogeneity or the cosmological principle. Second, the simplest deduction of the observed isotropy of the universe from our location is that the universe must be spherically symmetric about either the Milky Way or some point which is astronomically nearby. But spherical symmetry about any point in the universe implies that point is the Center, and this brings us to the discussion of the creation model.

A Creation Model of the Universe: The Fundamental Postulate

The fundamental premise of the Judeo-Christian creation model of the universe is determined by the scripture, "The Lord has established His throne in the heavens, and His kingdom ruleth over all." Psalm 103:19 (RSV). On the basis of this statement it is evident that the Creator has established, or fixed, His throne at some point in the universe, which in my view is none other than the Center of the universe. It is axiomatic that a fixed point in the universe requires the existence of a fixed or absolute reference frame. Previously [p. 287] it was noted that the CMR has been recognized as establishing an absolute reference frame (45); so it is quite clear that the fundamental postulate of this creation model of the universe is based on tangible scientific evidence.

The Revolving Steady State Model of the Universe: A Brief Description

Assuming there is a Center (C) to the universe, I propose that the galaxies are not receding from each other as presently supposed, but instead are revolving at different distances and at different tangential speeds around C. On this basis all galaxies must have a tangential velocity around C. Measurements have shown that our solar system, and hence the Milky Way, has a cosmic velocity through the CMR (46), and it is this velocity which is identified with the tangential velocity of the Milky Way around C. In this view C must lie somewhere in that plane which passes through the MW which is also perpendicular to the cosmic velocity vector of the MW. It is evident that the RSS model pictures the galaxies orbiting C in any one of many different-sized concentric shells which suggests the alternate designation 'Shell Model of the Universe.'

As originally conceived this Revolving Steady State (RSS) model envisions a universe with galaxies which move in circular orbits under the gravitational field produced by all of them. The field is assumed to be stationary and spherically symmetric. Decades ago Einstein made a general relativity study (47) of circulating particles constrained by this type of gravitational field, but his analysis did not mention redshifts, nor was there any hint that he considered his analysis had any reference to the structure of the universe.

The RSS Model and Galactic Redshifts

Assuming the galaxies are revolving in different orbital planes and with different tangential velocities v around some universal center C, initially I thought that if the Milky Way was one of the innermost galaxies, then most of the galactic redshifts as observed on earth might be due to a combination of gravitational and transverse Doppler effects. (A literature search showed that Burcev (48) had proposed over a decade ago that quasars were possibly stellar objects whose redshifts might be attributable to the transverse Doppler effect.)

Although questions have arisen about this explanation for the galactic redshifts in the RSS model, it seems worthwhile to explain my original rationale and the objections which now appear to present themselves. In particular, in the Newtonian-based RSS model the galaxies of mass m and tangential velocity v remain in circular orbits by gravitational attraction of the total mass M within the sphere of orbital radius R. In this scenario, mv²/R = mMG/R², or v² = GM/R, where G is the gravitational constant. Thus an observer on an innermost galaxy located at a distance R₁ from C would in theory see light from a more distant galaxy (at R₂ from C) shifted in frequency because of the transverse Doppler effect and the change in gravitational potential V(R) = −GM/R. The presumed limiting distance R' at which galaxies could remain in stable orbits would be when the tangential velocity v = c, the velocity of light. Beyond this presumed galactic cutoff distance the RSS model tentatively assumes a rapidly diminishing mass/energy density so that we do not encounter an infinite gravitational potential (see discussion of equations (2) and (3) for more details).

The frequency shifts expected in the RSS model can be compared to an earth-bound [p. 288] observer comparing the frequency of a light signal emitted from his position on the rotating earth's surface, where the tangential velocity is v₁, and the gravitational is V₁, with the frequency of the same signal emitted from an overhead satellite which is orbiting with velocity v₂ in a gravitational potential V₂. The experimentally confirmed (41) equation for the redshift, as derived from the principle of equivalence, is:

(1)	z = (V1 − V2) / c2 − (v12 − v22) / 2c2.

The same equation applies in the RSS model except that v₁ and V₁ are the cosmic velocity and gravitational potential of the Milky Way at R₁ from C whereas v₂ and V₂ represent the same quantities for a more distant galaxy at R₂ from C.

Another source of frequency shifts arises because the Milky Way (MW) is not exactly at C. In this case the more distant galaxies, which are rotating away from or toward the MW, produce first order Doppler redshifts or blueshifts. The blueshifts, which would be most pronounced for nearby galaxies, can be eliminated for all practical purposes if it is assumed that the more distant galaxies are rotating away from the MW. This scenario would result in a recessional redshift which, because it depends on the cosine of the angle between the velocity vector of the outer galaxy and the line of sight from the MW to that galaxy, would diminish with distance. Thus, of itself this redshift could at most be only a part of the total galactic redshift observed on the earth. Of course, a significant distance-related redshift, irrespective of its origin, could overshadow most blueshifts expected from galaxies rotating toward the MW and eliminate the need for assuming rotation away from the MW.

We now return to the discussion of the redshifts expected on the basis of eq. (1). If the ρ, the mass/energy density of the universe is assumed to be constant then M = 4 πρ R³/3, and substitution of the appropriate quantities into eq. (1) leads to the formal result that z is proportional to R², which is of the same form of the redshift relation proposed in references (33,34,37-39). On a similar basis, if the density is assumed to vary inversely as R, then one can obtain an expression for z which is proportional to R, which is of the same form as the Hubble relation (49).

Of course, astronomers measure apparent magnitudes, not distances, and, for there to be a quantitative comparison between the above results and the redshift distribution, the light flux relation for the RSS model must be formulated so as to include the combined effect of the redshift and gravitational focusing. This formulation has yet to be done; thus on this basis alone it would be premature to claim the forgoing results are consistent with the galactic redshift relation proposed by Nicoll and Segal (38). Moreover it should be remembered that if the universe is revolving, then an extraneous factor has been included into the data which comprise the redshift distribution, and this would preclude any immediate comparison. But regardless of the outcome of the above calculations, there seems to be a more fundamental objection to the preceding formulation.

In particular, we must carefully investigate whether the gravitational potential V = −GM/R used in the above calculations is the correct expression for the potential function. It is of crucial importance to know whether it is correct for it is used as the basis for the derivation of the Hubble relation (31,32) in Big Bang cosmology. According to Silk (31) and Weinberg (32), its use in computing the potential at the surface of an arbitrarily large, but finite sphere, of radius R within an infinite universe is justified by a theorem [p. 289] due to Birkhoff. Part of the proof of this theorem implicitly assumes that the universe is structured according to the Cosmological Principle. Now the creation model of the universe proposed herein is also of infinite extent, but the Cosmological Principle does not hold, so that there is no basic reason why this theorem should yield the correct gravitational potential in the RSS model. But should it hold for the Big Bang model?

To answer this question we first note that the negative gradient of the potential V = −GM/R yields a repulsive force per unit mass F/m = GM/R² whereas there is an experimentally confirmed theorem in classical mechanics which definitely requires an attractive force per unit mass F/m = −GM/R² to exist at any point R within a sphere enclosing a uniform mass distribution. This latter result is an integral part of both the RSS and the Big Bang models. Thus the potential V = −GM/R is just as wrong for the Big Bang model as it would be for the RSS model because it yields an incorrect sign for the force. Even Silk's (31) elementary treatment (see page 332) makes it clear that the derivation of the Friedmann equation for the Big Bang expanding universe is based on the potential V = −GM/R. Here we have a logical contradiction in the theoretical development of the primeval fireball, which is of course the basis for predicting the Hubble relation in the Big Bang.

An expression for the potential (50,51) which does yield the correct attractive force is given by

(2)	V(R) = −GM/R     − G ∫R∞ 4 πρ r dr     where M = 4π ∫oR ρr2dr.

The problem here is that for a finite, uniform density we encounter an infinite potential due to the presumed infinite size of the universe. This result is the same for both the Big Bang model and the RSS model.

Alternatively, a finite potential can be obtained from eq. (2) by assuming the density diminishes more rapidly than 1/R³ after R', where v = c. As a first approximation this assumption truncates the potential at R'. In this case the upper integration limits in eq. (2) must be changed from infinity to R', and we have the following potential:

(3)	V(R) = −GM/R     − G ∫RR' 4 πρ r dr     where M is defined in eq. (2).

If this potential is used in eq. (1) to compute z for the RSS model, then for a uniform density for all R less than R', we find the redshift is zero. If, however, the density increases as R^0.22 then we can formally obtain a relation (51) similar to that deduced by Hawkins (34). Again, however, it is premature to make any claims about this result until more work is done.

Another possibility for obtaining redshifts in the RSS model is to assume the mass/energy density diminishes as 1/R⁴. In this case the galactic orbits are no longer circular but spirals, and there is a recessional component to the velocity which leads to a first order Doppler shift and a Hubble type z R relation. For this view to have any credibility most of the mass/energy of the universe must be in a form other than the matter and radiation energy presently observed and/or inferred in stellar systems and intergalactic dust. In this context it is perhaps worth mentioning that Ellis (52) has proposed that there may be a large amount of undetected mass/energy in other forms (e.g., neutrinos) which could raise the cosmic mass/energy density to more than a million times the present density estimates of 10⁻³¹to 10⁻²⁹g/cm³.

[p. 290]

Of course the RSS model does not require that the redshifts are velocity dependent. In this respect it is well known that years ago proponents of a static or steady state universe proposed a variety of distance-dependent interpretations of the redshift which were non-recessional in nature (see North's (42) review for details and references). The investigation of the origin of the redshifts in the RSS model should include a reexamination of these alternatives.