The overwhelming majority of university and state funded cosmologists believe that the observable universe has expanded from a much smaller and much hotter and denser volume of space over the last 13 billion years or so. Some believe that the original volume of the observable universe may have had a size as small as a grapefruit, or possibly the size of a single atom, or that it had a quantum size or even the infinite density of a zero-sized singularity. The eruption of the universe from the initially very compact state commonly gets called the Big Bang.

Several items of evidence led to this novel idea.

Firstly, it would seem that if we inhabited a universe that tried to stay still then its own gravity would cause it to collapse.

Secondly, light from distant galaxies appears shifted towards the red or lower energy end of the spectrum, and the greater the distance to the far galaxy the more pronounced this red shift becomes. Cosmologists have interpreted the galactic redshifts as evidence for the galaxies flying away from us and stretching out the light waves and lowering their energy as the universe expands.

Thirdly, a thin drizzle of microwave radiation permeates all of space and it comes in from very deep space, from way beyond the local galaxies. This radiation has the name of the Cosmic Microwave Background Radiation (CMBR). Cosmologists have interpreted this as the remnant of a time when the early universe had a very high temperature, and that subsequent expansion has stretched and cooled the radiation from the early fireball.

Fourthly, the universe contains about 25% helium and 75% hydrogen, with only a fraction of a percent of the heavier elements that make up planets and rocks and us. Cosmologists use this observation to support a rather curious circular argument which says that if hydrogen constitutes the primordial form of matter but it gets transmuted into helium in stars, then 13 billion years of star activity will not suffice to produce that much helium. Ergo much of the helium must have got made in the violence of the Big Bang.

A whole massive edifice of official scientific theory depends on these three and a half items of evidence. Hardly anyone dares to question the big bang idea in principle, for fear of loosing their academic funding, so they just argue about the precise details of it and try to fit new observations within the theory.

However the theory has many holes in it, and the attempt to patch them has led to all sorts of fudges and the multiplication of dubious sub-hypotheses.

For a start the Big Bang theory does not explain the origin of the universe nor how the mass of billions of galaxies each containing billions of stars could have got into a state of near infinite density and almost zero size. Maybe it perhaps collapsed into this state from a state not unlike it’s present one and then somehow bounced back. Maybe it does this endlessly, but cosmologists generally think that our universe’s expansion has started to accelerate with no chance of it ever collapsing again.

The purported age of the universe at a mere 13 billion years in BB theory seems too short for a lot of the mega-structures that we can observe in the universe to have evolved. Plus some galaxies look like they have been in business for at least this time, if not more.

Plus cosmologists seem to have encountered a couple of problems with the way that gravity seems to work on very large scales. A lot of galaxies seem to spin too fast. They do not appear to contain enough matter that we can see to hold themselves together by gravity, and according to conventional gravity ideas they should fly apart. His has led to the ad-hoc hypothesis that they must contain a lot of so-called ‘dark matter’ a mysterious substance that does not behave much like ordinary matter at all, although it still does gravity. I’m surprised that they did not call it Phlogiston instead, in memory of the imaginary substance that the ancients though of as the cause of fire.

Additionally another problem has arisen with gravity. One might expect that after an initial BB explosion, the expansion of the universe would begin to slow down as the gravity of all the separating pieces began to pull on each other and slow each other down. However from observations of the apparent speed of far galaxies, most cosmologists have concluded that the apparent expansion rate has actually increased rather than decreased with time. They put this acceleration down to yet another ad-hoc mysterious substance that they call dark energy which exhibits anti-gravity, (or levity as some wag put it).

On top of all these problems with gravity comes the fairly recent observation that our space probes to the limits of the solar system have somehow mysteriously decelerated more than we expected from conventional gravity calculations.

Big Bang theory thus looks increasingly dubious as the anomalies pile up and the epicycle style ad-hoc adjustments keep multiplying to paper them over. The three and a half major items of evidence for the Big Bang hypothesis do however submit to at least one alternative interpretation.

Einstein originally favoured the idea that the universe might consist of a hypersphere which represents the four dimensional equivalent of a sphere. Such a structure has a finite but unbounded extent, it does not go on forever, but you cannot ever reach the edge of it because its gravity causes it to close in on itself so on a very long journey you would find yourself just going round it again. The earth itself has a finite surface, and unless you try to go underground or into the sky it remains unbounded, it doesn’t have edges and you cannot fall off. In a hypersphere the three dimensional ‘surface’ has this same property of finite and unbounded extent.

A hyperspherical universe would have a definite shape, although we cannot easily visualise it, and it would not have infinite extent and all the paradoxes and nonsense that go with the idea of infinite anything. However a hyperspherical universe would collapse in on itself, so Einstein added a fudge factor he called the cosmological constant which had anti-gravity effects to prevent it doing so. His looked grossly inelegant, so Godel suggested instead that it could remain stable if it rotated. However if it rotated in the same sort of way that planets rotate about stars then astronomers would easily notice the effect, and they hadn’t.

Then Hubble came up with the red-shift to distance relationship and the Hyperspherical Universe model became generally abandoned in favour of an Expanding Universe model. Finally the discovery of the CMBR seemed to settle the issue as evidence of the remnant of a primeval fireball following the Big Bang.

However several features of a hypersphere seem to have become overlooked in the rush to form a new theory and these features can account for the non-collapse of the universe, the red-shifts, and the CMBR. Moreover they can also explain the apparent acceleration of the apparent expansion, the apparently anomalous rotation of galaxies, and the mysterious deceleration of our space probes as well. This paper will deal with each of these effects in turn:

A ‘rotating’ universe. Godel found a solution to Einstein’s equations of general relativity that allowed for a rotating universe:

W = 2 ( piGd)^1/2, where W = angular velocity, G = gravitational constant, and d = density.

Now this solution assumes a simple spherical universe rotating about a single spatial axis like a spinning ball, and plainly we do not observe such a phenomenon in the heavens.

For a hypersphere the corresponding equation becomes:

W = (2piGd)^1/2

The angular velocity of a hypersphere represents something a little more complicated than a simple rotation as it involves an extra dimension. A hypersphere undergoes ‘vorticitation’ in which all points on its 3 dimensional ‘surface’ move to the opposite position on the other side of the hypersphere and then back again.

Now a hypersphere has the property that GM/L = c^2, where M = its mass, and L = its length (antipode distance), and c = lightspeed. Thus it has an orbital velocity of lightspeed and an escape velocity of root 2 lightspeed, so nothing can escape from it.

A hyperspherical universe will have a natural centripetal acceleration of -c^2/L due to its gravity and a natural centrifugal acceleration of c^2/L due to its vorticitation, and these balance to give a stable universe that does not collapse or expand.

The opposing centripetal and centrifugal accelerations give rise to an omni-directional resistance to linear motion and an omni-directional boost to orbital motion.

We can measure this acceleration A = c^2/L by recording the amount of deceleration of our space probes which does not arise from the gravity of our star. This ‘Anderson Acceleration’ comes out at about 8.74 x 10^-10 m/s^2, a very tiny deceleration that we only notice over vast distances.

With this figure we can calculate the mass, antipode length, and vorticitation rate of our hyperspherical universe to give the following figures:

(Remember to use 2L^3/pi for hyperspherical surface volume when calculating density)

Mass ~ 10^53 kilograms.

Antipode length ~ 10^26 metres (About 11 billion light years).

Temporal horizon ~ 10^17 seconds.

Vorticitation rate ~ 0.006 arc-seconds per century.

Vorticitation cycle ~ 22 billion years.

The observed universe actually appears slightly larger than the antipode distance shown because of the hyperspherical lensing arising from the small positive curvature to space-time.

Galactic rotation.

The omni-directional boost to orbital motion, the acceleration A, contributes to all orbital velocities V, in the following way:

V = (Gm/r + rA)^1/2

This has negligible effects at planetary scales where the + rA factor has immeasurably small effects, but on galactic scales it explains the unexpectedly high orbital velocities, without the need for dark matter.

Red-Shift.

The omni-directional resistance to linear motion, c^2/L, arising from centripetal/centrifugal effects in the vorticitating hypersphere acts not only on space-probes but also on light and all other forms of electromagnetic radiation. As light refuses to travel at anything less than lightspeed in empty space, it simply looses energy rather than velocity, and thus light reaching an observer from faraway galaxies will appear red-shifted in proportion to the distance that it has travelled.

c- AT = 0, an apparent temporal horizon will exist at a time T, the travel time that it takes to red-shift light (almost*) to oblivion.

The Cosmic Microwave Background Radiation.

Light that has travelled an almost antipodal distance to an observer will arrive highly red-shifted and hence very low on energy. However space contains a thin gas containing about one hydrogen atom per cubic metre, at a temperature of only a couple of degrees above absolute zero. When the highly red-shifted light from distant sources drops down to an energy level corresponding to the temperature of the hydrogen in the interstellar and intergalactic medium* it will start to become absorbed and re-emitted by it, and this effect will dominate over further red-shifting. Thus the CMBR that we observe corresponds to the temperature of the universe in general, which comes in at about a rather chilly 2.7 degrees above absolute zero, because apart from the widely spaced hotspots of stars, it mostly consists of freezing cold space. The CMBR does not come from a primeval fireball some 13 billion years ago, it results from radiation that has circulated the finite and unbounded universe for a time that may exceed the temporal horizon distance several times for some lucky photons.

Hyperspherical lensing.

In a hypersphere, spacetime itself has a small positive curvature and light and other forms of radiation have to follow that curvature. This lensing effect leads to two optical illusions if observers assume a ‘flat’ space without curvature. (I.e., if they assume that the light that they see has travelled to them in straight lines). Firstly it makes the observable universe look about a quarter larger than it should, and secondly it makes the universe look like it has an accelerating expansion. The following entire paper deals with this concept, as it involves some rather challenging geometry.

However, now for something rather astonishing:

Macrocosm and Microcosm.

Godel’s equation for a rotating cosmos, W = 2 (piGd)^1/2, led him to exclaim:

‘Matter everywhere rotates relative to the compass of inertia with the angular velocity of twice the square root of pi times the gravitational constant times density’

Note the presence of the word ‘everywhere’. This solution of Einstein’s field equations supposedly applied to matter at all scales. However the solution did not appear physical because we do not seem to inhabit a spherical universe. However the hyperspherical variant of this equation, W = (2piGd)^1/2, does seem to apply to matter everywhere at all scales.

In cosmological terms it can explain the non-collapse of the universe.

In astrophysical terms it can explain the apparently anomalous rotations of galaxies.

In terms of solar system mechanics it makes very little difference because of the comparatively large ratio of masses to distances.

However its effect re-appears on the quantum scale, indeed it seems to dominate what happens there.

Taking W = (2piGd)^1/2, and applying d = m divided by 2L^3/pi, and Gm/L = c^2, and

W = 2pif, where f = frequency, we obtain f = c/2L, the familiar formula for all fermionic fundamental particles showing the relationship between frequency and wavelength!

This strongly suggests that fundamental particles also consist of vorticitating hyperspheres, just like the entire universe itself.

As Above, So Below, as Hermes Trismegistus apparently wrote on his Emerald Tablet.

I haven’t a clue how to derive the hyperspin equation:

w = (2piGM/V)^1/2

from the fearsome field equations, but I have a strong intuitive feeling that it does constitute a valid and exact solution because it gives such a beautiful result with such explanatory power.

P.S. I suspect that the spacetime GR matrices may require a 6 x 6 rather than a 4 x 4 expression to allow a complete unification with quantum physics.