Cosmic Dark Matter and Energy
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Cosmic Darkness Revealed

Recent past astronomical observations appears to have thrown a dark shroud over the standard cosmological BB theory. Since cosmologists cannot explain these findings, they have invented various unseen dark forces To account for these observed facts as stated below:

1. Dark Matter

Newton/Einstien equations cannot explain the observed high rotational velocities of stars in

Galaxies and Clusters, without invoking a halo of unobservable or hidden matter engulfing the

System and composing up to 90% of the total mass required. Hence the name Dark matter

to describe this ghostly mass.

2. Dark Energy

According to the latest far distance star’s red shift data and there interpretation per Hubble

Cosmic expansion model, the universe is expanding with an acceleration. Acceleration

means there must be a global intrinsic pressure force within space to expand itself and

grow at an increasing pace. Because the origin of this pressure force energy is unknown, it

is dubbed the name, Dark Energy.

3. Red shift Periodicity

This has no Dark name, it is probably because it is ignored by main stream cosmology.

I would like to dub it as the Dark Intervals. This red shift periodicity of observed star light

is also now an established cosmic fact without an explanation.

1. Three dark Secrets in one global theroy.

In the light of Einstiens geometrical interpretation and extension of Newtons gravitational equations

I wish to further analyse and provide a simple natural global extension of Newton’s gravitational

Formula to accommodate the new unexplained astronomical findings.

Starting with the famous equation:

Force F = -GMm/r^2

1) It is clear and natural that the force is directly proportional to the product of the two masses.

2) It is clear that a constant of proportionality G(Newtons Gravitational Constant) is experimentally


3) It is clear that this force is mutually attractive and therefore the negative sign.

So, what is left is the 1/r^2 inverse distance square law of forces that is so taken for granted.

2. Re-visiting the inverse distance square law of Gravitation.

First, this describes the local gravitational field surrounding the mass adequately.

Second, at r=0 the formula blows up, this is unsatisfactory because infinite forces should not

and can not exist in nature. That is, I do not believe that the so called singularities exist in

nature(Therefore no black hole singularities either). This situation is easily remedied by limiting the

gravitational force to be a large constant force at r = 0 like

F = -GMm/(a+r^2)

If ever a maximum universal gravitational force limit per unit mass can be established, then ‘a’ will be


Third, this is a local gravitational 3-D field at a distance ‘r’ and cannot represent a far reaching

global 4-D field universe for reasons to follow.

Why is this an exact inverse square law?

The answer is in the local curvature of space as defined by the Gaussian Curvature, which is an intrinsic

Geometrical property of space surrounding the gravitational mass, leading to the Newtonian

gravitational force law.

Since the local radius of curvature is completely symmetrical in space surrounding the gravitating mass,

the two principal curvatures are the same and therefore the Gaussian Curvature is given by 1/r^2

leading to a perfect local inverse distance square force law.

3.The real topology of the universe.

Some sensible assumptions towards the existence of an additional fourth spatial dimension:

  1. The universe cannot be infinite in space and time. This is reasonable in that if so, it has spread all

Its energy and time Into nothingness and become a barren, dark dead place that cannot support life.

2. So the universe must be bounded in order to have action and energy.

3. To estimate the kind of bounds to apply, I resort to what astronomers have discovered so far about

the cosmos and why it is that some of the data cannot be reconciled with the standard cosmology.

4. The 3 dimensions we are familiar with is extremely large, allowing for the observed large galactic

formations and varieties that exist in deep space, but it may still have a large but finite boundary.

5. The fourth dimension does not span the same physical scale as the other 3 but is curled up and

bounded into a comparatively smaller scale and occupying throughout the extent of the other 3.

6. The regular 3 dimensional space have a flat curvature in the absence of matter.

7. The 4th dimension have a finite curvature even in the absence of matter.

8. The overall curvature of all 4 dimensional space in the absence of matter must still be flat as

evidenced by current observations.

The most promising topology that fits the bill is therefore a kind of a Cylindrical Universe.

With the regular 3D space extending to very large distances and the 4th dimension curved into a

medium large circle at every point In 3D space, with a radius of curvature R at all points in space

as depicted in figure below.

The very large scale Universe may still be bounded by taking the form of a large narrow torus,

but I will not consider that for my current discussion. Note at this time I am assuming that the

4th (w) dimension is an additional large curved closed cylindrical spatial dimension where matter

can travel into and occupy this space.

It appears that after all we do live in a 4D space + 1D time universe, but the 4th spatial dimension

cannot be perceived at a local scale. As for travel to this dimension, matter and light will follow

geodesic paths across all 4 dimensions. I will consider Time as an extra non spatial pseudo


This discussion is therefore non relativistic, to keep it simple and within my scope.

4. Reformulating the inverse square law of gravitation to the new

global cosmic geometry.

In the absence of matter the Gaussian curvature of a cylindrical universe is flat in all space.

Let me show what happens to the local Gaussian curvature of this space in the presence of matter.

The two principal curvatures are determined as follows.

Where ‘R’ is the constant radius of curvature of the 4D(w) cylindrical space.

‘r’ is the distance from a central mass M in the 4D space(x,y,z,w).

‘m’ is a test mass at distance r from mass M

‘G’ is Newtons gravitational constant.

First figure is a cross section of the cylinder. The space at a distance r from a mass on this has two

curvatures superimposed and therefore have a total curvature of (1/R + 1/r). This is one of the

principal curvatures.

The next figure shows a plane section along the cylinder and therefore provide a curvature of ‘1/r’

which is the other principal Curvature. Therefore the Gaussian curvature at a point distance r from a

central mass is:

(1/r)(1/r + 1/R) = 1/r^2 + 1/rR

As seen, this provides the normal inverse square law term and the new term inverse distance of


So we can rewrite the modified Newtonian gravitational force law as:

F = -GMm( 1/r^2 + 1/rR )

Or the force per unit test mass(without m) is

F = -GM( 1/r^2 + 1/rR ) ………………………. (1)

This gives the modified global gravitational force law.

In the large scalel universe, assuming a large cylindrical topology, Newtons gravitational law is

therefore modified as above with a natural physical reason.

5. No to Dark Matter(Problem of anomalous Galactic Rotation curves)

Let us apply this formula to orbital motions around the central mass M.

We therefore obtain the orbital velocity V as:

V = Sqrt GM( 1/r + 1/R) ……………….…….(2)

This therefore gives us a flat rotation curve at large r distances from the central mass ‘M’.

Within my limited resources and information available I fitted this equation to a crude match of the

rotation velocity curve of the Milky Way Galaxy and obtained the following parameters:

V = Sqrt 195000(r/(22+r^2) + 1/6.5) ……………..(3)

Where distances are in Kpc and velocity in Km/s.

Note the modification of the inverse square law term just so to account for the distributed galactic

central mass, to give a more realistic inner rotation curve part.

Approximately GM = 195,000, and R = 6.5 Kpc or 22,000 LY

Note, that approximately the Radius of Curvature of the 4th (w) dimension is 22,000 LY’s.

Which is fairly small compared to the galactic dimensions, but enough to make a difference to

gravity at large scales. At smaller distance scales the inverse square law completely swamps the

cosmic curvature part 1/R but may still be detectable.

The circumference of the curved dimension is 2Phi R approximately 133,200 LY. It appears that a

galaxy can almost occupy the curved 4th dimension circumferential distance.

6. Yes to Dark Energy(Problem of acclerated cosmic expansion)

I will now show that Dark energy is a natural consequence of the new gravitational force

law.Gravitational Potential Energy in space surrounding the central mass is given by,

E = Integral F*dr

This gives: Gravitational Energy = Integral -GM( 1/r^2 + 1/rR )

Hence Energy = GM( 1/r - (1/R)ln r )………………………(4)

This equation is telling us that at large distances r the spatial energy is negative.

It appears that this kind of spatial topology naturally has negative energy every

where, except near mass. Therefore it is a natural answer to the so called Dark Energy problem.

That is, Dark Energy is nothing but a natural consequence of the cylindrical 4D topology

of space curvature.

Now, at a certain distance r1 from a central mass M, where R = r1 ln (r1), a bubble of zero

energy exists.

Below this distance r1 the spatial energy is positive. So surrounding all objects there is a halo of

positive energy trying to shrink space and outside this zero energy bubble space wants to expand.

This zero energy bubble radius works out to be approximately 14,675 LY in the case of the Milky

Way Galaxy.

There appears to be a Positive Dark Energy sphere surrounding the center of Galactic objects.

7. Yes to Red Shift Periodicity (Problem of quantized red shifts)

This last problem of red shift periodicity happens to be an illusion created by the new spatial

topology. It just so happens that light from the very distance stars are seen directly as well as after

circumnavigating the cylindrical space once, twice and a multiple times. Each time the light wraps

around the cylindrical circumference and travels the Length, it additionally travels a multiple

amount of distance exactly equal to the Circumference of the 4th dimension. We therefore observe

an apparent equidistant Spacing of each star image and hence conceive a pattern of equally spaced

red shifts according to the general expansion red shift rule of space. I think I have clarified the idea.

But lets look at some details.

The figure above shows a star S and an observer O at a large distance receiving light that

circumnavigated the additional cylindrical extent of the 4th Dimension once and twice around and

so on a multiple number of this circumference.

Since the extra distance around the cylindrical space is relatively small, the apparent spacing is of

the order of

2 phi * R

Which is approximately 133,200 LY’s, This gives us a basic apparent distance quantization.

According to Hubble’s Law the basic apparent velocity quantization therefore is about 2.665 Km/s.

This I believe is the source of basic periodic red shifts. This is exactly what is observed,

and encourages further analysis of the constant parameters in the equation using a wide set of

galactic data. Additionally this may also explain why super clusters appear to form into long thin

filaments and leave large voids in between.

8. Conclusion

I have not yet worked out exact numbers to clearly justify this view of the Universe. I have made a

crude effort to find a match of the formula to a sketch of the rotation curve of the Milky way I came


I am sure, further refinements are needed and it would be interesting to even see a relativistic

extension of this formula, bringing in the missing time dimension to formulate a 5 dimensional

extension of GR.

Finally, I am convinced that such a simple formula that naturally explains all major cosmic

mysteries, needs to be scrutinized further.


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