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Cosmological relativity

Cosmological relativity is an extension of the principals of Special and General Relativity to cosmological scales. Developed by Dr Moshe Carmeli, this theory is a combination of Einstein's original special and general relativity; however its starting point is the expansion of the Universe and not the propagation of light. It has profound results for cosmology in general and in particular Young Earth Creation cosmology. So far this theory fits all experimental findings.

Cosmic Time

Cosmic time is the time that the universe would need to expand from a zero size point for a given red shift. In the Big Bang cosmology it would be the time since the Big Bang. Any cosmology that starts with the universe as larger than a point would actually be younger than cosmic time.

According to Cosmological Relativity τ is constant for all space and time such that is at any place in the Universe and at any time in its history an observer would measure the same Current cosmic time. Also like Einstein Relativity the laws of nature are the same for all space and time. The result is that there is no absolute cosmic time but it relative to the time and place of the observer just like velocity in Special relativity. Also like velocity in Special relativity cosmic time dose not simply add from one observer to another. Instead cosmic time is added by the following formula:

The key to Cosmological Relativity is that there is no absolute cosmic time that is that any observer at any point in space and at any time will see τ = 13.56 Gyr.


5D cosmology

Cosmological relativity’s line element for an expanding Universe in negligible gravity is:

ds2 = τ22 - ( dx2 + dy2 + dz2 )

This is similar to the Special relativity line element.

ds2 = c2dt2 - ( dx2 + dy2 + dz2 )

When time is added to Cosmological relativity’s line element we get:

ds2 = τ22 - ( dx2 + dy2 + dz2 ) + c2dt2

The result is a theory of 5 dimensions.

Special Relativity

Cosmological Special Relativity has much in common with Einstein’s Special relativity. Both theories deal with the special case of no gravity forming the bases for the more general concept. The main difference is that cosmic time (t) replaces velocity (v) as the critical quantity and observed cosmic time (τ= 13.56 Gyr) is replaces the velocity of light (c) as the constant. Both theories have essentially the same formulae but Cosmological Special Relativity substitutes ”t” for “v” and “τ” for “c”.

In Cosmological Special Relativity τ = H0-1 = 13.56 Gyr, where H0 = Hubble’s constant.

Thus both theories have similar transformations between reference frames.

Thus both theories have similar formulae for relative mass. (m)

Similar formulae for relative length. (L)

It is in area of time (t) and velocity (v) that the two theories are the most different since they basically switch places.

In Cosmological Special Relativity we get an added relationship for the acceleration (a) of the expansion of the universe.

Cosmological Special Relativity also has relativistic formulae for the universes’ density (ρ) and temperature (T).

Even though both the universes’ density (ρ) and temperature (T) are shown to be larger in the past it seem likely that they are purely relativistic affects ant that at those times the measured values would be what they are today.

Cosmological Special Relativity and Special relativity are not exclusive but the work together both being more significant under the right circumstances. Special relativity as v approaches c and Cosmological Special Relativity as t approaches τ.

General Relativity

Cosmological General Relativity like Einstein’s General relativity deals with the general case where gravity is present.


In its 4D form of space-velocity Cosmological General Relativity gives only state of the universe in an instant of time.

While in Cosmological Special Relativity τ = H0-1, when gravity is considered as it is in Cosmological General Relativity, the τ = h-1, and its relationship H0 becomes:

According Cosmological General Relativity, the presence of gravity resulting from mater and energy reduces the vacuum pressure that tends to accelerate the expansion of the universe. This vacuum pressure (p) is denoted by:

As a result the value of Ωm different affects on the expansion of the universe.

Ωm > 1

Ωm = 1

Ωm < 1

When this is applied to the unbounded universe of the Big bang, the result is that for the first 5.08 Gyr after the Big bang there would be a decelerating expansion. At this point the expansion becomes constant for a brief time and then started to accelerate as it is today.

Next we have ΩT which denotes the curvature of space on cosmic scales. The difference between ΩT and Ωm is ΩΛ. Such that.

ΩT = Ωm + ΩΛ

Now ΩΛ = (H0 / h)2 = 0.764

The result is: ΩT = Ωm + ΩΛ = 0.245 + 0.764 = 1.009 ≈ 1

This shows that the universe is flat ( Euclidean ) on a large scale.


When the time dimension is added to Cosmological General Relativity the result is a 5D theory that reproduces all of the results of General Relativity with additional affects that solve a number of problems in cosmology. It results in a 5D space – time – velocity manifold that is an extension of General Relativity for cosmology. 

Accelerating expansion

While the discovery that the acceleration of the expansion of the universe was a surprise to most scientists, it was actually predicted by Cosmological General Relativity. This means that Cosmological General Relativity has made a successful prediction which is important to any scientific theory. The success of this prediction should have brought attention to Cosmological Relativity, but instead current theory was simply patched with a mysterious unobserved substance called dark energy.

Galactic Rotation

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B).
From: Galaxy rotation curve - Wikipedia

In this diagram “A” is the typical rotation curve of a spiral galaxy as predicted by the established principle of gravitational mechanics. However “B” is what is actually observed.

Dr. John G. Hartnett has shown that Cosmological General Relativity naturally produces the observed curve “B”. It is a result of adding the extra velocity. As a result the rotation curve of spiral galaxies is exactly what Cosmological General Relativity says they should be.

Here is yet another case where Cosmological Relativity is shown to fit reality better than current theory. Such results are strong evidence in support of the theory.

This is a good example of how the general scientific community has to be dragged kicking and screaming to radically new concepts. Cosmological Relativity fits the data so well that it deserve serious consideration but the general scientific community prefers to keep patching existing theory.

Dark Matter

Since Cosmological Relativity naturally produces the rotation curves of spiral galaxies. It also fits the gravitational lensing often accredited to dark mater. The result is that Cosmological Relativity essentially eliminates any need for so called dark matter.

Dark Energy

Cosmological Relativity totally eliminates the need for dark energy since the accelerating expansion is an intrinsic part of its 5D space – time – velocity manifold.

Bonded Universe

Dr. John G. Hartnett has applied Cosmological relativity a bounded universe. Under General relativity the gravity potential of a bounded universe would induce a large scale curvature to space for which there is no evidence. He found that do to the accelerating expansion Cosmological relativity would eliminate this curvature, making space as flat as it would be in an unbounded universe. This would be true as long as the radius ( r ) at least cτ.

He showed that observations are consistent with a bounded universe in side a white hole with our galaxy at or near the center. This is not to be confused with Dr HumphreysWhite hole cosmology since in this model the universe is still inside the white hole’s event horizon. However there are similarities in the two cosmologies.

Young Earth Cosmology

Dr. John G. Hartnett has shown that Cosmological relativity is observationally consistent with a finite bounded universe. He has since shown that the 5D Cosmological relativistic line element shows that the universe is young by Earth clocks and that light from the most distant could have stars arrived at the Earth with in the Creation week.

5D line element

ds2 = τ22 - ( dx2 + dy2 + dz2 ) + c2dt2

Starting with this line element, Hartnett shows that the gamma functions of both Special relativity (λE)and Cosmological Special relativity (λc) can each be derived.

When deriving the gamma function of Special relativity the result is:

This shows that Special relativistic affects are greatly affected by the acceleration of the expansion of the universe. In fact as /dt approaches 0 it becomes:

This is the standard Special relativistic gamma function.

The result is that Special relativity is most accurate when the universe’s expansion is not accelerating. This suggests that today the universe either expanding at a constant rate or not at all.

When deriving the gamma function of Cosmological Special relativity the result is:

This shows that Cosmological Special relativistic affects are greatly affected by the acceleration of the expansion of the universe. In fact as /dt get larger it becomes:

This is the standard Cosmological Special relativistic gamma function. Based on the above 5D line element a = 0 the Cosmological Special relativistic gamma function is would not be in affect and the Special relativistic gamma function would function in its original form.

The result is that Cosmological Special relativity is most accurate when the universe’s expansion is accelerating vary fast. This suggests that in the past the universe had a period of rapidly accelerating expansion.

Combined these results show that at some time in the past the universe experienced a rapid accelerating expansion but that today the expansion is either constant or stopped. It also tilts the observational evidence from being neutral towards favoring a bounded over an unbounded universe. Such a rapidly accelerating expansion would have left clear observational evidence in an unbounded universe because without a center time dilation would not make local expansion rates seem slower than would be seen a center. The time dilation affect at the center relative to any distance from the center would be:

With a velocity v = 0 the relationship becomes:

Observation shows that in a bounded universe the Earth would be near the center. So based on the Biblical account, it is likely that the Earth was at the center of the expansion.

Since the rapid acceleration of the universe’s expansion has stopped Earth’s time is now approximately the same as the rest of the universe, thus there is no blue shift as would be expected as a result of time dilation.

It is theorized that during the first few day of creation the universe had a period of rapidly accelerating expansion, resulting in a high degree of time dilation on Earth. This concept is similar to Dr HumphreysWhite hole cosmology but it lacks the gravitational distortion of a massive white hole.

One way light travel time to Earth

While Hartnett has worked out a relationship between the distance from Earth and acceleration of the expansion of the universe in the form of an exponential function that the one way light travel time to Earth could easily have been no more than a few days in Earth time and even possibly less than one day.  The  exact time depends on the expansion rate.

The following graph shows the results for various distances (r) with η set to two different values.

Note that at η = 1013 that the light even from 13.56 billion ly would have reached Earth in about a day.

While these results are not exact they do show that Cosmological relativity in a bounded universe can get even the most distant star light possible to Earth with in the creation week. The result is that Hartnett’s cosmology is a viable young Earth cosmology.


While Cosmological relativity is not yet generally accepted, it is a viable theory of physics that has already shown to naturally explain several problems in cosmology, including some it was not developed to explain.

It also results in a viable young Earth cosmology when applied to a bounded universe.

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Dr. Moshe Carmeli

Dr. John G. Hartnett

Carmeli & Hartnett