[27] **viXra:1504.0247 [pdf]**
*submitted on 2015-04-30 22:04:59*

**Authors:** Yingtao Yang

**Comments:** 15 Pages.

The theory of electrodynamic space-time relativity (TESTR) is the study of the transformation of time and space between two electrodynamic inertial frames of reference, which have both inertial velocity difference and electric potential difference. It is a fundamental space-time theory of theoretical physics based on the Einstein’s special theory of relativity (STR), the electric potential limit postulate and the high-precision experimental facts of the inversion proportional square law of Coulomb’s force. It also proposed new basic physical concepts, such as electric potential limit, quaternion velocity, quaternion electric potential and etc., revealing the inherent relationships between the quaternion velocity, the quaternion electric potential and time-space. This paper discusses in detail the process of establishing the theory of complex electrodynamic space-time relativity and theory of quaternion electrodynamic space-time relativity as well as their various conversions and transformations. At the same time, proved that the special theory of relativity is a special case of TESTR, and found another important special case: the theory of electric potential relativity (TEPR). The basic effects of TESTR were also discussed, proposing the equations for superposition of quaternion velocity, and quaternion potential of TESTR respectively. It predicts some important new space-time change effects, which provides theoretical basis for the experimental validation of TESTR.

**Category:** Relativity and Cosmology

[26] **viXra:1504.0234 [pdf]**
*replaced on 2017-06-18 03:48:58*

**Authors:** Sjaak Uitterdijk

**Comments:** 3 Pages.

The article shows that a lot of misunderstanding and confusion has been originated after Einstein published his article about the STR. Fundamental errors, manipulative mathematics and an unfounded believe in the transformation formulas of the STR caused this chaos.

**Category:** Relativity and Cosmology

[25] **viXra:1504.0230 [pdf]**
*submitted on 2015-04-29 01:57:34*

**Authors:** Kenneth M. Sasaki.

**Comments:** 5 pages, 2 figures, 5 labeled equations, and 17 references. Keywords: Space, Time, and the Luminiferous Ether (Luminiferous Aether). Author's e-mail address: bicycle_physics@yahoo.com.

This work proves that the ether exists – at each event in space-time, there exists a state of translation only relative to which light speed is isotropic – proving as well that Special Relativity is inconsistent both internally and with observation.

**Category:** Relativity and Cosmology

[24] **viXra:1504.0223 [pdf]**
*submitted on 2015-04-28 03:24:07*

**Authors:** Fu Yuhua

**Comments:** 10 Pages.

Based on author’s published papers, summarizing some problems that special and general relativity cannot solve or induce wrong results, such as: special twin paradox that two brothers’ states of motion are quite same, contradictions between relativity and principle of conservation of energy, and the like. The two main shortcomings of relativity are as follows: firstly, applying mathematical principle (rather than physical principle) as the main principle to solve physics problems; secondly, as establishing relativity, the principle of conservation of energy is not considered. Referring to "partial and temporary unified theory of natural science so far" including all the equations of natural science so far, the related formulas and equations of relativity can be improved and restricted (or constrained) by principle of conservation of energy, and thus these formulas and equations can satisfy the principle of conservation of energy.

**Category:** Relativity and Cosmology

[23] **viXra:1504.0209 [pdf]**
*submitted on 2015-04-26 18:36:47*

**Authors:** James E. Beichler

**Comments:** 21 Pages. This paper is presently being published in Proceedings of Vigier IX Symposium

Too many physicists believe the ‘phallacy’ that the quantum is more fundamental than relativity without any valid supporting evidence, so the earliest attempts to unify physics based on the continuity of relativity have been all but abandoned. This belief is probably due to the wealth of pro-quantum propaganda and general ‘phallacies in fysics’ that were spread during the second quarter of the twentieth century, although serious ‘phallacies’ exist throughout physics on both sides of the debate. Yet both approaches are basically flawed because both relativity and the quantum theory are incomplete and grossly misunderstood as they now stand. Had either side of the quantum versus relativity controversy sought common ground between the two worldviews, total unification would have been accomplished long ago. The point is, literally, that the discrete quantum, continuous relativity, basic physical geometry, theoretical mathematics and classical physics all share one common characteristic that has never been fully explored or explained – a paradoxical duality between a dimensionless point (discrete) and an extended length (continuity) in any dimension – and if the problem of unification is approached from an understanding of how this paradox relates to each paradigm, all of physics and indeed all of science could be unified under a single new theoretical paradigm.

**Category:** Relativity and Cosmology

[22] **viXra:1504.0182 [pdf]**
*submitted on 2015-04-22 16:24:54*

**Authors:** Frederik Vantomme

**Comments:** 24 Pages. The original paper is written in LaTex format.

We explore the possibility that black holes and Space could be the geometrically Compactified Transverse Slices ("CTS"s) of their higher (+1) dimensional space. Our hypothesis is that we might live somewhere in between partially compressed regions of space, namely 4d_{L+R} hyperspace compactified to its 3d transverse slice, and fully compressed dark regions, i.e. black holes, still containing all _{L}d432-1-234d_{R} dimensional fields. This places the DGP, ADD, Kaluza-Klein, Randall-Sundrum, Holographic and Vanishing Dimensions theories in a different perspective.

We first postulate that a black hole could be the result of the compactification (fibration) of a 3d burned up S^{2} star to its 2d transverse slice; the 2d dimensional discus itself further spiralling down into a bundle of one-dimensional fibres.

Similarly, Space could be the compactified transverse slice (fibration) of its higher 4d_{L+R} S^{3} hyper-sphere to its 3d transverse slice, the latter adopting the topology of a closed and flat left+right handed trefoil knot. By further extending these two ideas, we might consider that the Universe in its initial state was a "Matroska" 4d_{L+R} hyperspace compactified, in cascading order, to a bundle of one-dimensional fibres. The Big Bang could be an explosion from within that broke the cascadingly compressed Universe open.

[21] **viXra:1504.0172 [pdf]**
*submitted on 2015-04-22 02:41:47*

**Authors:** Rodrigo de Abreu

**Comments:** 9 Pages. Luzboa A arte da Luz em Lisboa, 14-19, Extra]muros[ (2004).

The traditional presentation of special relativity is made from a rupture with previous ideas, such as the notion of absolute motion, emphasizing the antagonism of the Lorentz’s views and Einstein’s ideas. However, a weaker formulation of the postulates allows to recover all the results from Einstein’s special relativity and reveals that both viewpoints are merely diﬀerent perspectives of one and the same theory.

**Category:** Relativity and Cosmology

[20] **viXra:1504.0167 [pdf]**
*submitted on 2015-04-21 08:40:29*

**Authors:** Peter J Carroll

**Comments:** 15 Pages. A rough outline of this hypothesis has already attracted over 300,000 reads on my website. One of your contributing physicists suggested that I tidy it up and offer it to viXra. Regards, Pete.

The author proposes that a reinterpretation of cosmological redshift as arising from the small positive spacetime curvature of a 4-rotating Hyperspherical Universe of constant size can eliminate the current requirement for spacetime singularities, cosmic inflation, dark matter, and dark energy from cosmological models.

**Category:** Relativity and Cosmology

[19] **viXra:1504.0158 [pdf]**
*submitted on 2015-04-20 09:13:30*

**Authors:** Radwan M. Kassir

**Comments:** 5 journal pages

For relatively moving inertial frames, the constancy of the speed of light principle physically leads to time dilation in the transverse direction. This time dilation is irreconcilable in the longitudinal direction unless a length contraction in the relative motion direction is postulated. However, time dilation is contradictorily coupled with length expansion, a fact erroneously twisted in the special relativity and related text books, as demonstrated in this paper. The typical physical demonstration of the length contraction is shown to be inconsistent and contradicts its derivation from the Lorentz transformation. The misinterpretation of the Lorentz Transformation in predicting the length contraction is revealed. The constancy of the speed of light is consequently unviable.

**Category:** Relativity and Cosmology

[18] **viXra:1504.0154 [pdf]**
*replaced on 2015-05-03 10:08:50*

**Authors:** Ramzi Suleiman

**Comments:** 22 Pages.

Einstein's theory of special relativity (SR) theory dictates, as a force majeure, an ontic view, according to which relativity is a true state of nature. For example, the theory’s solution to the famous twin paradox prescribes the "traveling" twin returns truly and verifiably younger than the "staying" twin, thereby implying the “traveling” twin returns to the future.
I propose an epistemic view of relativity, according to which relativity results from difference in Information about Nature between observers who are in motion relative to each other. The proposed theory, termed Information Relativity (IR) theory is based on two axioms: 1. the laws of physics are the same in all inertial frames of reference (SR's first axiom); 2. All translations of information from one frame of reference to another are carried by light or by another carrier with equal velocity (information-carrier axiom). For the case of constant relative velocities, I derive the theory's time and distance transformations and compare them with the corresponding SR's transformations. I show that despite IR's contradiction with Lorentz's Invariance Principle, it accounts as good as SR for the results of a class of time measurement experiments, including Michelson-Morley's type of experiments as well as the time dilation detected in muon decay and in "around-the-world atomic clocks" experiments. More important, the theory accounts for the linear Sagnac effect, which starkly disobeys LI and SR. It also predicts with precision the (v-c)⁄c values reported in several neutrino velocity experiments, conducted by OPERA and other collaborations. I outline the necessary conditions for a stringent comparative test between IR and SR, and explain why the experimental designs of the linear Sagnac and the neutrino velocity experiments qualify as stringent tests of both theories.

**Category:** Relativity and Cosmology

[17] **viXra:1504.0136 [pdf]**
*submitted on 2015-04-17 21:50:01*

**Authors:** Brian B.K. Min

**Comments:** 13 Pages.

We postulate that our space is filled by the “Gamma elements” having energy and mass with the size approximately given by the wavelength of the highest energy gamma rays and that time and distance are both discretized by the process of light propagation from one Gamma element to the next. These postulates provide us with a theoretical ground to explain why the speed of light, c, should remain constant to all observers regardless of their inertial frames of reference. In the cosmological scale, the energy of the Gamma elements filling space has been equated to the energy represented by the cosmological constant, i.e., the dark energy. When applied to the expanding universe, the EST model brings additional 25% of the total mass simply as the relativistic correction to the non-relativistic results; hence the dark matter is closely identified as merely the relativistic correction to the dark energy predicted by the Friedman equation. The agreement with the observed magnitudes convincingly supports this interpretation of dark energy and dark matter.

**Category:** Relativity and Cosmology

[16] **viXra:1504.0132 [pdf]**
*submitted on 2015-04-16 23:25:44*

**Authors:** V.B. Smolenskii

**Comments:** 1 Page.

we prove that a negative length and mass are absent in nature if there are negative charges with not equal to one factors in the form of dimensionless fundamental constants.

**Category:** Relativity and Cosmology

[15] **viXra:1504.0127 [pdf]**
*submitted on 2015-04-15 23:49:17*

**Authors:** Reginald T Cahill

**Comments:** 17 Pages.

Experiments have repeatedly revealed the existence of a dynamical structured fractal 3-space, with a speed relative to the Earth
of some 500km/s from a southerly direction. Experiments have ranged from optical light speed anisotropy interferometers to
zener diode quantum detectors. This dynamical space has been missing from theories from the beginning of physics. This
dynamical space generates a growing universe, and gravity when included in a generalised Schrodinger equation, and light
bending when included in generalised Maxwell equations. Here we review ongoing attempts to construct a deeper theory of
the dynamical space starting from a stochastic pattern generating model that appears to result in 3-dimensional geometrical
elements, “gebits”, and accompanying quantum behaviour. The essential concept is that reality is a process, and geometrical
models for space and time are inadequate.

**Category:** Relativity and Cosmology

[14] **viXra:1504.0125 [pdf]**
*submitted on 2015-04-16 00:00:48*

**Authors:** Reginald T cahill

**Comments:** 23 Pages.

The anisotropy of the velocity of EM radiation has been repeatedly detected, including the Michelson-Morley experiment of 1887, using a variety of techniques. The experiments reveal the existence of a dynamical space that has a velocity of some 500km/s from a southerly direction. These consistent experiments contradict the assumptions of Special Relativity, but are consistent with the assumptions of neo-Lorentz Relativity. The existence of the dynamical space has been missed by physics since its beginnings. Novel and checkable phenomena then follow from including this space in Quantum Theory, EM Theory, Cosmology, etc, including the derivation of a more general theory of gravity as a quantum wave refraction effect. The corrected Schrodinger equation has resulted in a very simple and robust quantum detector, which easily measures the speed and direction of the dynamical space. This report reviews the key experimental evidence.

**Category:** Relativity and Cosmology

[13] **viXra:1504.0124 [pdf]**
*submitted on 2015-04-16 00:03:56*

**Authors:** Reginald T Cahill

**Comments:** 8 Pages.

In 2014 Jiapei Dai reported evidence of anisotropic Brownian motion of a toluidine blue
colloid solution in water. In 2015 Felix Scholkmann analysed the Dai data and detected
a sidereal time dependence, indicative of a process driving the preferred Brownian motion
diusion direction to a star-based preferred direction. Here we further analyse the
Dai data and extract the RA and Dec of that preferred direction, and relate the data
to previous determinations from NASA Spacecraft Earth-flyby Doppler shift data, and
other determinations. It is shown that the anisotropic Brownian motion is an anisotropic
“heating” generated by 3-space fluctuations: gravitational waves, an eect previously
detected in correlations between ocean temperature fluctuations and solar flare counts,
with the latter being shown to be a proxy for 3-space fluctuations. The dynamical 3-
space does not have a measure of energy content, but can generate energy in matter
systems, which amounts to a violation of the 1st Law of Thermodynamics.

**Category:** Relativity and Cosmology

[12] **viXra:1504.0096 [pdf]**
*submitted on 2015-04-12 12:57:54*

**Authors:** George R. Briggs

**Comments:** 1 Page.

Abstract: Recent conclusions regarding the behavior of giant black holes obeying quantum-mechanical rules indicate that these rules are not obeyed for the large-universe. For example, the existence of fermibosonic matter in the large-scale universe need not be prohibited as it is using quantum-mechanical rules

**Category:** Relativity and Cosmology

[11] **viXra:1504.0081 [pdf]**
*submitted on 2015-04-10 05:59:29*

**Authors:** Hasmukh K. Tank

**Comments:** Single-page letter

It is proposed hare that: Just as, a photon, while experiencing the ‘gravitational red-shift’, dose not loose its velocity, and chooses to loose its energy, in the form of frequency, so exactly, the photons emitted from the luminous bodies, like the receding galaxies, may be partly loosing their energy due to ‘gravitational red-shift’; depending upon the ‘cosmic-gravitational-potential’ of a given galaxy. The ‘cosmological red-shift’ may be a combination of ‘gravitational red-shift’ and ‘Doppler-shift’. Thus ‘cosmological red-shift’ may not be wholly representing the ‘recessional-velocity’ of a galaxy. The recessional-velocity may be much lesser than it is currently believed.

**Category:** Relativity and Cosmology

[10] **viXra:1504.0055 [pdf]**
*submitted on 2015-04-07 16:03:48*

**Authors:** Jerry Zhompson

**Comments:** 11256 Pages. please excuse poor quality english as natives not speaker

Please excuses the poor english of the quality foreign speaker:
we proves einstein was is wrong about stuff

**Category:** Relativity and Cosmology

[9] **viXra:1504.0053 [pdf]**
*submitted on 2015-04-07 05:36:54*

**Authors:** Rodney Bartlett

**Comments:** 15 Pages.

Whenever human understanding of the size of the universe is at a breakthrough point, a new idea about the nature of gravity introduces itself to the world. For thousands and thousands of years, the magnitude of the cosmos was limited to the stars that could be seen in the night sky (not that people knew what they were looking at). Just over 400 years ago, a tremendous breakthrough came. The telescope arrived, and drastically changed our view of the heavens. A mere 60 years later (a drop in the ocean of historical time), gravity was compared to the fall of an apple and Isaac Newton proposed that the moon traces out the curve of its orbit by constantly "falling" towards Earth.
Things progressed steadily for over 200 years - telescopes grew bigger, planets and stars were discovered, and the universe became as large as the Milky Way galaxy. About the same time that we were starting to wonder if there other galaxies out there (a concept that would vastly increase the universe's size again), another gravitational breakthrough came. Albert Einstein reinterpreted the moon’s being constantly tugged towards Earth by our planet’s gravity. He said the moon is “pushed” towards Earth by the hills and valleys of curved space-time surrounding this world.
Since then, things have – despite the inevitable dead ends science embarks on but sooner or later corrects - steadily progressed once more. Complacency seems to have arisen, because many appear to think real science never means anything except continual slow progress. There’s a new idea in the world, however – that the universe may be infinite. This would drastically increase the size of the universe once more, and herald another breakthrough in comprehension of gravity.
The ideas of Newton and Einstein embrace the entire universe, and the truth in their theories has been repeatedly confirmed. It’s only logical that elements of both Newtonian and relativistic gravity must be present in a new “infinite universe gravity” (IUG). The universe can’t possibly be larger than infinite – even hypothetical multiverses and cyclic universes would be included in its infinity if they existed. So you might think an idea of infinite gravity would be the final breakthrough in understanding gravity. But it would be terrible if learning could reach an end – the infinite nature of gravity implies it might undergo infinite refinements over the eons.

**Category:** Relativity and Cosmology

[8] **viXra:1504.0051 [pdf]**
*replaced on 2015-04-25 00:20:44*

**Authors:** Andrew Wutke

**Comments:** 18 Pages. Please sent any comments or suggestion to the email address within. I want to improve the content and eliminate factual errors or ambiguities.

This paper presents the proof of the apparent nature of relative simultaneity originally derived from Einstein’s Special Theory of Relativity (STR). The proof does not challenge the validity of the STR but uncovers fundamental and widespread error in understanding of practical implications of Lorentz transformations. It is demonstrated that more than a century long debates generally miss the point. This results in counterintuitive claims of coexisting multiple time realities by mere equivalence of equal clock indications and simultaneity. Such claims have little empirical significance but they are substantial in education and philosophy which has become utterly confused after universal acceptance of the STR and rejections of Henri Bergson’s challenge. There is nothing more to “relative simultaneity” other than the effect of identical clocks being shifted by an offset which depends on synchronisation method.

**Category:** Relativity and Cosmology

[7] **viXra:1504.0043 [pdf]**
*submitted on 2015-04-05 21:39:34*

**Authors:** Marcelo Carvalho; Alexandre Lyra de Oliveira

**Comments:** 20 Pages.

Using the concept of absolute time introduced in a previous work \cite{carvalho} we define two coordinate systems for spacetime, the Galilean and the Lorentzian systems. The relation between those systems allows us to develop a tensor
calculus that transfer the Maxwell electrodynamics to the Galilean system. Then, by using a suitable Galilean limit, we show how this transformed Maxwell theory in the Galilei system results in the Galilei electrodynamics formulated by Levy Leblond and Le Bellac.

**Category:** Relativity and Cosmology

[6] **viXra:1504.0035 [pdf]**
*submitted on 2015-04-04 20:15:21*

**Authors:** George R. Briggs

**Comments:** 2 Pages.

Abstract: A very careful count of the different particles and antiparticles in our universe confirms and extends a similar conclusion made on 8-22-2014; namely, the exotic 4-quark tetraquark particle is the sole marker for E8 symmetry in our universe and also marks the existence of the extremely long-lived proton particle.

**Category:** Relativity and Cosmology

[5] **viXra:1504.0034 [pdf]**
*submitted on 2015-04-05 03:16:39*

**Authors:** Omar A.H. Shabsigh, Pro. Dr.

**Comments:** 26 Pages. Extreme

This article discusses the upper limit imposed on the speed of traveling of any mass as being the speed of light in vacuum. The article shows, based on the results of Special Relativity, that such a limit does not really exist. We shall prove that Special Relativity is theoretically valid under the constraints and assumptions made by Einstein and has no practical applications.

**Category:** Relativity and Cosmology

[4] **viXra:1504.0023 [pdf]**
*submitted on 2015-04-02 13:02:08*

**Authors:** Eric Thompson

**Comments:** 79 pages, equations, diagrams, images

A fundamental assumption, that basic electric charge is an inherent property of elementary particles, is overturned. Therefore, if basic charge does not come from within, it could only come from without. Hence we re-introduce the aether and show how it is responsible not only for electromagnetism, but also how its flowing nature is responsible for gravitational effects. Inertia, light propagation, and the large scale structure of the cosmos also fall out simply and naturally from this basic concept. A great deal of pruning is done to current theories.

**Category:** Relativity and Cosmology

[3] **viXra:1504.0020 [pdf]**
*submitted on 2015-04-02 07:02:27*

**Authors:** U.V.S. Seshavatharam, S.Lakshiminarayana

**Comments:** 11 Pages. New supporting references: J. Cosmol. Astropar. P. (2013) doi: 10.1088/1475-7516/2013/03/007, Int. J. Mod. Phys. D (2013) doi: 10.1142/S0218271813500120

Throughout the cosmic evolution, currently believed cosmic ‘critical density’ can be shown to be a default result of the ‘positively curved’ light speed rotating black hole universe. As there is no observational or experimental evidence to
Friedmann’s second assumption, the density classification scheme of Friedmann cosmology must be reviewed at fundamental level and possibly can be relinquished. The observed cosmic redshift can be reinterpreted as an index of ‘cosmological’ light emission mechanism. Clearly speaking, during cosmic evolution, as cosmic time increases,
hydrogen atom emits photons with increased quanta of energy. Thus past light quanta emitted from old galaxy will have less energy and show a red shift with reference to our galaxy. Note that in 1947 Edwin Hubble himself thought for a new
mechanism for understanding the observed galactic redshift data. By considering the ‘Planck mass’ as the initial mass of the baby cosmic black hole, initial physical and thermal parameters of the cosmic black hole can be defined and current
physical and thermal parameters of the cosmic black hole can be fitted and understood. Uncertainty relation and all other microscopic physical constants play a crucial role in understanding the halt of the present cosmic expansion.

**Category:** Relativity and Cosmology

[2] **viXra:1504.0009 [pdf]**
*submitted on 2015-04-01 14:26:21*

**Authors:** Fernando Loup

**Comments:** 46 Pages.

Warp Drives are solutions of the Einstein Field Equations that
allows superluminal travel within the framework of General
Relativity. There are at the present moment two known solutions:
The Alcubierre warp drive discovered in $1994$ and the Natario
warp drive discovered in $2001$. However the major drawback
concerning warp drives is the huge amount of negative energy
density able to sustain the warp bubble.In order to perform an
interstellar space travel to a "nearby" star at $20$ light-years
away in a reasonable amount of time a ship must attain a speed of
about $200$ times faster than light.However the negative energy
density at such a speed is directly proportional to the factor
$10^{48}$ which is $1.000.000.000.000.000.000.000.000$ times
bigger in magnitude than the mass of the planet Earth!!. With the
correct form of the shape function the Natario warp drive can
overcome this obstacle at least in theory.Other drawbacks that
affects the warp drive geometry are the collisions with hazardous
interstellar matter(asteroids,comets,interstellar dust etc)that
will unavoidably occurs when a ship travels at superluminal speeds
and the problem of the Horizons(causally disconnected portions of
spacetime).The geometrical features of the Natario warp drive are
the required ones to overcome these obstacles also at least in
theory. Some years ago starting from $2012$ to $2014$ a set of
works appeared in the current scientific literature covering the
Natario warp drive with an equation intended to be the original
Natario equation however this equation do not obeys the original
$3+1$ Arnowitt-Dresner-Misner($ADM$) formalism and hence this
equation cannot be regarded as the original Natario warp drive
equation.However this new equation satisfies the Natario criteria
for a warp drive spacetime and as a matter of fact this equation
must be analyzed under a new and parallel contravariant $3+1$
$ADM$ formalism.In this work we introduce also a second new
Natario equation but using a parallel covariant $3+1$ $ADM$
formalism. We compare both the original and parallel $3+1$ $ADM$
formalisms wether in contravariant or covariant form using the
approach of Misner-Thorne-Wheeler($MTW$) and Alcubierre and while
in the $3+1$ spacetime the parallel equations differs radically
from the original one when we reduce the equations to a $1+1$
spacetime all the equations becomes equivalent.We discuss the
possibilities in General Relativity for these new equations.

**Category:** Relativity and Cosmology

[1] **viXra:1504.0007 [pdf]**
*submitted on 2015-04-01 06:51:00*

**Authors:** N.S. Baaklini

**Comments:** 10 pages, 7 equations, 17 references

In our framework for 'realistic non-singular cosmology' we consider a more radical situation where the present photonic temperature of the universe is higher (for instance ~16 K) than that suggested by the microwave background. This leads to a minimal scale of ~0.08, and a maximum temperature of ~192 K, for an oscillating cosmology whose main protagonists are whole galaxies rather that stars, with an age of the current expansion of ~8.9 Gyr. We show
that this scheme is quite compatible with the supernovae data for magnitudes and redshifts, provided that the Hubble fraction is ~0.55.

**Category:** Relativity and Cosmology