Relativity and Cosmology

A Simple Mathematical Solution of the Cosmological Constant Problem.

Authors: Stéphane Wojnow
Comments: 4 Pages.

Assuming a vacuum density of the cosmological constant in quantum mechanics, we providea simple mathematical solution to the cosmological constant problem, i.e. the disagreement of theorder of a factor 10^122 between the theoretical and the measured value of the vacuum energy . Wegive an interpretation with Casimir effect and a non-exclusive route for our solution to makephysical sense.
Category: Relativity and Cosmology

Redshift Distances in Flat Friedmann-Lemaître-Robertson-Walker Spacetime

Authors: Steffen Haase
Comments: 57 Pages.

In the present paper we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the general astrophysical literature.Using the Friedmann-Lemaitre-Robertson-Walker the radial physical distance is described by R(t) = a(t)r. In this equation the radial co-moving coordinate is named r and the time-depending scale parameter is named a(t). We use the co-moving coordinate r_e (the subscript e indicates emission) describing the place of a galaxy which is emitting photons and r_a (the subscript a indicates absorption) describing the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the physical distance - the real way of light - is calculated by D = a(t_0)r_a - a(t_e)r_e ≡ R_0a - R_ee. Here means a(t_0) the today’s (t_0) scale parameter and a(t_e) the scale parameter at the time t_e of emission of the photons. The physical distance D is therefore a difference of two different physical distances from a coordinate origin being on r = 0.Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place r_e and are than traveling to the co-moving coordinate place r_a. During this traveling the time is moving from t_e to t_0 (t_e ≤ t_0) and therefore the scale parameter is changing in the meantime from a(t_e) to a(t_0).Using this right physical distance we calculate the redshift distance and some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics (quasars, SN Ia and black hole). We get the today’s Hubble parameter H_0a ≈ 65.66 km/(s Mpc) as a main result. This value is a little bit smaller than the Hubble parameter H_0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data which is discussed in the specialist literature.Furthermore, we find for the radius of the so-called Friedmann sphere R_0a ≈ 3,096.92 Mpc. This radius corresponds to the maximum possible distance of seeing within an expanding universe. Photons, which were emitted at this distance, are infinite red shifted.The today’s mass density of the Friedmann sphere results in ρ_0m ≈ 7.82 x 10-29 g/cm^3. For the mass of the Friedmann sphere we get M_Fs ≈ 2.86 x 10+56 g.The mass of black hole within the galaxy M87 has the value M_BH, M87 ≈ 2.36 x 10+45 g. The redshift distance of this object is D ≈ 19.45 Mpc but its today’s distance is only D_0 ≈ 6.27 Mpc.
Category: Relativity and Cosmology

A Changed Understanding of Gravity

Authors: Peter R. Lamb
Comments: 48 Pages.

A simple but profound change to the understanding of gravity is that gravitational potential arises from changes in the energy stored in objects as mass. This replaces gravity as a distortion of the surrounding fabric of spacetime while mass remains constant. The stored energy is released as kinetic energy when objects move closer to each other. Mass reduces when the magnitude of the background and the speed of light increase. Massless photons do not lose energy in escaping a gravitational field. Instead, the energy stored in atoms increases. The apparent redshift of photons is a blueshift of atoms and massive clocks run faster. The revised understanding avoids the singularities at the centre of black holes. Changes in gravity, which propagate at the speed of light, can now cross the supposed event horizon, allowing black holes to rotate around each other. The increased speed of light, going back in time, means that the standard supernovae candles are more distant than assumed from their wavelength shift. This entirely removes the need for an accelerating expansion and yields the current rate at which time is slowing. The amount is in excellent agreement with the observed Pioneer anomaly. Moreover, it is demonstrated that the apparent, but now unneeded, dark energy is a necessary consequence of the assumption that mass is independent of the surrounding density of matter. It is also shown that the current explanation of the Pioneer frequency drift is untenable. The revised theory, labelled Full Relativity, overcomes the need for other ad hoc hypotheses, including dark matter and cosmic inflation, while yielding the standard predictions of General Relativity. It links inertia to the asymmetry of contributions to the background field from the chiral components due to matter and antimatter. The asymmetry determines the rotation frequency of the trapped angular momentum seen in the Compton wavelength of quantum mechanics. The dependence of inertia on asymmetry then explains the observed galaxy rotation curves and gravitational lensing without the need for dark matter. Various tests which will distinguish between the two forms of Relativity are put forward. Finally, gravity can now be linked with the other three forces in a way that is consistent with the Standard Model of particle physics.
Category: Relativity and Cosmology

Invalidity of the Principle of Invariance of Space-Time Interval for the Case of Two Relatively Moving Observers

Authors: Fang Zhou
Comments: 34 Pages. In Chinese

In the article, a comprehensive and detailed analysis on Lorentz Transformation is presented. There exist essential and fatal errors in derivation of Lorentz Transformation which, in result, lead to absurdity. In consequence, the mistakes in proposed equations for derivation of Lorentz Transformation make the transformation mathematically depicting an observation process of two relatively rest observers instead of moving observers. The ‘Principle of Invariance of Space-Time Interval’ is invalid for the case of two relatively moving observers. In addition, the paper produces a deduction of Galilean-Zhou Transformation, which shows that Galilean-Zhou Transformation completely conform the real observation process of two relatively moving observers. It is expected that Galilean-Zhou Transformation would supersede Lorentz Transformation.
Category: Relativity and Cosmology

Common Recognition of Metric Tensor for Special and General Relativity Theory

Authors: Tsuneaki Takahashi
Comments: 3 Pages.

Regard to metric tensor, it is necessary to have common concept and calculation for Special and General Relativity Theory. It is tried here based on the result of research for both.
Category: Relativity and Cosmology

Einstein Field Equations and Geodesic Equation Paradox for a Gravitational Plane Wave Pulse Colliding with a Mass

Authors: Karl De Paepe
Comments: 3 Pages.

We consider a gravitational plane wave pulse colliding with a point mass. The path of the mass can be determined using the Einstein field equations. We expect, for small mass, that this path to be approximately a geodesic. We show this need not be the case.
Category: Relativity and Cosmology

Apparent Constancy of the Speed of Light and Apparent Change of Time of Light Emission Relative to an Inertial Observer in Absolute Motion

Authors: Henok Tadesse
Comments: 64 Pages.

Many experiments have been performed over decades and centuries to investigate the problem of absolute motion and the speed of light, with reported results ranging from complete null results and very small fringe shifts to large first order effects. All classical and modern theories, including ether theory, emission theory, and special relativity theory, have failed to consistently explain all of these experiments. In this paper, a new model of motion and the speed of light is proposed that can consistently explain many of the known light speed experiments including the Michelson-Morley experiments, stellar aberration, moving source, moving observer and moving mirror experiments, the Bryan G Wallace Venus radar range data anomaly, the GPS, the Ives-Stilwell experiments, the Marinov, the Silvertooth , and the Sagnac effect. The new model is proposed as follows. 1. Light always behaves as if it is emitted from the point where the source is relative to the observer/ detector at the instant of emission. 2. The speed of light in vacuum is always constant c relative to the observer/detector. 3. The effect of absolute motion of the observer/ detector is to create an apparent change in time of emission. 4. Light behaves as if it is reflected from the point in space where the mirror is/was at the moment of emission, with the speed of the reflected light equal to c ± 2v , where v is a component of the mirror velocity relative to the observer, which is perpendicular to the plane of the mirror. The new theory not only can explain why the Michelson-Morley experiments give null results, but also why the Silvertooth experiment gives large first order effect. It also reconciles the Michelson-Morley experiment and the Sagnac effect. This paper also solves one of the profound puzzles in physics: the speed of electrostatic and gravitational fields. Is the speed of gravity finite or infinite? The answer is that the speed of gravity has dual nature: finite and infinite. Suppose that the Sun disappeared at t = 0. Would Sun’s gravity on Earth disappear instantaneously or with the delay of the speed of light? At t = -8.3 minutes, the Sun ‘anticipates’ its own disappearance after 8.3 minutes and sends a zero gravitational field towards the Earth, which travels at the speed of light and reaches the Earth at t = 0, coinciding exactly with the instance of disappearance of the Sun!
Category: Relativity and Cosmology

The Electron and Weak Points of the Metric System

Authors: Gerd Pommerenke
Comments: 74 Pages.

Object of this work is to find out the reason, why we get only nearly correct results with calculations using natural constants. The possibility to increase accuracy is analyzed in order to obtain more exact results than with the CODATA values. A special role in this connection plays the electron. The calculations are based on the model published in [1] and as the latest version in [6]. The idea stems from Cornelius LANCZOS, outlined at a lecture on the occasion of the Einstein-Symposium 1965 in Berlin [2]. The model defines the expansion of the universe as a consequence of the existence of a metric wave field. That field also should be the reason for all relativistic effects, both SR and GR. In the context of this work the properties of the electron are analyzed with the result, that it’s well suited as a scale basis of the metric system. Furthermore some weak points of latter one have been found, being the reason for the imprecise results when using the CODATA values. The reason are fixed values used to the definition of base units, which in turn depend on other values as well as on time and on the reference frame. In the end a consistent system is presented, which yields exact results of the basic natural constants, with which nearly all other natural u201econstants" can be calculated by means of five fixed values only. The bottom line is the meaning of the PLANCK-units and the electron mass as glue to the reference frame. Exactly set up the system would allow the calculation error to be reduced to almost zero, as the errors of different measured values are not "passed through".
Category: Relativity and Cosmology

Das Elektron Und Schwachpunkte Des Metrischen Systems

Authors: Gerd Pommerenke
Comments: 74 Pages. German version

Ziel dieser Arbeit ist es herauszufinden, warum wir bei Berechnungen mit Naturkonstanten nur annähernd korrekte Ergebnisse erhalten. Es wird die Möglichkeit einer Verbesserung analysiert, um genauere Ergebnisse als mit den CODATA-Werten zu erhalten. Eine besondere Rolle spielt in diesem Zusammenhang das Elektron.Die Berechnungen basieren auf dem in [1] veröffentlichten Modell und in der neuesten Version in [6]. Die Idee stammt von Cornelius LANCZOS und wurde in einem Vortrag anlässlich des Einstein-Symposiums 1965 in Berlin [2] dargelegt. Das Modell definiert die Expansion des Universums als Folge der Existenz eines metrischen Wellenfeldes. Dieses Feld sollte auch der Grund für die Existenz aller relativistischen Effekte sein, sowohl SR als auch GR.Im Rahmen dieser Arbeit werden die Eigenschaften des Elektrons analysiert mit dem Ergebnis, dass es sich gut als Bezugsgröße des metrischen Systems eignet. Darüber hinaus wurden einige Schwachstellen des Systems gefunden, die der Grund für die ungenauen Ergebnisse bei Verwendung der CODATA-Werte sind.Der Grund sind fest definierte Werte von Basiseinheiten, die wiederum von anderen Werten sowie von der Zeit und vom Bezugssystem abhängen. Am Ende wird ein konsistentes System vorgestellt, das exakte Ergebnisse der grundlegenden Naturkonstanten liefert, mit denen nahezu alle anderen Naturkonstanten anhand von nur fünf festen Werten berechnet werden können. Im Endeffekt wird auch die Bedeutung der Planckschen Einheiten als Verbindung zum Bezugssystem genauer ersichtlich.Mit exakten Grundwerten ließe sich der Berechnungsfehler auf nahezu Null reduzieren, da die Fehler unterschiedlicher Messwerte nicht "durchgereicht" werden.
Category: Relativity and Cosmology

The Resolution of Hawking's Information Paradox in Dark_Energy and Dark Matter with Baryonic Matter Distribution

Authors: Tony Bermanseder
Comments: 7 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

Hawking's Black Hole Information Paradox is resolved in a Dark Energy distribution.
Category: Relativity and Cosmology

Scale-Invariant Conformal Waves

Authors: Carsten S.P. Spanheimer
Comments: 7 Pages.

Investigating conformal metrics on (pseudo-) Riemannian spaces, a ‘scale-invariant’ choice for the Lagrange density leads to homogeneous d’Alembert eqations which allow for source-free wave phenomena in any number of dimensions. This suggests to apply a scale-invariant action principle rather than the Hilbert-Einstein action to general relativity to also find general, non-conformal solutions.
Category: Relativity and Cosmology

The Beginning of a New General Theory of Relativity: Part 1

Authors: Valentín Ibáñez Fernández
Comments: 17 Pages. In Russian

Inside the inertial moving system, a new distribution of forces1,2 appears, causing a change in the laws of classical mechanics. There are complex algebraic equations of gravitational fields for the empty space of Newton's rest frame and later in Einstein's system of motion in general relativity. Newton's theory of gravity led to the strange conclusion that in the space of the universe, a constant force is propagating, directed towards the center of huge masses such as the Sun. From these ideas, we will come to the strange conclusion that the universe with all the planets around the sun is contracting and all the planets tend to the Sun with time. In his general theory of relativity, Einstein put forward another philosophical hypothesis that the universe does not contract, but expands in time and there are no gravitational forces present in it. The result of this new philosophical hypothesis led to the appearance in the universe of moving space to a huge mass of planets and even to their satellites. After analyzing this work, in which the theory of a freely falling body as the basis of gravity has not changed, we can come to the conclusion that huge streams of mythical material space move to the earth with the speeds of a freely falling body (SPB). This movement of the atmosphere or any material medium in the universe would have such a speed of movement of the SPT that we would constantly feel the streams of air falling on us from above and they would be immeasurably greater than all the winds on planet Earth. We do not feel it. Such a superficial, but scientific physics philosophical analysis puts forward the need to deeply analyze of the general theory of relativity from the point of view of experimental data in terrestrial space. Find flaws in the theory of motion of matter that led the general theory of relativity to a mathematical abstraction, in which time in a moving system changes, a beam of light is bent in the vicinity of huge masses of matter and leads to the formation of black holes in the universe, etc.

Внутри инерциальной движущейся системы появляется новое распределение сил 1,2, вызывающих изменение законов классической механики. Существуют сложные алгебраические уравнения гравитационных полей для пустого пространства системы покоя Ньютона и в последствии в системы движения Эйнштейна в общей теории относительности. Но теория гравитации Ньютона привела к странному выводу, что в пространстве вселенной распространяя постоянная сила, направленная к центру огромных масс таких как Солнце. Но тогда из этих представлений мы прейдём к странному выводу, что вселенная со всеми планетами вокруг солнца сжимается и все планеты стремится со временем к Солнцу. В своей общей теории относительности Эйнштейн выдвинул другую философскую гипотезу, что вселенная не сжимается, а расширятся во времени и в ней не присутствуют силы гравитации. Результат этой новой гипотезы философской привёл к появлению во вселенной движущегося пространства к огромным масса планет и даже к их сателлитам. И проанализировав эту работу, в которой теория свободно падающего тела как основа гравитации не изменилась, можно прейти к выводу что огромные потоки пространства мифического материального, движутся на землю со скоростями свободно падающего тела (СПТ). Это движение атмосферы или любой материальной среды во вселенной имела бы такую скорость движения СПТ, что мы бы ощущали постоянно потоки воздуха, падающего на нас сверху и они бы были неизмеримо больше всех ветров на планете Земля. Но мы этого не ощущаем. Такой поверхностный, но научный физика философский анализ выдвигает необходимость глубоко проанализировать общую теорию относительности с точки зрения экспериментальных данных в земном пространстве и найти в теории движения материи изъяны которые привели общую теории относительности к математической абстракции, в которой время в движущейся системе меняется, луч света искривляется в близи огромных масс материи и приводит во вселенной к образованию черных дыр и т.д.
Category: Relativity and Cosmology

Dark Matter Models the Gravitation of the Expanding Universe

Authors: Arto Annila, Marten Wikstrom
Comments: 6 Pages.

All ordinary matter, extending from the dense past to the dilute present, causes gravitation across the universe. Motions deriving from this tiny universal gravitational field are on display over vast distances. On the one hand, distant galaxies move away; on the other, galaxies in clusters move about. Also, stars and gas clouds orbit around in balance with the local galactic and universal gravitation. This insight into galaxy velocity dispersion and rotation renders dark matter and modified gravity hypotheses redundant.
Category: Relativity and Cosmology

Gravitation as a Secondary Effect of Electromagnetic Interaction

Authors: Markus Schönlinner
Comments: 25 Pages.

The unification of gravitation and quantum physics is a still unsolved problem. A convincing solution is not in sight and a simple solution is virtually excluded. It seems that modern physics entered into a dead end here. Most of the proposals for solution try to enforce a breakthrough in the pursued direction with ever more complexer approaches. However, there is a path to circumvent these difficulties. By abandoning one of the prerequisites of the General RelativityTheory, a new degree of freedom is won in return. With that, a theory of gravitation can be formulated, wherein the unification of the forces is possible. In the following, we start with the assumption, that gravitation can be understood as secondary effect of electromagnetic interaction. In doing so, the unification of the forces is taken as a prerequisite and is imposed as a new basic postulate. The covariance principle, a pillar of the General Relativity Theory, is abandoned instead. Under these assumptions, a consistent model of gravitation can be established and justified. It describes gravitation with a variable index of refraction of the vacuumand leads, as a consequence, to a system of variable scales. In weak gravitational fields, the theory agrees well with the General Relativity Theory. In strong fields, however, fundamental differences arise.
Category: Relativity and Cosmology

New Derivation of Redshift Distance Without Using Power Expansions. II. Additional Redshift Distances, Analyzing the Data of More Quasars, of Some Snia, of the One Black Hole in Galaxy M87 as Well as a Newer Estimation of H_0

Authors: Steffen Haase
Comments: 33 Pages.

In this part of the two-part series of essays, we first derive some equations for further physical redshift distances. We then analyze a catalog with 132,975 quasars, for which both the apparent magnitude m and the redshift z are given, in order to find the today’s value of the parameter β_0 of the theory presented. We then use this value to determine the today’s value of the radius R_0a of the Friedmann sphere using a magnitude redshift diagram of 19 SNIa. With the help of the known values of R_0a and β_0, statements about astrophysical data from the black hole in the galaxy M87 can be made. In addition, the today’s Hubble parameter H_0 results from both parameters. Furthermore, we calculate the values of the further physical redshift distances for the black hole in M87 and all 19 SNIa. The resulting parameter values are: β_0 ≈ 0.731, R_0a ≈ 2,712.48 Mpc and H_0 ≈ 65.638 km / (s ∙ Mpc). The today’s mass density of the Friedmann sphere is ρ_0 ≈ 4.843 x 10-27 g / cm 3. For the mass of the Friedmann sphere we find M_FK ≈ 1.206 x 1056 g. Annotation: Knowledge of the first part [1] of the series of articles is a prerequisite for understanding this article.
Category: Relativity and Cosmology

Discussion of Cosmological Acceleration and Dark Energy

Authors: Felix Lev
Comments: 11 Pages. Published in "Proceedings to the 25th Workshop What Comes Beyond the Standard Models, Bled, July 4-10, 2022", pp. 271-278. : http://bsm.fmf.uni-lj.si/bled2022bsm/talks/BledProceedings2022_Acceptable_06_12.pdf

The title of this workshop is: "What comes beyond standard models?". Standard models are based on Poincare invariant quantum theory. However, as shown in the famous Dyson's paper "Missed Opportunities" and in my publications, such a theory is a special degenerate case of de Sitter invariant quantum theory. I argue that the phenomenon of cosmological acceleration has a natural explanation as a consequence of quantum de Sitter symmetry in semiclassical approximation. The explanation is based only on universally recognized results of physics and does not involve models and/or assumptions the validity of which has not been unambiguously proved yet (e.g., dark energy and quintessence). I also explain that the cosmological constant problem and the problem why the cosmological constant is as is do not arise.
Category: Relativity and Cosmology

Time-Universe Relationship

Authors: Y. K. Thaker, M. M. Wagh
Comments: 3 Pages.

As we know from the theory of relativity by Albert Einstein, time depends on one's frame of reference, that is, for an object in a low gravitational field, time will move faster in comparison to an object in a high gravitational field where time will move slower relation lets us to conclude that time is relative.
Category: Relativity and Cosmology

The Accelerated Expansion of the Universe, Dark Energy and the Nature of Gravity

Authors: Andrey Stadnichenko
Comments: 1 Page. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

Gravity, accelerated expansion of the universe, dark energy are the consequences of the rotation of our universe.
Category: Relativity and Cosmology

Dark Matter and Dark Energy as a Manifestation of Gravity in the Universe

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 5 Pages.

Using Newton's law of gravity, one can correctly explain both the anomalies in the motion of stars in galaxies and the accelerated recession of galaxies in the observable Universe. That is, the concepts of “dark matter” and “dark energy” are not required. For an explanation, one must apply ordinary Newtonian gravity and take into account the dependence of the mass distribution on distance in galaxies (2D) and the observable Universe (3D). This turns out to be quite enough.
Category: Relativity and Cosmology

Analyse der Messungen von D. C. Miller in Cleveland 1927–1929
Analysis of D. C. Miller's Measurements in Cleveland 1927–1929

Authors: Sebastian Pliet
Comments: 5 Pages. In German

Dayton C. Miller machte nach den Experimenten auf dem Mount Wilson weitere Experimente mit dem selben Interferometer. Diese Daten werden analysiert, um die Ergebnisse einer Analyse der Daten vom Mount Wilson zu bestätigen. Eine Bestätigung wird nicht gefunden, es gibt aber Hinweise auf das erwartete theoretische Signal.

After the experiments on Mount Wilson, Dayton C. Miller carried out further experiments with the same interferometer. These data are analysed to confirm the results of an analysis of the Mount Wilson data. Confirmation is not found, but there is evidence of the expected theoretical signal.
Category: Relativity and Cosmology

Analysis of D. C. Miller's Measurements in Cleveland 1927–1929 (English Version)

Authors: Sebastian Pliet
Comments: 5 Pages.

After the experiments on Mount Wilson, Dayton C. Miller carried out further experiments with the same interferometer. These data are analysed to confirm the results of an analysis of the Mount Wilson data. Confirmation is not found, but there is evidence of the expected theoretical signal.
Category: Relativity and Cosmology

Consolidating Electromagnetic Waves from Separate Sources

Authors: Moshe Segal
Comments: 7 Pages.

The author of this article published several articles [1], [2], [3], which argue that Electromagnetic (EM) waves from different sources can and do consolidate, contrary to the acceptable notion presented in an article [4] that EM waves from separate sources cannot consolidate. This article adds further support to the statement that EM waves from separate sources can consolidate, support that everybody can experience, from everyday experience, which can also be recorded on photos. However, as described in articles [1], [2], [3], if EM waves from separate sources do consolidate, this causes paradoxes, which must be addressed. This additional support, provided by this article, to the statement that EM waves from separate sources can consolidate,still cannot be considered as a complete and full proof that EM waves from separate sources can consolidate, but it provides support to the claim that an experiment as described in article [1] to implement and test such consolidations of EM waves from separate sources, is an important endeavor. Such an experiment, which can control the various details of such EM waves consolidations, might validate that such EM waves consolidations do occur and hopefully, might also provide explanations to the paradoxes that occur in such EM waves consolidations, hopefully, explanations that agree with the explanations provided in articles [1], [2], [3].
Category: Relativity and Cosmology

A New Gravitational Time Dilation Equation

Authors: Michael Leon Fontenot
Comments: 24 Pages.

In a previous paper, I showed that the gravitational time dilation equation, which has been accepted since Einstein published it in 1907, is incorrect. It is incorrect because it is inconsistent with the required outcome at the reunion of the twins in the famous twin ‘paradox’ of special relativity. In this paper, I describe a new gravitational time dilation (GTD) equation which IS consistent with the required outcome at the reunion of the twins. And my new GTD equation gives the same instantaneous change of the home twin’s (her) age, according to the traveling twin (him), when he instantaneously changes his velocity, as is given by the CMIF simultaneity method, but without requiring the assumption that the CMIF method requires. Therefore, my GTD equation asserts that it is the SINGLE correct simultaneity method.
Category: Relativity and Cosmology

Time Damping Theory: a Method of Calculating Satellite Time Dilation

Authors: Yang Long
Comments: 7 Pages.

Time damping refers to the effect that matter is damped in the gravitational field, resulting in the slow time velocity of matter.
Category: Relativity and Cosmology