We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models based on GR and modified gravity models without dark energy. We derive the consistency relation in GR which is written only in terms of observables - the Hubble parameter, the density perturbations, the peculiar velocities and the lensing potential. The breakdown of this consistency relation implies that the Newton constant which governs large-scale structure is different from that in the background cosmology, which is a typical feature in modified gravity models. We propose a method to perform this test by reconstructing the weak lensing spectrum from measured density perturbations and peculiar velocities. This reconstruction relies on Poisson's equation in GR to convert the density perturbations to the lensing potential. Hence any inconsistency between the reconstructed lensing spectrum and the measured lensing spectrum indicates the failure of GR on cosmological scales. The difficulties in performing this test using actual observations are discussed.
Using cosmological relativity theory, we derive the formula for the cosmological redshift written explicitly in terms of 1 - "Omega", where "Omega" = "rho"/"rho"_c is the ratio of the average mass density to the critical "closure" density. Based on the present-day data of observed redshifts, we conclude that "Omega" is less than one.
Recent observations of distant supernovae imply, in defiance of expectations, that the universe growth is accelerating, contrary to what has always been assumed that the expansion is slowing down due to gravity. In this paper a general-relativistic cosmological theory that gives a direct relationship between distances and redshifts in an expanding universe is presented. The theory is actually a generalization of Hubble's law taking gravity into account by means of Einstein's theory of general relativity. The theory predicts that the universe can have three phases of expansion, decelerating, co…
We present a fractal dust model of the Universe based on Mandelbrot's proposal to replace the standard Cosmological Principle by his Conditional Cosmological Principle within the framework of General Theory of Relativity. This model turns out to be free from the de-Vaucouleurs paradox and is consistent with the SNe1a observations. The expected galaxy count as a function of red-shift is obtained for this model. An interesting variation is a steady state version, which can account for an accelerating scale factor without any cosmological constant in the model.
Here we report timing measurements of the relativistic binary pulsar PSR J1141-6545 that constrain the component masses and demonstrate that the orbital period derivative \dot Pb = (-4+/-1)x10^-13 is consistent with gravitational wave emission as described by the general theory of relativity. The mass of the neutron star and its companion are 1.30+/-0.02 Mo and 0.986+/-0.020 Mo respectively, suggesting a white dwarf companion, and extending the range of systems for which general relativity provides a correct description. On evolutionary grounds, the progenitor mass of PSR J1141-6545 should be …
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster. Mach principle is that the matter of the whole universe can affect local dynamic systems. That is, the matter of the whole universe sets up the local absolute reference frames. However, Einstein's general theory of relativity is against the absolute reference frames of Mach Principle.
There have been a number of papers proposing that the light speed of a homogeneous and isotropic universe is variable. This paper outlines a simple way that the vectors and tensors of special relativity can be extended to allow such a variable light speed and show how the field equation of general relativity can also be extended with particular application to such a universe.
Nature succeeds in accelerating extended and massive objects to relativistic velocities. Jets in Active Galactic Nuclei and in galactic superluminal sources and gamma-ray bursts fireballs have bulk Lorentz factors from a few to several hundreds. A variety of effects then arises, such as the beaming of the produced radiation, light aberration, time contraction and the Doppler frequency shift. I will emphasize that special relativity applied to real (i.e. extended) observed objects inevitably must take into account that any piece of information is carried by photons. Being created in different p…
An attempt is made for a new type of analysis of the time-variability of the fine-structure constant trying to fit the most recent result from the laboratory measurements, the Oklo constraint and the data from the QSO absorption lines all in consistency with the accelerating universe.
A general-relativistic theory of cosmology, the dynamical variables of which are those of Hubble's, namely distances and redshifts, is presented. The theory describes the universe as having a three-phase evolution with a decelerating expansion followed by a constant and an accelerating expansion, and it predicts that the universe is now in the latter phase. The theory is actually a generalization of Hubble's law taking gravity into account by means of Einstein's theory of general relativity. The equations obtained for the universe expansion are elegant and very simple. It is shown, assuming Om…
Astronomers measure distances to faraway galaxies and their velocities. They do that in order to determine the expansion rate of the Universe. In Part I of these lectures the foundations of the theory of the expansion of the Universe was given. In this part we present the theory. A formula for the distance of the galaxy in terms of its velocity is given. It is very simple: $r(v)=cτ/β\sinhβv/c$, where $τ$ is the Big Bang time, $β=\sqrt{1-Ω_m}$, and $Ω_m$ is the mass density of the Universe. For $Ω_m<1$ this formula clearly indicates that the Universe is expanding with acceleration, as experimen…
While modern cosmology, founded in the language of general relativity, is almost a century old, the meaning of the expansion of space is still being debated. In this paper, the question of radar ranging in an expanding universe is examined, focusing upon light travel times during the ranging; it has recently been claimed that this proves that space physically expands. We generalize the problem into considering the return journey of an accelerating rocketeer, showing that while this agrees with expectations of special relativity for an empty universe, distinct differences occur when the univers…
Considering the hyperbolic nature of the universe, the Hubble's law and the inverse square laws such as, the Coulomb's law and Newton's gravitational law, should be modified in accordance with the special theory of relativity. Consequently there is no the Hubble's length, which might be the observable boundary of our universe, does not appear in point of view of the special theory of relativity, and the Newton's third law still hold in the special theory of relativity. Recent astronomical observations of type Ia supernovae support the modified Hubble's law which also leads a view that the cosm…
After a brief introduction to the sixteenth and seventeenth century views of the Universe and the nineteenth century paradox of Olbers, we start the history of the cosmic expansion with Hubble's epochal discovery of the recession velocities of spiral galaxies. By then Einstein's theories of relativity were well known, but no suitable metric was known. Prior to introducing General Relativity we embark on a non-chronological derivation of the Robertson-Walker metric directly from Special Relativity and the Minkowski metric endowed with a Gaussian curvature. This permits the definition of all rel…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational interaction on local physics. A reanalysis of the situation suggests that all relativistic effects that are presently attributed to kinematics of relative motion in flat space-time are in fact gravitational effects of the nearly homogeneous and isotropic Universe. The correct theory of relativity is the one with a preferred cosmic rest frame. Yet, the theory pre…
In the standard cosmological theory one uses the Einstein concepts of space and time as were originally introduced for the special theory of relativity and the general relativity theory. According to this approach all physical quantities are described in terms of the continuum spatial coordinates and time. Using general relativity theory a great progress has been made in understanding the evolution of the Universe. Cosmologists usually measure spatial distances and redshifts of faraway galaxies as expressed by the Hubble expansion. In recent years this fact was undertaken to develop new theori…
We present a new approach to early universe cosmology. Inflation is replaced by a phase transition in which both matter and geometry are created simultaneously. We calculate the spectrum of metric perturbations and show that it is flat. We then argue that as a consequence of the dynamic nature of the phase transition the spectrum is likely not completely flat but tilted. We argue that the tilt is related to $η$, one of the critical exponents characterizing the phase transition. This exponent generically lies between 0.03 and 0.06. It thus coincides with the observed tilt of the perturbation sp…
We consider the dynamics of tensor and scalar gravitational fields in the Relativistic Theory of Gravitation with the Minkowskian vacuum metric and generalize the formulation to the massless graviton. The potential of scalar field is determined in the presence of cosmological term under clear physical motivations. We find cosmological inflationary solutions and analyze conditions providing the transition to the regime of hot expanding universe.
We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy. The consistency relation should be satisfied if general relativity is the correct theory of gravity and dark energy clustering is negligible. As an extension, we also provide the DGP counterpart of the relation.
There are obvious discrepancies among various experimental constraints on the variation of the fine-structure constant, $α$. We attempt to discuss the issue in the framework of de Sitter invariant Special Relativity (${\cal SR}_{c,R}$) and to present a possible solution to the disagreement. In addition, on the basis of the observational data and the discussions presented in this Letter, we derive a rough theoretical estimate of the radius of the Universe.
Reexamination of general relativistic experimental results shows the universe is governed by Einstein's static-spacetime general relativity instead of Friedmann-Lemaitre expanding-spacetime general relativity. The absence of expansion redshifts in a static-spacetime universe suggests a reevaluation of the present cosmology is needed.
Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an alternative cosmological model, based on a linearly expanding universe with Omega=1, can fully account for these observations. This model is also able to resolve the other problems associated with the standard Big Bang model. A scale-invariant form of the field equations of General Relativity is postulated, based on the replacement of the Newtoni…
In this paper we study a type of model for closed inflationary universe models using the Jordan-Brans-Dicke theory. Herein we determine and characterize the existence of $Ω>$1, together with the period of inflation. We have found that our model, which takes into account a Jordan-Brans-Dicke type of theory, is less restrictive than the one used in Einstein's theory of general relativity. Our results are compared to those found in Einstein's theory of Relativity.
Recent discussions suggest the possibility that short distance physics can significantly modify the behavior of quantum fluctuations in the inflationary universe, and alter the standard large scale structure predictions. Such modifications can be viewed as due to a different choice of the vacuum state. We show that such changes generally lead to violations of the well-known consistency relation between the scalar to tensor ratio and the tensor spectral index. Vacuum effects can introduce an observable modulation to the usual predictions for the scalar and tensor power spectra.
Recent astronomical observations verify the new scenario resulting from new conservation laws and a new relativity principle fixed either by dual properties of light or by new gravitational (G) tests and the Einstein's equivalence principle. This scenario is radically different from the classical one. During a free fall, the relative masses of free bodies, with respect to the observer at rest in a G field, remain constants. The energy released during the stops in different G potentials (GP) comes not from the G field but from the bodies. The relative properties of the bodies at rest with respe…
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity…
The observational data on CMB radiation revealed that our Universe can be an ordinary physical object moving with respect to the Earth observer with the occasional initial data. This fact allows us to apply the theory of irreducible unitary representations of the Poincare group in order to describe the Universe in the framework of the fundamental operator quantization of General Relatvity and Standard Model of elementary particles. The simplest fit of the observational CMB data is given that includes occasional gauge-invariant and frame-covariant initial data and their units of measurement.
Black holes are popping up all over the place: in compact binary X-ray sources and GRBs, in quasars, AGNs and the cores of all bulge galaxies, in binary black holes and binary black hole-neutron stars, and maybe even in the LHC! Black holes are strong-field objects governed by Einstein's equations of general relativity. Hence general relativistic, numerical simulations of dynamical phenomena involving black holes may help reveal ways in which black holes can form, grow and be detected in the universe. To convey the state-of-the art, we summarize several representative simulations here, includi…
Closed, singularity-free, inflationary cosmological models have recently been studied in the context of general relativity. Despite their appeal, these so called emergent models suffer from a number of limitations. These include the fact that they rely on an initial Einstein static state to describe the past eternal phase of the universe. Given the instability of such a state within the context of general relativity, this amounts to a very severe fine tuning. Also in order to be able to study the dynamics of the universe within the context of general relativity, they set the initial conditions…
