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p. 18-51
Received: 16 October 2014 / Accepted: 15 December 2014 / Published: 26 December 2014
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Abstract: In this paper, we comprehensively review the five-dimensional (5D) fully-covariant theory of gravitation developed by Zhang two decades ago and its recent applications in astrophysics and cosmology. This 5D gravity describes not only the fields, but also the matter and its motion in a 5D spacetime. The greatest advantage of this theory is that there does not exist any unknown parameter, so that we can apply it to explain astrophysical and cosmological issues by quantitatively comparing the results obtained from it with observations and to predict new effects that could not be derived from any other gravitational theories. First, the 5D covariant description of matter and its motion enabled Zhang to analytically derive the fifteenth component of the 5D energy-momentum tensor of matter (${\stackrel{-}{T}}^{44}$ ), which significantly distinguishes this 5D gravity from other 5D gravitational theories that usually assumed a ${\stackrel{-}{T}}^{44}$ with an unknown parameter, called the scalar charge s, and, thus, to split the 5D covariant field equation into (4 + 1) splitting form as the gravitational, electromagnetic, and scalar field equations. The gravitational field equation turns into the 4D Einstein’s field equation of general relativity if the scalar field is equal to unity. Then, Zhang solved the field equations and obtained an exact static spherically-symmetric external solution of the gravitational, electromagnetic and scalar fields, in which all integral constants were completely determined with a perfect set of simple numbers and parameters that only depend on the mass and electric charge of the matter, by comparing with the obtained weak internal solution of the fields at a large radial distance. In the Einstein frame, the exact field solution obtained from the 5D fully-covariant theory of gravitation reduces to the Schwarzschild solution when the matter is electrically neutral and the fields are weak in strength. This guarantees that the four fundamental tests (light deflection, gravitational redshift, perihelion advance and radar echo delay) of the 4D Einstein’s general relativity in the case of weak fields are also the tests of the 5D fully-covariant theory of gravitation. In the case of strong fields, especially when the matter is highly charged, however, the results from the 5D fully-covariant theory of gravitation are significantly different from the 4D Einstein’s general relativity. Applying this 5D gravity and its exact field solution, Zhang has recently developed a new redshift mechanism, called electric redshift, a new supernova explosion mechanism with gravitational field shielding, a new gravitationless black hole model, a modified neutron star mass-radius relation, a modified Friedmann equation for the accelerating universe, and so on. This paper provides an overview of this 5D fully-covariant theory of gravitation, including also its solution properties and astrophysical applications.
p. 601-622
Received: 6 October 2014 / Revised: 27 November 2014 / Accepted: 11 December 2014 / Published: 17 December 2014
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Abstract: I review the connection between dynamics and the baryonic mass distribution in rotationally-supported galaxies. The enclosed dynamical mass-to-light ratio increases with decreasing galaxy luminosity and surface brightness. The correlation with surface brightness appears to be the more fundamental, with the dependence on luminosity following simply from the weaker correlation between luminosity and surface brightness. In addition to this global relation, there is also a local relation between the amplitude of the mass discrepancy and the acceleration predicted by the observed distribution of baryons. I provide an empirical calibration of this mass discrepancy-acceleration relation. The data are consistent with the operation of a singe effective force law in disk galaxies, making this relation tantamount to a natural law. I further provide formulae by which the radial dark matter distribution can be estimated from surface photometry. The form of the dark matter halo depends uniquely on the distribution of baryons in each galaxy and, in general, is neither a cusp nor a core. It remains difficult to see how galaxy formation models can reproduce the observed behavior, which is uniquely predicted by MOND.
p. 577-600
Received: 16 October 2014 / Revised: 14 November 2014 / Accepted: 2 December 2014 / Published: 12 December 2014
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Abstract: In this work we analyze kinematical conformal cosmology (KCC), an alternative cosmological model based on conformal Weyl gravity (CG), and test it against current type Ia supernova (SNIa) luminosity data and other astrophysical observations. Expanding upon previous work on the subject, we revise the analysis of SNIa data, confirming that KCC can explain the evidence for an accelerating expansion of the Universe without using dark energy or other exotic components. We obtain an independent evaluation of the Hubble constant, H _{0 } = 67:53 kms ^{-1} Mpc^{-1} , very close to the current best estimates. The main KCC and CG parameters are re-evaluated and their revised values are found to be close to previous estimates. We also show that available data for the Hubble parameter as a function of redshift can be fitted using KCC and that this model does not suffer from any apparent age problem. Overall,
p. 520-576
Received: 21 July 2014 / Revised: 10 November 2014 / Accepted: 14 November 2014 / Published: 4 December 2014
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Abstract: Starting from the weak field limit, we discuss astrophysical applications of Extended Theories of Gravity where higher order curvature invariants and scalar fields are considered by generalizing the Hilbert-Einstein action linear in the Ricci curvature scalar R. Results are compared to General Relativity in the hypothesis that Dark Matter contributions to the dynamics can be neglected thanks to modified gravity. In particular, we consider stellar hydrostatic equilibrium, galactic rotation curves, and gravitational lensing. Finally, we discuss the weak field limit in the Jordan and Einstein frames pointing out how effective quantities, as gravitational potentials, transform from one frame to the other and the interpretation of results can completely change accordingly.
p. 496-519
Received: 13 September 2014 / Revised: 15 October 2014 / Accepted: 20 October 2014 / Published: 28 October 2014
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Abstract: We consider the dynamics of a barotropic cosmological fluid in an anisotropic, Bianchi type I space-time in Eddington-inspired Born–Infeld (EiBI) gravity. By assuming isotropic pressure distribution, we obtain the general solution of the field equations in an exact parametric form. The behavior of the geometric and thermodynamic parameters of the Bianchi type I Universe is studied, by using both analytical and numerical methods, for some classes of high density matter, described by the stiff causal, radiation, and pressureless fluid equations of state. In all cases the study of the models with different equations of state can be reduced to the integration of a highly nonlinear second order ordinary differential equation for the energy density. The time evolution of the anisotropic Bianchi type I Universe strongly depends on the initial values of the energy density and of the Hubble function. An important observational parameter, the mean anisotropy parameter, is also studied in detail, and we show that for the dust filled Universe the cosmological evolution always ends into isotropic phase, while for high density matter filled universes the isotropization of Bianchi type I universes is essentially determined by the initial conditions of the energy density.
p. 410-465
Received: 30 May 2014 / Revised: 7 July 2014 / Accepted: 8 July 2014 / Published: 28 July 2014
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Abstract: In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.
p. 382-409
Received: 17 April 2014 / Revised: 25 June 2014 / Accepted: 26 June 2014 / Published: 15 July 2014
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Abstract: Beginning roughly two hundred years after the big-bang, a tresino phase transition generated Compton-scale composite particles and converted most of the ordinary plasma baryons into new forms of dark matter. Our model consists of ordinary electrons and protons that have been bound into mostly undetectable forms. This picture provides an explanation of the composition and history of ordinary to dark matter conversion starting with, and maintaining, a critical density Universe. The tresino phase transition started the conversion of ordinary matter plasma into tresino-proton pairs prior to the the recombination era. We derive the appropriate Saha–Boltzmann equilibrium to determine the plasma composition throughout the phase transition and later. The baryon population is shown to be quickly modified from ordinary matter plasma prior to the transition to a small amount of ordinary matter and a much larger amount of dark matter after the transition. We describe the tresino phase transition and the origin, quantity and evolution of the dark matter as it takes place from late in the early Universe until the present.
p. 292-299
Received: 10 April 2014 / Revised: 18 June 2014 / Accepted: 19 June 2014 / Published: 10 July 2014
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Abstract: For disk galaxies (spirals and irregulars), the inner circular-velocity gradient d_{R} V_{0} (inner steepness of the rotation curve) correlates with the central surface brightness ∑_{*,0} with a slope of ~0.5. This implies that the central dynamical mass density scales almost linearly with the central baryonic density. Here I show that this empirical relation is consistent with a simple model where the central baryonic fraction ƒ_{bar,0} is fixed to 1 (no dark matter) and the observed scatter is due to differences in the baryonic mass-to-light ratio M_{bar} / L_{R} (ranging from 1 to 3 in the R -band) and in the characteristic thickness of the central stellar component Δz (ranging from 100 to 500 pc). Models with lower baryonic fractions are possible, although they require some fine-tuning in the values of M_{bar} /L_{R} _{ } and Δz. Regardless of the actual value of ƒ_{bar,0} , the fact that different types of galaxies do not show strong variations in ƒ_{bar,0} is surprising, and may represent a challenge for models of galaxy formation in a Λ Cold Dark Matter (ΛCDM) cosmology.
p. 259-262
Received: 18 April 2014 / Accepted: 25 April 2014 / Published: 2 May 2014
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Abstract: New analyses of extended data records collected with the Lunar Laser Ranging (LLR) technique performed with improved tidal models were not able to resolve the issue of the anomalous rate $\dot{e}$ of the eccentricity e of the orbit of the Moon, which is still in place with a magnitude of $\dot{e}=(5\pm 2)\times {10}^{-12}y{r}^{-1}$ . Some possible cosmological explanations are offered in terms of the post-Newtonian effects of the cosmological expansion and of the slow temporal variation of the relative acceleration rate $\ddot{S}{S}^{{}^{-1}}$ of the cosmic scale factor S. None of them is successful since their predicted secular rates of the lunar eccentricity are too small by several orders of magnitude.
p. 160-188
Received: 27 November 2013 / Revised: 18 February 2014 / Accepted: 19 February 2014 / Published: 4 March 2014
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Abstract: We discuss the production of massive relic coherent gravitons in a particular class of ƒ(R) gravity, which arises from string theory, and their possible imprint in the Cosmic Microwave Background. In fact, in the very early Universe, these relic gravitons could have acted as slow gravity waves. They may have then acted to focus the geodesics of radiation and matter. Therefore, their imprint on the later evolution of the Universe could appear as filaments and a domain wall in the Universe today. In that case, the effect on the Cosmic Microwave Background should be analogous to the effect of water waves, which, in focusing light, create optical caustics, which are commonly seen on the bottom of swimming pools. We analyze this important issue by showing how relic massive gravity waves (GWs) perturb the trajectories of the Cosmic Microwave Background photons (gravitational lensing by relic GWs). The consequence of the type of physics discussed is outlined by illustrating an amplification of what might be called optical chaos.
p. 72-80
Received: 17 December 2013 / Revised: 21 January 2014 / Accepted: 5 February 2014 / Published: 17 February 2014
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Abstract: Dark energy with negative pressure and positive energy density is believed to be responsible for the accelerated expansion of the universe. Quite a few theoretical models of dark energy are based on tachyonic fields interacting with itself and normal (bradyonic) matter. Here, we propose an experimental model of tachyonic dark energy based on hyperbolic metamaterials. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. We demonstrate that this model has a self-interacting tachyonic sector having negative effective pressure and positive effective energy density. Moreover, a composite multilayer SiC-Si hyperbolic metamaterial exhibits closely separated tachyonic and bradyonic sectors in the long wavelength infrared range. This system may be used as a laboratory model of inflation and late time acceleration of the universe.
p. 13-21
Received: 10 November 2013 / Accepted: 27 December 2013 / Published: 3 January 2014
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Abstract: By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S ^{-1} of the cosmic scale factor S (t ), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S ^{-1 } around the present epoch t_{0} , a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H_{0} at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period P_{b} ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S^{-1} (t) . More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose “elastic” parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ_{1} of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ_{1} ≲ 2 x 10^{-13} year^{-3 } level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10^{-8 } year^{-3} .
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