Description: 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 ( T - 44 ), which significantly distinguishes this 5D gravity from other 5D gravitational theories that usually assumed a 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.

Description: A brief account of the present status of the recent nonlocal generalization of Einstein’s theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenböck’s torsion and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline–Kuhn approach to modified gravity. To account for the observational data regarding dark matter,  nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.

Description: 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.

Description: 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, H0 = 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,

Description: 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.

Description: 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.

Description: We analytically calculate some orbital effects induced by the Lorentz-invariance/ momentum-conservation   parameterized   post-Newtonian (PPN)  parameter α3 in   a gravitationally bound binary system made of a primary orbited by a test particle.  We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary’s spin axis ψˆ.  We use our results to put preliminary  upper bounds on α3 in the weak-field regime by using the latest data from Solar System’s planetary dynamics. By linearly combining the supplementary perihelion  precessions ∆w˙ of the Earth, Mars and Saturn, determined by astronomers with the Ephemerides of Planets and the Moon (EPM) 2011 ephemerides for the general relativistic  values of the PPN parameters β = γ = 1, we infer |α3| ;5 6 × 10−10.   Our result is about three orders of magnitude better than the previous weak-field  constraints existing  in the literature and of the same  order of magnitude of the constraint expected from the future BepiColombo mission to Mercury. It is, by construction, independent of the other preferred-frame PPN parameters α1, α2, both preliminarily constrained down to a ≈ 10−6 level. Future analyses should be performed by explicitly including α3 and a selection  of other PPN parameters in the models fitted by the astronomers to the observations and estimating them in dedicated covariance analyses.

Description: A team of astronomers has recently reported an anomalous retrograde precession of the perihelion of Saturn amounting  to ∆ω˙ SATURN =  −0.006(2)  arcsec  per century (arcsec cy−1).   This unexplained  precession was obtained  after taking into account all classical and relativistic  effects in the context of the highly refined EPM2008 ephemerides. More recent analyzes  have  not confirmed this effect,   but they have  found similar discrepancies in other planets. Our objective in this paper is to discuss a non-standard model involving transversal gravitomagnetism  generated by the Sun as a possible  source of these anomalies.   In order to compute the Lense–Thirring  perturbations induced by the suggested interaction,  we should consider the orientation of the Sun’s rotational axis in Carrington elements and the inclination  of the planetary orbits with respect to the ecliptic plane. We find that an extra component of the gravitomagnetic field not predicted by General Relativity could explain the reported anomalies without conflicting with the Gravity  Probe B experiment and the orbits of the geodynamics satellites.

Description: 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.