Narrow Results

In this paper, we have investigated the classical tests of General Relativity like precession of perihelion, deflection of light and time delay by considering a phenomenological astrophysical object like Sun, as a neutral regular Hayward black hole in Rastall gravity. We have tabulated all our results for some appropriate values of the parameter $\sigma$. We have compared our values with $\sigma =0$, which corresponds to the Schwarzschild case. Also the value of $\sigma =0.7187\times 10^{-4}$ is of particular interest as it gives some promising results.

We find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity and test it with some solar system experiments. The result is that the theory agrees with the general relativistic observations in the solar system for a determined lower bound on the graviton mass.

We summarize an interesting set of solar system predictions that we have recently derived for modified Newtonian dynamics (MOND). Specifically, we find that strong MOND behavior may become evident near the saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizable oblate ellipsoid around the saddle point. While strong MOND behavior would be a spectacular "backyard" vindication of the theory, pinpointing the MOND bubbles in the setting of the realistic solar system may be difficult. Space missions such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region.

We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speed-up problem, laboratory and solar system tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

The nonequivalence between the metric and Palatini formalisms of f(R) gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metric-Palatini gravity, consisting of the superposition of the metric Einstein–Hilbert Lagrangian with an term constructed à la Palatini, the "true" gravitational field is described by the interpolation of these two nonequivalent approaches. The theory predicts the existence of a light long-range scalar field, which passes the local constraints and affects the galactic and cosmological dynamics. Thus, the theory opens new possibilities for a unified approach, in the same theoretical framework, to the problems of dark energy and dark matter, without distinguishing a priori matter and geometric sources, but taking their dynamics into account under the same standard.

In this paper, we revisit the solar system tests of f(R) gravity. When the sun sits in a vacuum, the field f′ is light, which leads to a metric different from the observations. We reobtain this result in a simpler way by directly focusing on the equations of motion for f(R) gravity in the Jordan frame (JF). The discrepancy between the metric in the f(R) gravity and the observations can be alleviated by the chameleon mechanism. The implications from the chameleon mechanism on the functional form f(R) are discussed. Considering the analogy of the solar system tests to the false vacuum decay problem, the effective potentials in different cases are also explored. The combination of analytic and numerical approaches enables us to ascertain whether an f(R) model can pass the solar system tests or not.

Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary function of the five possible scalars constructed from the irreducible parts of torsion. This theory is a generalization of the so-called New General Relativity theory. We find that only two scalars are different to zero in spherical symmetry and we solve the corresponding field equations analytically for conformal Teleparallel gravity, and then perturbatively around Schwarzschild geometry for the general perturbative theory around GR. Finally, we compute phenomenological effects from the perturbed solutions such as the photon sphere, perihelion shift, Shapiro delay, and the light deflection. We find their correspondent correction to the standard GR contribution and their dependence on the three model parameters.

APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) is a new effort in lunar laser ranging that uses the Apollo-landed retroreflector arrays to perform tests of gravitational physics. APOLLO achieved its first range return in October, 2005, and began its science campaign the following spring. The strong signal (> 2500 photons in a ten minute period) translates to one-millimeter random range uncertainty, constituting at least an order-of-magnitude gain over previous stations. One-millimeter range precision will translate into order-of-magnitude gains in our ability to test the weak and strong equivalence principles, the time rate of change of Newton's gravitational constant, the phenomenon of gravitomagnetism, and the inverse-square law.

We summarize an interesting set of solar system predictions that we have recently derived for modified Newtonian dynamics (MOND). Specifically, we find that strong MOND behavior may become evident near the saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizable oblate ellipsoid around the saddle point. While strong MOND behavior would be a spectacular “backyard” vindication of the theory, pinpointing the MOND bubbles in the setting of the realistic solar system may be difficult. Space missions such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region.