The Newtonian Limit of F(R) gravity

A general analytic procedure is developed to deal with the Newtonian limit of $f(R)$ gravity. A discussion comparing the Newtonian and the post-Newtonian limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic $f(R)$ theory, it is possible to obtain general solutions in term of the metric coefficients up to the third order of approximation. In particular, the solution relative to the $g_{tt}$ component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory $f(R)=R$. Furthermore, we show that the Birkhoff theorem is not a general result for $f(R)$-gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian limit and the emergence of massive gravitational wave solutions.Comment: 16 page

The post-Newtonian limit in C-theories of gravitation

C-theory provides a unified framework to study metric, metric-affine and more general theories of gravity. In the vacuum weak-field limit of these theories, the parameterized post-Newtonian (PPN) parameters $\beta$ and $\gamma$ can differ from their general relativistic values. However, there are several classes of models featuring long-distance modifications of gravity but nevertheless passing the Solar system tests. Here it is shown how to compute the PPN parameters in C-theories and also in nonminimally coupled curvature theories, correcting previous results in the literature for the latter.Comment: 5 pages, no figures; To appear in PRD as a rapid communicatio

Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of $f(R)$-gravity is equivalent to the one of Brans-Dicke gravity with $\omega_{BD} = 0$, so that the PPN parameters of these models turn out to be ill defined. In this paper, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with $\omega_{BD} = 0$ in order to characterize the homologous quantities of $f(R)$-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for a $f(R)$-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame.Comment: 9 page

Probing the Brans-Dicke Gravitational Field by Cerenkov Radiation

The possibility that a charged particle propagating in a gravitational field described by Brans-Dicke theory of gravity could emit Cerenkov radiation is explored. This process is kinematically allowed depending on parameters occurring in the theory. The Cerenkov effect disappears as the BD parameter omega tends to inftinity, i.e. in the limit in which the Einstein theory is recovered, giving a signature to probe the validity of the Brans-Dicke theory.Comment: 8 pages, no figure

Carter-like constants of the motion in Newtonian gravity and electrodynamics

For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/m)^L. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame-dragging (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.Comment: 4 page

Model-independent test of gravity with a network of ground-based gravitational-wave detectors

The observation of gravitational waves with a global network of interferometric detectors such as advanced LIGO, advanced Virgo, and KAGRA will make it possible to probe into the nature of space-time structure. Besides Einstein's general theory of relativity, there are several theories of gravitation that passed experimental tests so far. The gravitational-wave observation provides a new experimental test of alternative theories of gravity because a gravitational wave may have at most six independent modes of polarization, of which properties and number of modes are dependent on theories of gravity. This paper proposes a method to reconstruct the independent modes of polarization in time-series data of an advanced detector network. Since the method does not rely on any specific model, it gives model-independent test of alternative theories of gravity

The flight of the bumblebee: vacuum solutions of a gravity model with vector-induced spontaneous Lorentz symmetry breaking

We study the vacuum solutions of a gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB. The purely radial LSB result corresponds to new black hole solutions. When possible, Parametrized Post-Newtonian (PPN) parameters are computed and observational boundaries used to constrain the Lorentz symmetry breaking scale.Comment: 12 pages, 2 figure

Dynamical Masses in Modified Gravity

Differences in masses inferred from dynamics, such as velocity dispersions or X-rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models however must include some non-linear mechanism to restore General Relativity (GR) in dense environments, which is necessary to pass Solar System constraints on precisely these deviations. In this paper, we study the dynamics within virialized structures in the context of two modified gravity models, f(R) gravity and DGP. The non-linear mechanisms to restore GR, which f(R) and DGP implement in very different ways, have a strong impact on the dynamics in bound objects; they leave distinctive signatures in the dynamical mass-lensing mass relation as a function of mass and radius. We present measurements from N-body simulations of f(R) and DGP, as well as semi-analytical models which match the simulation results to surprising accuracy in both cases. The semi-analytical models are useful for making the connection to observations. Our results confirm that the environment- and scale-dependence of the modified gravity effects have to be taken into account when confronting gravity theories with observations of dynamics in galaxies and clusters.Comment: 18 pages, 16 figures; submitted to PRD; v2: typos corrected, references added, minor additions (Sec. IID

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter \omega of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton \lambda_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound \omega > 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit

A Quintessence Scalar Field in Brans-Dicke Theory

It is shown that a minimally coupled scalara field in Brans-Dicke theory yields a non-decelerated expansion for the present universe for open, flat and closed Friedmann-Robertson-Walker models.Comment: Latex file, 9 pages, no figures; to be published in Classical and Quantum Gravit