Parametrized post-Newtonian Parameters Research Articles

Parametrized post-Newtonian limit of Horndeski’s gravity theory

We discuss the parametrized post-Newtonian (PPN) limit of Horndeski's theory of gravity, also known under the name generalized G-inflation or ${\mathrm{G}}^{2}$-inflation, which is the most general scalar-tensor theory of gravity with at most second-order field equations in four dimensions. We derive conditions on the action for the validity of the post-Newtonian limit. For the most general class of theories consistent with these conditions we calculate the PPN parameters $\ensuremath{\gamma}(r)$ and $\ensuremath{\beta}(r)$, which in general depend on the interaction distance $r$ between the gravitating mass and the test mass. For a more restricted class of theories, in which the scalar field is massless, we calculate the full set of PPN parameters. It turns out that in this restricted case all parameters are constants and that the only parameters potentially deviating from observations are $\ensuremath{\gamma}$ and $\ensuremath{\beta}$. We finally apply our results to a number of example theories, including Galileons and different models of Higgs inflation.

Dilatonic dyon black hole solutions

Dilatonic black hole dyon solutions with an arbitrary dilatonic coupling constant and canonical sign for the scalar field kynetic term are considered. These solutions are defined up to solutions of two master equations for moduli functions. For the solutions are extended to = ±1, where corresponds to a ghost (phantom) scalar field. Some physical parameters of the solutions: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters β and γ are obtained. It is shown that PPN parameters do not depend on scalar field coupling λ and ϵ. Two groups of bounds on gravitational mass and scalar charge (for a fixed and arbitrary extremality parameter ) are found by using a certain conjecture on parameters of solutions when . These bounds are verified numerically for certain examples. Using the product we are led to the well-known lower bound on mass which was obtained earlier by Gibbons, Kastor, London, Townsend and Traschen by using spinor techniques.

Post-Newtonian approximation of teleparallel gravity coupled with a scalar field

We use the parameterized post-Newtonian (PPN) formalism to explore the weak field approximation of teleparallel gravity non-minimally coupling to a scalar field ϕ, with arbitrary coupling function ω(ϕ) and potential V(ϕ). We find that all the PPN parameters are identical to general relativity (GR), which makes this class of theories compatible with the Solar System experiments. This feature also makes the theories quite different from the scalar–tensor theories, which might be subject to stringent constraints on the parameter space, or need some screening mechanisms to pass the Solar System experimental constraints.

Parametrized post-Newtonian expansion and FRW scalar perturbations inn-DBI gravity

n-DBI gravity explicitly breaks Lorentz invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom. We look for observational consequences of this mode in two setups. Firstly, we compute the parametrized post-Newtonian (PPN) expansion of the metric to first post-Newtonian order. Surprisingly, we find that the PPN parameters are exactly the same as in General Relativity (GR), and no preferred-frame effects are produced. In particular this means that n-DBI gravity is consistent with all GR solar system experimental tests. We discuss the origin of such degeneracy between n-DBI gravity and GR, and suggest it may also hold in higher post-Newtonian order. Secondly, we study gravitational scalar perturbations of a Friedmann-Robertson-Walker space-time with a cosmological constant $\Lambda \geq 0$. In the case of de Sitter space, we show that the scalar mode grows as the universe expands and, in contrast with a canonical scalar field coupled to GR, it does not freeze on super horizon scales.

Parameterized post-Newtonian formalism for multimetric gravity

We discuss the post-Newtonian limit of multimetric gravity theories with metric tensors and a corresponding number of standard model copies, and construct an extension of the parameterized post-Newtonian (PPN) formalism. This extended formalism allows a characterization of multimetric gravity theories by a set of constant parameters. The multimetric PPN parameters we derive are a superset of the standard PPN parameters, which have been measured using high-precision experiments in the solar system. We apply our formalism to a class of theories which we previously discussed in the context of cosmology and gravitational waves, and which feature an accelerating expansion of the universe. A comparison between our results and the measured PPN parameters shows that multimetric gravity is fully compatible with solar system observations.

Post-Newtonian approximations in the Hořava-Lifshitz gravity with extra U(1) symmetry

In this paper, we first propose a universal coupling between the gravity and matter in the framework of the Ho\v{r}ava-Lifshitz theory of gravity with an extra U(1) symmetry for both the projectable and non-projectable cases. Then, using this universal coupling we study the post-Newtonian approximations and obtain the parameterized post-Newtonian (PPN) parameters in terms of the coupling constants of the theory. Contrary to the previous works in which only two PPN parameters were calculated, we obtain {\it all} PPN parameters. We then, for the first time in either projectable or non-projectable case, find that all the solar system tests carried out so far are satisfied in a large region of the parameters space. In particular, the same results obtained in general relativity can be easily realized here. A remarkable feature is that the solar system tests impose no constraint on the parameter $\lambda$ appearing in the kinetic part of the action. As a result, the solar system tests, when combined with the condition for avoidance of strong coupling, do not lead to an upper bound on the energy scale $M_{*}$ that suppresses higher dimensional operators in the theory. This is in sharp contrast to other versions of the HL theory.

Gravitational potential of a point mass in a brane world

In brane world models, combining the extra dimensional field modes with the standard four dimensional ones yields interesting physical consequences that have been proved from high energy physics to cosmology. Even some low energy phenomena have been considered along these lines to set bounds on the brane model parameters. In this work we extend to the gravitational realm a previous result which gave finite electromagnetic and scalar potentials and self energies for a source looking pointlike to an observer sitting in a 4D Minkowski subspace of the single brane of a Randall-Sundrum spacetime including compact dimensions. We calculate here the gravitational field for the same type of source by solving the linearized Einstein equations. Remarkably, it turns out to be also non singular. Moreover, we use gravitational experimental results of the Cavendish type and the Parameterized Post Newtonian (PPN) coefficients, to look for admissible values of the brane model parameters. The anti de Sitter radius hereby obtained is concordant with previous results based on Lamb shift in hydrogen. However, the resulting PPN parameters lie outside the acceptable value domain.

CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters α1, α2. Preliminary constraints on α1, α2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a α2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α1 = (0.8±4) × 10-6 and α2 = (4±6) × 10-6, respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense–Thirring precessions and the classical rates due to the Sun's oblateness J2, allows to infer α1 = (-1 ± 6) × 10-6, α2 = (-0.9 ± 3.5) × 10-5. Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of α1 and α2. Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate α1, α2 simultaneously with the other PPN parameters as well.

Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity

The current knowledge of Mercury’s orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform general relativity tests of the parametrized post-Newtonian (PPN) formalism. Our estimations of PPN parameters (γ and β) are more stringent than previous results.

New Constraints on Preferred Frame Effects from Binary Pulsars

AbstractPreferred frame effects (PFEs) are predicted by a number of alternative gravity theories which include vector or additional tensor fields, besides the canonical metric tensor. In the framework of parametrized post-Newtonian (PPN) formalism, we investigate PFEs in the orbital dynamics of binary pulsars, characterized by the two strong-field PPN parameters, and . In the limit of a small orbital eccentricity, and contributions decouple. By utilizing recent radio timing results and optical observations of PSRs J1012+5307 and J1738+0333, we obtained the best limits of and in the strong-field regime. The constraint on also surpasses its counterpart in the weak-field regime.

Solar System constraints on scalar tensor theories with nonstandard action

We compute the parametrized post-Newtonian (PPN), $\ensuremath{\gamma}$, for scalar tensor gravity theory when the action functional for the scalar field is a nonstandard one, namely, the Dirac-Born-Infeld type action, used in the literature for a tachyon field. We investigate two different cases (linear and conformal couplings) when the scalar field is nonminimally coupled to gravity via the scalar curvature. We find that the PPN parameter $\ensuremath{\gamma}$, which measures the amount of space curvature per unit rest mass, becomes a function of the effective mass of the scalar field. Using this PPN parameter, we calculate the time delay $\ensuremath{\Delta}\ensuremath{\tau}$ for the signal to travel the round-trip distance between a ground-based antenna and a reflector placed in a spacecraft which is produced due to the gravitational field of the Sun. We use this $\ensuremath{\Delta}\ensuremath{\tau}$ to compare our result with that obtained by the Cassini mission and derive the constraints on the model parameters.

Testing gravitational physics with satellite laser ranging

Laser ranging, both Lunar (LLR) and Satellite Laser Ranging (SLR), is one of the most accurate techniques to test gravitational physics and Einstein’s theory of General Relativity. Lunar Laser Ranging has provided very accurate tests of both the strong equivalence principle, at the foundations of General Relativity, and of the weak equivalence principle, at the basis of any metric theory of gravity; it has provided strong limits to the values of the so-called PPN (Parametrized Post-Newtonian) parameters, that are used to test the post-Newtonian limit of General Relativity, strong limits to conceivable deviations to the inverse square law for very weak gravity and accurate measurements of the geodetic precession, an effect predicted by General Relativity. Satellite laser ranging has provided strong limits to deviations to the inverse square gravity law, at a different range with respect to LLR, and in particular has given the first direct test of the gravitomagnetic field by measuring the gravitomagnetic shift of the node of a satellite, a frame-dragging effect also called Lense-Thirring effect. Here, after an introduction to gravitomagnetism and frame-dragging, we describe the latest results in measuring the Lense-Thirring effect using the LAGEOS satellites and the latest gravity field models obtained by the space mission GRACE. Finally, we describe an update of the LARES (LAser RElativity Satellite) mission. LARES is planned for launch in 2011 to further improve the accuracy in the measurement of frame-dragging.

Multimetric extension of the parametrized post-Newtonian formalism: Experimental consistency of repulsive gravity

Recently we discussed a multimetric gravity theory containing several copies of standard model matter each of which couples to its own metric tensor. This construction contained dark matter sectors interacting repulsively with the visible matter sector, and was shown to lead to cosmological late-time acceleration. In order to test the theory with high-precision experiments within the solar system we here construct a simple extension of the parametrized post-Newtonian (PPN) formalism for multimetric gravitational backgrounds. We show that a simplified version of this extended formalism allows the computation of a subset of the PPN parameters from the linearized field equations. Applying the simplified formalism we find that the PPN parameters of our theory do not agree with the observed values, but we are able to improve the theory so that it becomes consistent with experiments of post-Newtonian gravity and still features its promising cosmological properties.

LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON

A primary objective of the lunar laser ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of the highly accurate measurements of the distance between the Earth and the Moon provide unique information used to determine whether, in accordance with the equivalence principle (EP), these two celestial bodies are falling toward the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Thirty-five years since their initiation, analyses of precision laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-1.0 ± 1.4) × 10-13for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, Δ(MG/MI). This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of Δ(MG/MI)SEP= (-2.0 ± 2.0) × 10-13. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter η of (4.4 ± 4.5) × 10-4, where η = 4β - γ - 3 and both γ and β are parametrized post-Newtonian (PPN) parameters. Using the recent result for the parameter γ derived from the radiometric tracking data from the Cassini mission, the PPN parameter β (quantifying the nonlinearity of gravitational superposition) is determined to be β - 1 = (1.2 ± 1.1) × 10-4. We also present the history of the LLR effort and describe the technique that is being used. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR accuracy will further advance the research on relativistic gravity in the solar system and, most notably, will continue to provide highly accurate tests of the EP.

New Post-Newtonian Parameter to Test Chern-Simons Gravity

We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory.

Parametrized post-Newtonian expansion of Chern-Simons gravity

We investigate the weak-field, post-Newtonian (PN) expansion to the solution of the field equations in Chern-Simons (CS) gravity with a perfect fluid source. In particular, we study the mapping of this solution to the parametrized post-Newtonian (PPN) formalism to 1 PN order in the metric. We find that the PPN parameters of Chern-Simons gravity are identical to those of general relativity, with the exception of the inclusion of a new term that is proportional to the Chern-Simons coupling parameter and the curl of the PPN vector potentials. We also find that the new term is naturally enhanced by the nonlinearity of spacetime and we provide a physical interpretation for it. By mapping this correction to the gravito-electromagnetic framework, we study the corrections that this new term introduces to the acceleration of point particles and the frame-dragging effect in gyroscopic precession. We find that the CS correction to these classical predictions could be used by current and future experiments to place bounds on intrinsic parameters of Chern-Simons gravity and, thus, string theory.

Parametrized post-Newtonian limit of fourth order gravity inspired by scalar-tensor gravity

Based on the dynamical equivalence between higher order gravity and scalar-tensor gravity the parametrized post-Newtonian (PPN) limit of fourth order gravity is discussed. We exploit this analogy developing a fourth order gravity version of the Eddington PPN parameters. As a result, Solar System experiments can be reconciled with higher order gravity, if physical constraints descending from experiments are fulfilled.

Progress in Lunar Laser Ranging Tests of Relativistic Gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the equivalence principle (EP); they also enable several very accurate tests of relativistic gravity. These analyses give an EP test of Delta(MG/MI)EP=(-1.0+/-1.4) x 10(-13). This result yields a strong equivalence principle (SEP) test of Delta(MG/MI)SEP=(-2.0+/-2.0) x 10(-13). Also, the corresponding SEP violation parameter eta is (4.4+/-4.5) x 10(-4), where eta=4beta-gamma-3 and both beta and gamma are post-Newtonian parameters. Using the Cassini gamma, the eta result yields beta-1=(1.2+/-1.1) x 10(-4). The geodetic precession test, expressed as a relative deviation from general relativity, is Kgp=-0.0019+/-0.0064. The search for a time variation in the gravitational constant results in G /G=(4+/-9) x 10(-13) yr(-1); consequently there is no evidence for local (approximately 1 AU) scale expansion of the solar system.

Time transfer and frequency shift to the order1/c4in the field of an axisymmetric rotating body

Within the weak-field, post-Newtonian approximation of the metric theories of gravity, we determine the one-way time transfer up to the order ${1/c}^{4},$ the unperturbed term being of order $1/c,$ and the frequency shift up to the order ${1/c}^{4}.$ We adapt the method of the world function developed by Synge to the Nordvedt-Will parametrized post-Newtonian (PPN) formalism. We get an integral expression for the world function up to the order ${1/c}^{3}$ and we apply this result to the field of an isolated, axisymmetric rotating body. We give a new procedure enabling us to calculate the influence of the mass and spin multipole moments of the body on the time transfer and the frequency shift up to the order ${1/c}^{4}.$ We obtain explicit formulas for the contributions of the mass, of the quadrupole moment and of the intrinsic angular momentum. In the case where the only PPN parameters different from zero are $\ensuremath{\beta}$ and \ensuremath{\gamma}, we deduce from these results the complete expression of the frequency shift up to the order ${1/c}^{4}.$ We briefly discuss the influence of the quadrupole moment and of the rotation of the Earth on the frequency shifts in the ESA's Atomic Clock Ensemble in Space mission.

Relativistic celestial mechanics with PPN parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.