Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here, we show current results for relativistic parameters like a possible temporal variation of the gravitational constant G˙/G0=(−5.0±9.6)×10−15yr−1, the equivalence principle with Δmg/miEM=(−2.1±2.4)×10−14, and the PPN parameters β−1=(6.2±7.2)×10−5 and γ−1=(1.7±1.6)×10−4. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein’s theory is found and the results set improved limits for the different effects.

Relativistic Effects in Orbital Motion of the S-Stars at the Galactic Center

The Galactic Center star cluster, known as S-stars, is a perfect source of relativistic phenomena observations. The stars are located in the strong field of relativistic compact object Sgr A* and are moving with very high velocities at pericenters of their orbits. In this work we consider motion of several S-stars by using the Parameterized Post-Newtonian (PPN) formalism of General Relativity (GR) and Post-Newtonian (PN) equations of motion of the Feynman’s quantum-field gravity theory, where the positive energy density of the gravity field can be measured via the relativistic pericenter shift. The PPN parameters β and γ are constrained using the S-stars data. The positive value of the Tg00 component of the gravity energy–momentum tensor is confirmed for condition of S-stars motion.

Solar system tests of a new class of f(z) theory

Recently, a new kind of [Formula: see text] theory is proposed to provide a different perspective for the development of reliable alternative models of gravity in which the [Formula: see text] Lagrangian terms are reformulated as polynomial parametrizations [Formula: see text]. In the previous study, the parameters in the [Formula: see text] models have been constrained by using cosmological data. In this paper, these models will be tested by the observations in the solar system. After solving the Ricci scalar as a function of the redshift, one could obtain [Formula: see text] that could be used to calculate the standard Parametrized-Post-Newtonian (PPN) parameters. First, we fit the parametric models with the latest cosmological observational data. Then, the tests are performed by solar system observations. And last we combine the constraints of solar system and cosmology together and reconstruct the [Formula: see text] actions of the [Formula: see text] parametric models.

PPN parameters in gravitational theory with nonminimally derivative coupling

The nonminimal coupling of the kinetic term to Einstein’s tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parametrized post-Newtonian (PPN) parameters for the scalar–tensor theory of gravity with nonminimally derivative coupling. We find that under experimental constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein’s general relativity in the order of [Formula: see text], and the effect of the nonminimal coupling is negligible if we take the scalar field as dynamical dark energy. With the assumed conditions that the background scalar field is spatially homogeneous and evolves only on cosmological timescales and the contribution to stress–energy in the solar system from the background scalar field is subdominant, the scalar field is required to be massless.

The second post-Newtonian light propagation and its astrometric measurement in the solar system

The relativistic theories of light propagation are generalized by introducing two new parameters ς and η in the second post-Newtonian (2PN) order, in addition to the parametrized post-Newtonian (PPN) parameters γ and β. This new 2PN parametrized (2PPN) formalism includes the nonstationary gravitational fields and the influences of all kinds of relativistic effects. The multipolar components of gravitating bodies are taken into account as well at the first post-Newtonian (1PN) order. The equations of motion and their solutions of this 2PPN light propagation problem are obtained. Started from the definition of a measurable quantity, a gauge-invariant angle between the directions of two incoming photons for a differential measurement in astrometric observation is discussed and its formula is derived. For a precision level of a few microarcsecond (μas) for space astrometry missions in the near future, we further consider a model of angular measurement, the Laser Astrometric Test of Relativity (LATOR)-like missions. In this case, all terms with aimed at the accuracy of ~1μas are estimated.

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.

New Constraints on Preferred Frame Effects from Binary Pulsars

Preferred 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.