post-Newtonian Parameters Research Articles

Impact of Galaxy Dynamics on Modified Gravity Constraints from Strong Lensing Systems

AbstractGalaxy-galaxy strong lensing systems have been used in literature to test General Relativity by constraining the post-Newtonian parameter (γPPN). Nevertheless, these methods are prone to systematic errors, some of which arise from difficulties in modelling the dynamics of the lens galaxy. In this study, we address the systematic error related to the assumption of a constant anisotropy between the radial and tangential components of the velocity dispersion of stars within the lens galaxy, characterised by the parameter β. We considered two radial models for the anisotropy parameter, the Osipkov-Merritt and Mamon & Lokas, as well three Gaussian priors for constant β. Our analysis showed that the choice of β has a strong impact on the value of γPPN, with radial models leading to lower values of this parameter.

Direct Tests of General Relativity under Screening Effect with Galaxy-scale Strong Lensing Systems

Observations of galaxy-scale strong gravitational lensing (SGL) systems have enabled unique tests of nonlinear departures from general relativity (GR) on the galactic and supergalactic scales. One of the most important cases of such tests are constraints on the gravitational slip between two scalar gravitational potentials. In this paper, we use a newly compiled sample of strong gravitational lenses to test the validity of GR, focusing on the screening effects on the apparent positions of lensed sources relative to the GR predictions. This is the first simultaneous measurement of the post-Newtonian parameter (γ PN) and the screening radius (Λ) without any assumptions about the contents of the universe. Our results suggest that the measured parameterized post-Newtonian is marginally consistent with GR (γ PN = 1) with increasing screening radius (Λ = 10–300 kpc), although the choice of lens models may have a significant influence on the final measurements. Based on a well-defined sample of 5000 simulated strong lenses from the forthcoming LSST, our methodology will provide a strong extragalactic test of GR with an accuracy of 0.5%, assessed up to scales of Λ ∼ 300 kpc. For the current and future observations of available SGL systems, there is no noticeable evidence indicating some specific cutoff scale on kiloparsec-megaparsec scales, beyond which new gravitational degrees of freedom are expressed.

Gravity Assist as a Test of Relativistic Gravity

We consider the gravity assist maneuver, that is, a correction of spacecraft motion at its passing near a planet, as a tool for evaluating the Eddington post-Newtonian parameters $\beta$ and $\gamma$, characterizing vacuum spherically symmetric gravitation fields in metric theories of gravity. We estimate the effect of variation in $\beta$ and $\gamma$ on a particular trajectory of a probe launched from the Earth's orbit and passing closely near Venus, where relativistic corrections slightly change the impact parameter of probe scattering in Venus's gravitational field. It is shown, in particular, that a change of $10^{-4}$ in $\beta$ or $\gamma$ leads to a shift of about 50 km in the probe's aphelion position.

Prospects of strongly lensed fast radio bursts: simultaneous measurement of post-Newtonian parameter and Hubble constant

ABSTRACT Strong gravitational lensing effect is a powerful tool to probe cosmological models and gravity theories. Recently, the time-delay cosmography from strong lensing and the stellar kinematics of the deflector, which encode the Hubble constant and the post-Newtonian parameter via two distance ratios reflecting the lensing mass and dynamical mass, respectively, have been proposed to investigate these two parameters simultaneously. Among strong-lensing systems with different sources, strongly lensed fast radio bursts (FRBs) have been proposed as precision probes of the universe since the time-delay ∼ 10 d between images could be measured extremely precisely because of their short duration of a few milliseconds. In this work, we investigate the ability of strongly lensed FRBs on simultaneously estimating these two parameters via simulations. Take the expected FRB detection rate of upcoming facilities and lensing probability into consideration, it is likely to accumulate 10 lensed FRBs in several years and we find that H0 could be determined to an $\sim 1.5{{\,\rm per\,cent}}$ precision and γPPN could be constrained to an $\sim 8.7{{\,\rm per\,cent}}$ precision simultaneously from them. These simultaneous estimations will be helpful for properly reflecting the possible correlation between these two fundamental parameters.

Post-Newtonian gravity and Gaia-like astrometry

Context. Relativistic models of light propagation adopted for high-precision astrometry are based on the parametrised post-Newtonian formalism, which provides a framework for examining the effects of a hypothetical violation of general relativity on astrometric data. Astrometric observations are strongly affected by the post-Newtonian (PPN) parameter γ describing the strength of gravitational light deflection. Aims. We study both analytically and numerically how a deviation in the PPN parameter γ from unity, which is the value predicted by general relativity, affects the parallax estimations in Gaia-like astrometry. Methods. Changes in the observable quantities produced by a small variation in PPN γ were calculated analytically. We then considered how such variations of the observables are reflected in the parallax estimations, and we performed numerical simulations to check the theoretical predictions. Results. A variation in the PPN γ results in a global shift of parallaxes and we present a formula describing the parallax bias in terms of the satellite barycentric distance, the angle between the spin axis and the direction to the Sun, and the PPN γ uncertainty. Numerical simulations of the astrometric solutions confirm the theoretical result. The up-to-date estimation of PPN γ suggests that a corresponding contribution to the Gaia parallax zero point unlikely exceeds 0.2 μas. The numerical simulations indicate that the parallax shift is strongly dependent on ecliptic latitude. It is argued that this effect is due to an asymmetry in the Gaia scanning law and this conclusion is fully validated by additional simulations with a reversed direction of the precession of the spin axis around the direction to the Sun.

Vainshtein screening in Horndeski theories nonminimally and kinetically coupled to ordinary matter

We study the Vainshtein screening mechanism in Horndeski theories in the presence of a scalar field $\phi$ nonminimally and kinetically coupled to ordinary matter field. A general interacting Lagrangian describing this coupling is characterized by energy transfer $f_1$ and momentum exchange $f_2$. For a spherically symmetric configurations on top of the cosmological background, we investigate the static perturbations in linear and nonlinear regimes with respect to the scalar field perturbation. In the former regime, the parametrized post-Newtonian parameter generally deviates from unity as long as the matter coupling or $G_{4,\phi}$ exists. On the other hand, in the latter regime, we show that the nonlinear self-interaction term of scalar field successfully activates the Vainshtein mechanism even in the presence of the couplings $f_1$ and $f_2$. The gravitational potentials recover the Newtonian behavior deep inside the Vainshtein radius. The bounds on coupling terms not to substantially change the Vainshtein radius are also given.

A test of general relativity with ESA’s JUICE mission

The ESA’s JUICE mission is planned for launch in April 2023. After a 8.3-year interplanetary cruise it will reach the Jovian system in mid 2031. The mission is devoted to the study of Jupiter and three of the Galilean moons (Europa, Callisto and Ganymede). The 3GM (Geodesy and Geophysics of Jupiter and the Galilean Moons) radio-science package onboard the spacecraft comprises a Ka-band Transponder (KaT) that will enable a highly stable two-way coherent Ka/Ka link to study the gravity fields of the three Jovian satellites and their internal structure, and an Ultra Stable Oscillator (USO) to probe the atmosphere of Jupiter and the ionospheres of the three moons. The KaT can be used together with the onboard Deep Space Transponder (DST), enabling a full multi-frequency radio link system capable to suppress the dispersive noise, due to solar plasma and ionospheric effects, at nearly all solar elongation angles. The cruise phase of the mission provides three opportunities to perform classical tests of general relativity by measuring the relativistic time-delay and the frequency shift experienced by radio signals during superior solar conjunctions. A similar experiment, performed by Cassini in 2002, provided the most accurate measurement of the post-Newtonian parameter γ so far, with an accuracy of 2.3×10-5. The MORE experiment onboard the ESA/JAXA BepiColombo mission to Mercury is expected to improve the result obtained by Cassini up to a factor of 10 while orbiting the planet. Less significant improvements are expected in the cruise phase. The advanced radio-tracking system of JUICE and the favorable dynamical environment experienced in the outer solar system make a repetition of the Cassini and BepiColombo cruise experiments quite significant. In this work, we show the results of numerical simulations of JUICE superior conjunction experiments. We have found that 3GM can estimate γ with an accuracy at the level of 4.8×10-7, which represents a constraint on the value of γ 50 times tighter than the one obtained by Cassini and about four times better than the expected result from BepiColombo at the end of the mission.

The orbital evolution and gravitational waves of OJ 287 in the 4th post-Newtonian order

We computed the orbital evolution and the emitted gravitational radiation of the supermassive black hole binary OJ 287. Here we used the initial data provided by the outburst structure of the system. We considered the spin–spin, spin–orbit, and the next-to-next leading order fourth post-Newtonian (4PN) corrections in our analysis. In this way, we could make an accurate examination of unstable orbits (3M < r < 6M) of the secondary black hole. We tested the 4PN terms by analyzing the total and radiated energy, compared the post-Newtonian parameters and the separation of the two black holes for 3PN and 4PN. In conclusion, the 4PN corrections provided a significantly more accurate tool for analyzing unstable orbits than earlier 3PN terms. Furthermore, in this paper, we show the strain of gravitational waves emitted by OJ 287 during its complete orbital evolution including unstable orbits.

Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for F(T) gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.

Post-Newtonian parameters of ghost-free parity-violating gravities

We investigate the slow-motion and weak-field approximation of the general ghost-free parity-violating (PV) theory of gravity in the parametrized post-Newtonian (PPN) framework and derive the perturbative field equations, which are modified by the PV terms of this theory. The complete PPN parameters are obtained by solving the perturbative field equations. We find that all the PPN parameters are exactly the same as those in general relativity, except for an extra parameter κ, which is caused by the new curl-type term in the gravitomagnetic sector of the metric in this theory. We calculate the precession effects of gyroscopes in this theory and constrain the model parameters by the observations of the Gravity Probe B experiment.

Consistent equivalence principle tests with fast radio bursts

ABSTRACT Fast radio bursts (FRBs) are astrophysical transients of still debated origin. So far several hundred events have been detected, mostly at extragalactic distances, and this number is expected to grow significantly over the next years. The radio signals from the burst experience dispersion as they travel through the free electrons along the line-of-sight characterised by the dispersion measure (DM) of the radio pulse. In addition, each photon also experiences a gravitational Shapiro time delay while travelling through the potentials generated by the large-scale structure. If the weak equivalence principle (WEP) holds, the Shapiro delay is the same for photons of all frequencies. In case the WEP is broken, one would expect an additional dispersion to occur which could be either positive or negative for individual sources. Here, we suggest to use angular statistics of the DM fluctuations to put constraints on the WEP parametrized by the post-Newtonian parameter γ. Previous studies suffer from the problem that the gravitational potential responsible for the delay diverges in a cosmological setting, which our approach avoids. We carry out a forecast for a population of FRBs observable within the next years and show that any significant detection of the DM angular power spectrum will place the tightest constraints on the WEP to date, Δγ &amp;lt; 10−15.

Galaxy-scale Test of General Relativity with Strong Gravitational Lensing

Abstract Although general relativity (GR) has been precisely tested at the solar system scale, precise tests at a galactic or cosmological scale are still relatively insufficient. Here, in order to test GR at the galactic scale, we use the newly compiled galaxy-scale strong gravitational lensing (SGL) sample to constrain the parameter γ PPN in the parameterized post-Newtonian (PPN) formalism. We employ the Pantheon sample of Type Ia supernova observations to calibrate the distances in the SGL systems using the Gaussian Process method, which avoids the logical problem caused by assuming a cosmological model within GR to determine the distances in the SGL sample. Furthermore, we consider three typical lens models in this work to investigate the influences of the lens-mass distributions on the fitting results. We find that the choice of lens models has a significant impact on the constraints on the PPN parameter γ PPN. By using a minimum χ 2 comparison and the Bayesian information criterion as evaluation tools to make comparisons for the fitting results of the three lens models, we find that the most reliable lens model gives the result of γ PPN = 1.065 − 0.074 + 0.064 , which is in good agreement with the prediction of γ PPN = 1 by GR. As far as we know, our 6.4% constraint result is the best result so far among recent works using the SGL method.

Direct Estimate of the Post-Newtonian Parameter and Cosmic Curvature from Galaxy-scale Strong Gravitational Lensing

Abstract Einstein’s theory of general relativity (GR) has been precisely tested on solar system scales, but extragalactic tests are still poorly performed. In this work, we use a newly compiled sample of galaxy-scale strong gravitational lenses to test the validity of GR on kiloparsec scales. In order to solve the circularity problem caused by the presumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter γ PPN and the cosmic curvature Ω k by combining observations of strong lensing and Type Ia supernovae. This is the first simultaneous measurement of γ PPN and Ω k without any assumptions about the contents of the universe or the theory of gravity. Our results show that γ PPN = 1.11 − 0.09 + 0.11 and Ω k = 0.48 − 0.71 + 1.09 , indicating a strong degeneracy between the two quantities. The measured γ PPN, which is consistent with the prediction of 1 from GR, provides a precise extragalactic test of GR with a fractional accuracy better than 9.0%. If a prior of the spatial flatness (i.e., Ω k = 0) is adopted, the PPN parameter constraint can be further improved to γ PPN = 1.07 − 0.07 + 0.07 , representing a precision of 6.5%. On the other hand, in the framework of GR (i.e., γ PPN = 1), our results are still marginally compatible with zero curvature ( Ω k = − 0.12 − 0.36 + 0.48 ), supporting no significant deviation from a flat universe.

Is It Possible to See the Breaking Point of General Relativity near the Galactic Center Black Hole? Consideration of Scalaron and Higher-dimensional Gravity

Abstract The Galactic center black hole is a putative laboratory to test general relativity (GR) and constrain its alternatives. f(R) scalaron gravity is an interesting alternative to GR and has tremendous prospects for astrophysics and fundamental physics near the black hole. In this work, we search for breaking points of GR through estimation of pericenter shift of stellar orbits with semimajor axis a = (45–1000) au. The black hole spin is taken as the maximum χ = 0.99, and orbital eccentricity is taken as e = 0.9. We work with theoretical scalaron field amplitude and coupling, predicted by Kalita, and also consider the constraints reported by Hees et al. The scalaron mass is taken in the range (10−22–10−17) eV. It is found that GR suppresses scalaron gravity at all orbital radii for the theoretical values of scalaron field coupling predicted by Kalita. Breaking point arises only for higher scalaron coupling resulting from the Hees et al. observations within a few tens of au to a = 1000 au. We also estimate the pericenter shift with a power-law potential V(r) ∼ 1/r 2 arising in five-dimensional gravity and obtain allowed ranges of the five-dimensional Planck mass through existing bounds on the parameterized post-Newtonian parameters coming from the orbits of S-2, S-38, and S-55. The breaking point for GR arises for a five-dimensional Planck mass of about 104 GeV. Constraint on this parameter, expected from the astrometric capabilities of existing and upcoming large telescopes, is also presented.

On Shapiro time delay in massive scalar-tensor theories

The problem of defenition of the post-Newtonian parameter γ in massive scalar-tensor theories is considered. We demonstrate an equivalent correspondence between the post-Newtonian parameter γ and the parameter appearing in the equation of a null geodesic in massive scalar-tensor theories. We show that massive scalar-tensor theories can be distinguished from general relativity via the Shapiro time delay. All calculations are performed for hybrid metric-Palatini f(R)-gravity for the sake of illustration. The expression for Shapiro time delay in hybrid f(R)-gravity is obtained for the first time.

Light Deflection under the Gravitational Field of Jupiter—Testing General Relativity

Abstract We measured the relative positions between two pairs of compact extragalactic sources (CESs), J1925-2219 and J1923-2104 (C1–C2) and J1925-2219 and J1928-2035 (C1–C3), on 2020 October 23–25 and 2021 February 5 (totaling four epochs), respectively, using the Very Long Baseline Array at 15 GHz. Accounting for the deflection angle dominated by Jupiter, as well as the contributions from the Sun and planets other than Earth, the Moon, and Ganymede (the most massive of the solar system’s moons), our theoretical calculations predict that the dynamical ranges of the relative positions across four epochs in R.A. of the C1–C2 pair and C1–C3 pair are 841.2 and 1127.9 μas, respectively. The formal accuracy in R.A. is about 20 μas, but the error in decl. is poor. The measured standard deviations of the relative positions across the four epochs are 51.0 and 29.7 μas in R.A. for C1–C2 and C1–C3, respectively. These values indicate that the accuracy of the post-Newtonian relativistic parameter, γ, is ∼0.061 for C1–C2 and ∼0.026 for C1–C3. Combining the two CES pairs, the measured value of γ is 0.984 ± 0.037, which is comparable to the latest published results for Jupiter as a gravitational lens, reported by Fomalont &amp; Kopeikin, i.e., 1.01 ± 0.03.

Parametrized post-Newtonian limit of the Nieh-Yan modified teleparallel gravity

The recently proposed Nieh-Yan modified teleparallel gravity is a parity-violating gravity model that modifies the general relativity equivalent teleparallel gravity by a Nieh-Yan term. This model is healthy and simple in form. In this paper, we consider the application of this model to the Solar System and investigate its slow-motion and weak-field approximation in terms of the parametrized post-Newtonian formalism. We find that all the post-Newtonian parameters of the model are the same as those of general relativity, which makes the model compatible with the Solar System experiments.

Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling

We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made nondynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for the parametrized post-Newtonian parameter $\ensuremath{\gamma}$ and the propagation speed of gravitational waves. We also find that there is no modification to asymptotically flat black holes at rest with respect to the preferred frame. Due to a large degree of freedom to choose the time-dependent functions in the theory, the homogeneous and isotropic cosmological dynamics can be made close to or even identical to that of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We investigate the behavior of cosmological perturbations in the long- and short-wavelength limits and show that in both limits the effects of modified gravity appear only through the modification of the background evolution. Finally, it is remarked that in the presence of a Galileon field in the matter sector, the scalar degree of freedom is revived, ruining the essential feature of the theory.

GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.

Comparison of light-time formulations in the post-Newtonian framework for the BepiColombo MORE experiment

The ESA/JAXA BepiColombo mission, launched on 20 October 2018, is currently in cruise toward Mercury. The Mercury Orbiter Radio-science Experiment (MORE), one of the 16 experiments of the mission, will exploit range and range-rate measurements collected during superior solar conjunctions to better constrain the post-Newtonian parameter γ. The MORE radio tracking system is capable of establishing a 5-leg link in X- and Ka-band to obtain 2-way range-rate measurements with an accuracy of 0.01 mm s−1 @ 60 s sampling time and 2-way range measurements at centimeter level after a few seconds of integration time, at almost all solar elongation angles. In this paper, we investigate if the light-time formulation derived by Moyer, implemented in JPL’s orbit determination code MONTE, is still a valid approximation, in light of the recent advancements in radiometric measurement performance. Several formulations of the gravitational time delay, expressed as an expansion in powers of GM/c 2 r, are considered in this work. We quantified the contribution of each term of the light-time expansion for the first superior solar conjunction experiment of BepiColombo. The maximum 2-way error caused by Moyer approximation with respect to a complete second order expansion amounts to 17 mm. This is at the level of accuracy of the novel pseudo-noise (PN) ranging system at 24 Mcps used by MORE. A complete second order expansion is then recommended for present and future superior solar conjunction experiments. The perturbation caused by the planets in the Solar System is considered as well, resulting in significant effects due to the Jupiter, the Earth and the Saturn systems. For these bodies the classical Shapiro time delay is sufficient. The corrections due to the Sun oblateness and angular momentum are negligible. The aforementioned considerations are valid for all superior conjunction experiments involving state-of-the-art radio-tracking measurements.