post-Newtonian Parameters Research Articles

Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

The f(R) gravity can be cast into the form of a scalar–tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general f(R) gravity, using a scalar–tensor representation with the chameleon mechanism, we calculate the parametrized post-Newtonian parameters γ and β, the effective gravitational constant Geff, and the effective cosmological constant Λeff. In addition, for the general f(R) gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific f(R) models (Hu–Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.

Post-Newtonian parameters γ and β of scalar-tensor gravity for a homogeneous gravitating sphere

We calculate the parameters $\gamma$ and $\beta$ in the parametrized post-Newtonian (PPN) formalism for scalar-tensor gravity (STG) with an arbitrary potential, under the assumption that the source matter is given by a non-rotating sphere of constant density, pressure and internal energy. For our calculation we write the STG field equations in a form which is manifestly invariant under conformal transformations of the metric and redefinitions of the scalar field. This easily shows that also the obtained PPN parameters are invariant under such transformations. Our result is consistent with the expectation that STG is a fully conservative theory, i.e., only $\gamma$ and $\beta$ differ from their general relativity values $\gamma = \beta = 1$, which indicates the absence of preferred frame and preferred location effects. We find that the values of the PPN parameters depend on both the radius of the gravitating mass source and the distance between the source and the observer. Most interestingly, we find that also at large distances from the source $\beta$ does not approach $\beta = 1$, but receives corrections due to a modified gravitational self-energy of the source. Finally, we compare our result to a number of measurements of $\gamma$ and $\beta$ in the Solar System. We find that in particular measurements of $\beta$ improve the previously obtained bounds on the theory parameters, due to the aforementioned long-distance corrections.

Weak-field limit of Kaluza\u2013Klein models with spherically symmetric static scalar field: observational constraints

In a multidimensional Kaluza–Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter varOmega of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter gamma . We define under which conditions gamma can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have gamma approx 1 in the solar system, the mass of scalar field should be mu gtrsim 5.05times 10^{-49}g sim 2.83times 10^{-16}eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: varOmega = -,1/2.

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

Here we apply the full Will-Nordtvedt version of the Parameterized Post-Newtonian (PPN) formalism to a class of General Relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant $G$ is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the External Potential Effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales, for any of them the Solar System bounds need to be considered.

An analysis of the geodesy and relativity experiments of BepiColombo

BepiColombo is a ESA-JAXA mission aimed to a comprehensive exploration of Mercury, the innermost planet of the solar system. The Mercury Orbiter Radio science Experiment (MORE) will exploit a state of the art microwave tracking system, including an advanced Ka-band transponder, to determine the gravity field and the rotational state of the planet, and to perform extensive tests of relativistic gravity. In this work we analyze all the aspects of the radio science investigation, which include: (i) the solar conjunction experiment in cruise; (ii) the gravimetry and rotation experiments; (iii) the fundamental physics test. We report on the results of numerical simulations based on the latest mission scenario, with launch in October 2018 and arrival at Mercury in December 2025. We show that the gravity and rotation measurements expected from BepiColombo will allow to better characterize the size of an inner solid core inside the outer liquid core, and the properties of the outer mantle and the crust. We discuss how the current estimate of several parametrized post-Newtonian (PPN) parameters can be improved by MORE through the determination of the heliocentric motion of Mercury and by measuring the propagation time of radio waves. We also assess in a quantitative way the benefits of an extended mission.

Post-Newtonian parameter γ in generalized non-local gravity

We investigate the post-Newtonian parameter $\gamma$ and derive its formalism in generalized non-local (GNL) gravity,which is the modified theory of general relativity (GR) obtainedby adding a term $m^{2n-2}R\Box^{-n}R$ to the Einstein-Hilbert action.Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields $\phi^i$in addition to the metric tensor $g_{\mu\nu}$,the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters $\gamma$, we can compare our expressions and results with thosein Hohmann and Jarv et al. (2016),as well as current observational constraints on the values of $\gamma$ in Will (2006).Hence, we draw restrictions on the nonminimal coupling terms $\bar{F}$ around their background values.

Prospects of Dynamical Determination of General Relativity Parameter β and Solar Quadrupole Moment with Asteroid Radar Astronomy

Abstract We evaluated the prospects of quantifying the parameterized post-Newtonian parameter β and solar quadrupole moment with observations of near-Earth asteroids with large orbital precession rates (9 to 27 arcsec century−1). We considered existing optical and radar astrometry, as well as radar astrometry that can realistically be obtained with the Arecibo planetary radar in the next five years. Our sensitivity calculations relied on a traditional covariance analysis and Monte Carlo simulations. We found that independent estimates of β and can be obtained with precisions of 6 × 10−4 and 3 × 10−8, respectively. Because we assumed rather conservative observational uncertainties, as is the usual practice when reporting radar astrometry, it is likely that the actual precision will be closer to 2 × 10−4 and 10−8, respectively. A purely dynamical determination of solar oblateness with asteroid radar astronomy may therefore rival the helioseismology determination.

A fluid/gravity prescription of the post-Newtonian parameter

The KSS bound for the shear viscosity-to-entropy density ratio is employed in the fluid/gravity correspondence setup, to provide a theoretical bound for the post-Newtonian parameter in the Casadio-Fabbri-Mazzacurati black string solution that matches the observational bound [1]. This derived bound is here shown to vary according to the black string temperature, and, although the post-Newtonian parameter reaches bigger values as the temperature increases for fixed black string masses, it is still into the observational/experimental bound range. The Casadio-Fabbri-Mazzacurati-AdS black brane is shown to converge to the Schwarzschild-AdS black brane, for sufficiently high order expansion of the dual boundary energy-momentum tensor.

Post-Newtonian parameter γ and the deflection of light in ghost-free massive bimetric gravity

We consider the parametrized post-Newtonian (PPN) limit of ghost-free massive bimetric gravity with two mutually non-interacting matter sectors coupled to the two metrics. Making use of a gauge-invariant differential decomposition of the metric perturbations, we solve the field equations up to the linear PPN order for a static, point-like mass source. From the result we derive the PPN parameter $\gamma$ for spherically symmetric systems, which describes the gravitational deflection of light by visible matter. By a comparison to its value measured in the solar system we obtain bounds on the parameters of the theory. We further discuss the deflection of light by dark matter and find an agreement with the observed light deflection by galaxies. We finally speculate about a possible explanation for the observed distribution of dark matter in galactic mergers such as Abell 520 and Abell 3827.

New test of weak equivalence principle using polarized light from astrophysical events

Einstein's weak equivalence principle (WEP) states that any freely falling, uncharged test particle follows the same identical trajectory independent of its internal structure and composition. Since the polarization of a photon is considered to be part of its internal structure, we propose that polarized photons from astrophysical transients, such as gamma-ray bursts (GRBs) and fast radio bursts (FRBs), can be used to constrain the accuracy of the WEP through the Shapiro time delay effect. Assuming that the arrival time delays of photons with different polarizations are mainly attributed to the gravitational potential of the Laniakea supercluster of galaxies, we show that a strict upper limit on the differences of the parametrized post-Newtonian parameter $\gamma$ value for the polarized optical emission of GRB 120308A is $\Delta\gamma<1.2\times10^{-10}$, for the polarized gamma-ray emission of GRB 100826A is $\Delta\gamma<1.2\times10^{-10}$, and for the polarized radio emission of FRB 150807 is $\Delta\gamma<2.2\times10^{-16}$. These are the first direct verifications of the WEP for multiband photons with different polarizations. In particular, the result from FRB 150807 provides the most stringent limit to date on a deviation from the WEP, improving by one order of magnitude the previous best result based on Crab pulsar photons with different energies.

Test of the Weak Equivalence Principle using LIGO observations of GW150914 and Fermi observations of GBM transient 150914

About 0.4 s after the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a transient gravitational-wave (GW) signal GW150914, the Fermi Gamma-ray Burst Monitor (GBM) also found a weak electromagnetic transient (GBM transient 150914). Time and location coincidences favor a possible association between GW150904 and GBM transient 150914. Under this possible association, we adopt Fermi's electromagnetic (EM) localization and derive constraints on possible violations of the Weak Equivalence Principle (WEP) from the observations of two events. Our calculations are based on four comparisons: (1) The first is the comparison of the initial GWs detected at the two LIGO sites. From the different polarizations of these initial GWs, we obtain a limit on any difference in the parametrized post-Newtonian (PPN) parameter Δγ≲10−10. (2) The second is a comparison of GWs and possible EM waves. Using a traditional super-Eddington accretion model for GBM transient 150914, we again obtain an upper limit Δγ≲10−10. Compared with previous results for photons and neutrinos, our limits are five orders of magnitude stronger than those from PeV neutrinos in blazar flares, and seven orders stronger than those from MeV neutrinos in SN1987A. (3) The third is a comparison of GWs with different frequencies in the range [35 Hz, 250 Hz]. (4) The fourth is a comparison of EM waves with different energies in the range [1 keV, 10 MeV]. These last two comparisons lead to an even stronger limit, Δγ≲10−8. Our results highlight the potential of multi-messenger signals exploiting different emission channels to strengthen existing tests of the WEP.

Local tests of gravitation with Gaia observations of Solar System Objects

AbstractIn this proceeding, we show how observations of Solar System Objects with Gaia can be used to test General Relativity and to constrain modified gravitational theories. The high number of Solar System objects observed and the variety of their orbital parameters associated with the impressive astrometric accuracy will allow us to perform local tests of General Relativity. In this communication, we present a preliminary sensitivity study of the Gaia observations on dynamical parameters such as the Sun quadrupolar moment and on various extensions to general relativity such as the parametrized post-Newtonian parameters, the fifth force formalism and a violation of Lorentz symmetry parametrized by the Standard-Model extension framework. We take into account the time sequences and the geometry of the observations that are particular to Gaia for its nominal mission (5 years) and for an extended mission (10 years).

Testing the Einstein's equivalence principle with polarized gamma-ray bursts

Abstract The Einstein's equivalence principle can be tested by using parametrized post-Newtonian parameters, of which the parameter γ has been constrained by comparing the arrival times of photons with different energies. It has been constrained by a variety of astronomical transient events, such as gamma-ray bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most stringent constraint of Δγ ≲ 10−15. In this Letter, we consider the arrival times of lights with different circular polarization. For a linearly polarized light, it is the combination of two circularly polarized lights. If the arrival time difference between the two circularly polarized lights is too large, their combination may lose the linear polarization. We constrain the value of Δγp &amp;lt; 1.6 × 10−27 by the measurement of the polarization of GRB 110721A, which is the most stringent constraint ever achieved.

Cosmic Tsunamis in Modified Gravity: Disruption of Screening Mechanisms from Scalar Waves.

Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of some screening mechanisms, thereby threatening the viability of these modified gravity theories. Specifically, we show that the waves produced in the symmetron model can increase the amplitude of the fifth force and the parametrized post Newtonian parameters by several orders of magnitude.

Test of Weak Equivalence Principle with the Multi-band Timing of the Crab Pulsar

Abstract The Weak Equivalent Principle (WEP) can be tested through the parameterized post-Newtonian parameter γ, representing the space curvature produced by unit rest mass. The parameter γ in turn has been constrained by comparing the arrival times of photons originating in distant transient events, such as gamma-ray bursts, fast radio bursts, and giant pulses of pulsars. Those measurements normally correspond to an individual burst event with very limited energy bands and signal-to-noise ratios (S/Ns). In this paper, the discrepancy in the pulse arrival times of the Crab Pulsar between different energy bands is obtained by the phase difference between corresponding pulse profiles. This allows us to compare the pulse arrival times at the largest energy band differences, between radio and optical, radio and X-ray, and radio and gamma-ray respectively. Because the pulse profiles are generated by phase-folding thousands of individual pulses, the time discrepancies between two energy bands are actually measured from thousands of events at each energy band, which corresponds to a much higher S/N. The upper limit of the γ discrepancy set by such an extensively observed and well-modeled source is as follows: at the energy difference of , at the energy difference of , at , and at . This actually measures the arrival times of freely falling photons in the gravitational field of the Milky Way with the largest amount of events and with data of the highest S/N, which tests WEP at energy band differences that have never been reached before.

The determination of the post-Newtonian parameter γ during the cruise phase of BepiColombo

The post-Newtonian parameter γ, unity in general relativity, controls the delay and the deflection of photons induced by the space-time curvature produced by any mass. A precise determination of this parameter can be attained by exploiting the Shapiro time delay and the corresponding Doppler shift affecting the propagation of radio signals between a ground antenna and a spacecraft near a superior solar conjunction. In its cruise phase to Mercury (from October 2018 to December 2025), the spacecraft BepiColombo will experience eleven superior solar conjunctions, thus offering an excellent opportunity to test general relativity. The experiment will benefit from very accurate range and Doppler measurements, enabled by a multi-frequency radio link in X and Ka bands (8 and 34 GHz) and a high rate (24 Mcps) pseudo-noise ranging code. The multi-frequency link configuration allows the suppression of the plasma noise due to the solar corona. In this paper, we report the results of a comprehensive analysis based on the latest spacecraft trajectory and numerical simulations. The ultimate accuracies will be determined by operational constraints, number of exploitable conjunctions, and dynamical noise acting on the spacecraft. We find that γ can be determined up to with just one conjunction in July 2022, thus improving by a factor of 4 the result obtained by the Cassini mission in 2002. This accuracy can be further increased by selecting a limited number of favourable superior solar conjunctions, down to when all of them are combined.

Dilatonic dyon-like black hole solutions in the model with two Abelian gauge fields

Dilatonic black hole dyon-like solutions in the gravitational 4d model with a scalar field, two 2-forms, two dilatonic coupling constants lambda _i ne 0, i =1,2, obeying lambda _1 ne - lambda _2 and the sign parameter varepsilon = pm 1 for scalar field kinetic term are considered. Here varepsilon = - 1 corresponds to a ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when lambda ^2_i ne 1/2 for varepsilon = - 1. Some physical parameters of the solutions are obtained: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters beta and gamma . The PPN parameters do not depend on the couplings lambda _i and varepsilon . A set of bounds on the gravitational mass and scalar charge are found by using a certain conjecture on the parameters of solutions, when 1 +2 lambda _i^2 varepsilon > 0, i =1,2.

Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term

We study the parameterized post-Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in Bahamonde and Wright (Phys Rev D 92:084034 arXiv:1508.06580v4 [gr-qc], 2015). We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post-Newtonian parameters. These parameters for different situations are obtained and discussed.

Parameterized post-Newtonian cosmology

Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

Abstract The perihelion of Mercury’s orbit precesses due to perturbations from other solar system bodies, solar quadrupole moment (J 2), and relativistic gravitational effects that are proportional to linear combinations of the parametrized post-Newtonian parameters β and γ. The orbits and masses of the solar system bodies are quite well known, and thus the uncertainty in recovering the precession rate of Mercury’s perihelion is dominated by the uncertainties in the parameters J 2, β, and γ. Separating the effects due to these parameters is challenging since the secular precession rate has a linear dependence on each parameter. Here we use an analysis of radiometric range measurements to the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft in orbit about Mercury to estimate the precession of Mercury’s perihelion. We show that the MESSENGER ranging data allow us to measure not only the secular precession rate of Mercury’s perihelion with substantially improved accuracy, but also the periodic perturbation in the argument of perihelion sensitive to β and γ. When combined with the γ estimate from a Shapiro delay experiment from the Cassini mission, we can decouple the effects due to β and J 2 and estimate both parameters, yielding and J 2 = (2.25 ± 0.09) × 10−7. We also estimate the total precession rate of Mercury’s perihelion as 575.3100 ± 0.0015″/century and provide estimated contributions and uncertainties due to various perturbing effects.