PPN Parameters Research Articles

Constraining primordial black hole masses through f(R) gravity scalarons in Big Bang Nucleosynthesis

Big Bang Nucleosynthesis (BBN) is a strong probe for constraining new physics including gravitation. f(R) gravity theory is an interesting alternative to general relativity which introduces additional degrees of freedom known as scalarons. In this work we demonstrate the existence of black hole solutions in f(R) gravity and develop a relation between scalaron mass and black hole mass. We have used observed bound on the freezeout temperature to constrain scalaron mass range by modifying the cosmic expansion rate at the BBN epoch. The mass range of primordial black holes (PBHs) which are astrophysical dark matter candidates is deduced. The range of scalaron mass which does not spoil the BBN era is found to be 10-16–104 eV for both relativistic and non-relativistic scalarons. The window 10-16–10-14 eV of scalaron mass obtained from solar system constraint on PPN parameter is compatible with the BBN bound derived in this work. The PBH mass range is obtained as 106–10-14 M ⊙. Scalarons constrained by BBN are also eligible to accommodate axion like dark matter particles. The problem of ultra-light PBHs (M ≤ 10-24 M ⊙) not constrained by the present study of BBN is still open. Estimation of deuterium (D) fraction and relative D+3He abundance in the f(R) gravity scenario shows that the BBN history mimics that of general relativity. While the PBH mass range is eligible for non-baryonic dark matter, the BBN bounded scalarons provide with an independent strong field test of f(R) gravity. The PBH mass range obtained in the study is discussed in relation to future astronomical measurements.

Weak field and slow motion limits in energy–momentum powered gravity

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy–momentum powered gravity (EMPG), viz., the energy–momentum squared gravity (EMSG) of the form f(TμνTμν)=α(TμνTμν)η with α and η being constants. We have shown that EMPG with η≥0 and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, Mast, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass Meff(α,η,M)=M+Mempg(α,η,M), M being the actual physical mass and Mempg being the modification due to EMPG. Accordingly, while in GR we simply have the relation Mast=M, in EMPG we have Mast=M+Mempg. Within the framework of EMPG, if there is information about the values of {α,η} pair or M from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only Mast alone from astronomical observations, but M and Mempg separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by |peff/ρeff|≪1 (where peff=p+pempg and ρeff=ρ+ρempg), whereas this condition leads to |p/ρ|≪1 in GR.

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

The Hermean average perihelion rate ω˙2PN, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from −18 to −4 microarcseconds per century μascty−1, depending on the true anomaly at epoch f0. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate ω˙exp recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is σω˙exp≃8μascty−1, corresponding to a relative accuracy of 2×10−7 for the combination 2+2γ−β/3 of the PPN parameters β and γ scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a ≃10−7 accuracy level in constraining β and γ in an extended mission, despite ≃10−6 seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well.

On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid

We consider a family of four-dimensional black hole solutions from Dehnen et al. (Grav Cosmol 9:153 arXiv:gr-qc/0211049, 2003) governed by natural number q= 1, 2, 3 , dots , which appear in the model with anisotropic fluid and the equations of state: p_r = -rho (2q-1)^{-1}, p_t = - p_r, where p_r and p_t are pressures in radial and transverse directions, respectively, and rho > 0 is the density. These equations of state obey weak, strong and dominant energy conditions. For q = 1 the metric of the solution coincides with that of the Reissner–Nordström one. The global structure of solutions is outlined, giving rise to Carter–Penrose diagram of Reissner–Nordström or Schwarzschild types for odd q = 2k + 1 or even q = 2k, respectively. Certain physical parameters corresponding to BH solutions (gravitational mass, PPN parameters, Hawking temperature and entropy) are calculated. We obtain and analyse the quasinormal modes for a test massless scalar field in the eikonal approximation. For limiting case q = + infty , they coincide with the well-known results for the Schwarzschild solution. We show that the Hod conjecture which connect the Hawking temperature and the damping rate is obeyed for all q ge 2 and all (allowed) values of 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.

Axion homeopathy: screening dilaton interactions

Cosmologically active Brans-Dicke (or dilaton) scalar fields are generically ruled out by solar system tests of gravity unless their couplings to ordinary matter are much suppressed relative to gravitational strength, and this is a major hindrance when building realistic models of light dilatons coupled to matter. We propose a new mechanism for evading such bounds if matter also couples to a light axion, that exploits nonlinear target-space curvature interactions to qualitatively change how the fields respond to a gravitating source. We find that dilaton-matter couplings that would be excluded in the absence of an axion can become acceptable given an additional small axion-matter coupling, and this is possible because the axion-dilaton interactions end up converting the would-be dilaton profile into an axion profile. The trajectories of matter test bodies are then controlled by the much weaker axion-matter couplings and can easily be small enough to escape detection. We call this mechanism Axion Homeopathy because the evasion of the dilaton-coupling bounds persists for extremely small axion couplings provided only that they are nonzero. We explore the mechanism using axio-dilaton equations that are SL(2,ℝ) invariant (as often appear in string compactifications), since for these the general solutions exterior to a spherically symmetric source can be found analytically. We use this solution to compute the relevant PPN parameters, γ PPN and β PPN, and verify that their deviation from unity can be much smaller than it would have been in the absence of axion-matter couplings and can therefore evade the experimental bounds.

Cassini and extra force constraints to nonminimally coupled gravity with a screening mechanism

We consider a nonminimally coupled curvature-matter gravity theory at the Solar System scale. Both a fifth force of Yukawa type and a further non-Newtonian extra force that arises from the nonminimal coupling are present in the solar interior and in the solar atmosphere up to interplanetary space. The extra force depends on the spatial gradient of space-time curvature R. The conditions under which the effects of such forces can be screened by the chameleon mechanism and be made consistent with Cassini measurement of PPN parameter $\gamma$ are examined. This consistency analysis requires a specific study of Sun's dynamical contribution to the arising forces at all its layers.

Weak-field regime of the generalized hybrid metric-Palatini gravity

In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two scalar degrees of freedom, and perform a conformal transformation to the Einstein frame. Linear perturbations of the metric in a Minkowskian background are then studied for the metric and both scalar fields. The effective Newton constant and the PPN parameter $\ensuremath{\gamma}$ of the theory are extracted after transforming back to the (original) Jordan frame. Two particular cases where the general method ceases to be applicable are approached separately. A comparison of these results with observational constraints is then used to impose bounds on the masses and coupling constants of the scalar fields.

Vainshtein mechanism in Generalised Massive Gravity

We present a non-linear analysis of perturbations around cosmological solutions in Generalised Massive gravity. This Lorentz invariant theory is an extension of de Rham, Gabadadze, Tolley massive gravity that propagates 5 degrees of freedom while allowing stable open FLRW cosmologies.For a minimal model that supports a self-accelerating background, we study the dynamics of non-linear perturbations. We find that the equation for the scalar graviton is distinct from the analogues in Horndeski and DHOST theories. We numerically solve the equation to find a new type of nonlinear solution for the scalar mode, and confirm the presence of a Vainshtein screening mechanism. We show that the PPN parameter approaches its GR value at solar system scales and satisfies the current bounds.

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.

Model of a solar system in the conservative geometry

Pandres has shown that an enlargement of the covariance group to the group of conservative transformations leads to a richer geometry than that of general relativity. Using orthonormal tetrads as field variables, the fundamental geometric object is the curvature vector denoted by \(C_\mu \). From an appropriate scalar Lagrangian field equations for both free-field and the field with sources have been developed. We first review models which use a free-field solution to model the Solar System and why these results are unacceptable. We also show that the standard Schwarzschild metric is also unacceptable in our theory. Finally we show that there are solutions which involve sources which agree with general relativity PPN parameters and thus approximate the Schwarzschild solution. The main difference is that the Einstein tensor is not identically zero but includes small values for the density, radial pressure and tangential pressure. Higher precision experiments should be able to determine the validity of these models. These results add further confirmation that the theory developed by Pandres is the fundamental theory of physics.

Reconciling spontaneous scalarization with cosmology

We discuss the Damour--Esposito-Far\`ese model of gravity, which predicts the spontaneous scalarization of neutron stars in a certain range of parameter space. In the cosmological setup, the scalar field responsible for scalarization is subject to a tachyonic instability during inflation and the matter domination stage, resulting in a large value of the field today. This value feeds into the PPN parameters, which turn out to be in gross conflict with the Solar system measurements. We modify the original Damour--Esposito-Far\`ese model by coupling the scalar to the inflaton field. This coupling acts as an effective mass for the scalar during inflation. For generic couplings that are not extremely small, the scalar (including its perturbations) relaxes to zero with an exponential accuracy by the beginning of the hot stage. While the scalar exhibits growth during the subsequent cosmological stages, the resulting present value remains very small---in a comfortable agreement with the Solar system tests.

Post-Newtonian Limit of Hybrid Metric-Palatini f(R)-Gravity

Using the latest most accurate values of post-Newtonian parameters γ and β obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar–tensor representation. We show that the presence of a light scalar field in this theory does not contradict the experimental data based not only on the γ parameter (as was shown earlier), but also on all other PPN parameters. The application of parameterized post-Newtonian formalism to gravitational theories with massive fields is also discussed.

Dyon-Like Black Hole Solutions in the Model with Two Abelian Gauge Fields

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter e = ±1 before the scalar field kinetic term. Here e = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $$\lambda_i^2 \neq 1/2$$ for e = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented.

Evolution of INPOP planetary ephemerides and Bepi-Colombo simulations

AbstractWe give here a detailed description of the latest INPOP planetary ephemerides INPOP20a. We test the sensitivity of the Sun oblateness determination obtained with INPOP to different models for the Sun core rotation. We also present new evaluations of possible GRT violations with the PPN parameters β, γ and . With a new method for selecting acceptable alternative ephemerides we provide conservative limits of about 7.16 × 10-5 and 7.49 × 10-5 for β-1 and γ-1 respectively using the present day planetary data samples. We also present simulations of Bepi-Colombo range tracking data and their impact on planetary ephemeris construction. We show that the use of future BC range observations should improve these estimates, in particular γ. Finally, interesting perspectives for the detection of the Sun core rotation seem to be reachable thanks to the BC mission and its accurate range measurements in the GRT frame.

ПОСТНЬЮТОНОВСКИЙ ПРЕДЕЛ ГИБРИДНОЙF (R)-ГРАВИТАЦИИ

Using the latest most accurate values of post-Newtonian parameters $\gamma$ and $\beta$ obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar-tensor representation. We show that the presence of a light scalar field in this theory does not contradict the experimental data based not only on the $ \gamma $ parameter (as was shown earlier), but also on all other PPN parameters. The application of parameterized post-Newtonian formalism to gravitational theories with massive fields is also discussed.

Cosmic transients, Einstein’s Equivalence Principle and dark matter halos

Cosmic transients, such as gamma-ray bursts and fast radio bursts, have been used to constrain the Einstein's Equivalence Principle (EEP) through the parametrized-post-Newtonian (PPN) formalism. In this approach, the time delay of photons with different energies from these cosmic transients are used to obtain upper bounds on the difference of the PPN $\gamma$ parameter. In this work we assume that an important contribution to the time delay is due to the dark matter halo of the Milky Way and consider the dark matter mass distribution given by the Navarro--Frenk--White profile. We obtain the upper limit on the difference of the PPN parameter $\gamma$ for the polarized gamma-ray emission of GRB 110721A, $\Delta \gamma < 1.06 \times 10^{-28}$, the most stringent limit to date on the EEP. In addition, we show that a very similar upper bound is obtained if, instead of having a dark matter component, a visible matter density profile and a non-minimal gravitational coupling between curvature and matter are present.

Relativistic tests with lunar laser ranging

This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein’s theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein’s theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein’s theory are detected. A relative temporal variation of the gravitational constant is estimated as , the test of the equivalence principle gives and the Nordtvedt parameter , the PPN-parameters β and γ are determined as and and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of , β and γ, the initial value of the core rotation vector is constrained to a reasonable model value for the estimation of and geodetic precession. A constrained z-component of the initial lunar velocity is used for the estimation of the geodetic precession.

Gravitational focusing of imperfect dark matter

Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario, we consider a particular modification of standard gravity, which manifests as an imperfect low pressure fluid. While practically indistinguishable from a collection of non-relativistic weakly interacting particles on cosmological scales, it leaves drastically different signatures in the Solar system. The main effect stems from gravitational focusing of the flow of Imperfect Dark Matter passing near the Sun. This entails strong amplification of Imperfect Dark Matter energy density compared to its average value in the surrounding halo. The enhancement is many orders of magnitude larger than in the case of Cold Dark Matter, provoking deviations of the metric in the second order in the Newtonian potential. Effects of gravitational focusing are prominent enough to substantially affect the planetary dynamics. Using the existing bound on the PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique constant of the model.

TEST OF PARAMETRIZED POST-NEWTONIAN GRAVITY WITH GALAXY-SCALE STRONG LENSING SYSTEMS

ABSTRACT Based on a mass-selected sample of galaxy-scale strong gravitational lenses from the SLACS, BELLS, LSD, and SL2S surveys and using a well-motivated fiducial set of lens-galaxy parameters, we tested the weak-field metric on kiloparsec scales and found a constraint on the post-Newtonian parameter under the assumption of a flat ΛCDM universe with parameters taken from Planck observations. General relativity (GR) predicts exactly γ = 1. Uncertainties concerning the total mass density profile, anisotropy of the velocity dispersion, and the shape of the light profile combine to systematic uncertainties of ∼25%. By applying a cosmological model-independent method to the simulated future LSST data, we found a significant degeneracy between the PPN γ parameter and the spatial curvature of the universe. Setting a prior on the cosmic curvature parameter −0.007 &lt; Ω k &lt; 0.006, we obtained the constraint on the PPN parameter that . We conclude that strong lensing systems with measured stellar velocity dispersions may serve as another important probe to investigate validity of the GR, if the mass-dynamical structure of the lensing galaxies is accurately constrained in future lens surveys.