Solar System Experiments Research Articles

Constraining the attractive fifth force in the general free scalar–tensor gravity with solar system experiments

In this paper, we focus on the general free scalar–tensor gravity with three free coupling functions, which in the near-field region looks like general relativity (GR) plus a fifth force of Yukawa-type induced by the scalar field. We show that the fifth force is always attractive in the theory. We investigate the effects of the attractive fifth force and calculate in detail the fifth force-induced orbital precession rate δω/ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\omega /\\omega $$\\end{document} and the parameterized post-Newtonian parameters γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}, all of which depend on the fifth force parameters and the interaction distance. It turns out that, due to the attractive fifth force, δω/ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\omega /\\omega $$\\end{document} is always greater than zero, γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} is always less than one, β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} is greater than one at large distances, and additionally this class of theories is ruled out as an alternative theory to dark matter. We place stringent constraints on the fifth force parameters by combining the lunar laser ranging (LLR), Cassini, and Mercury precession experiments, and derive the upper bounds on the strength ratio of the fifth force to gravitational force at different scales from the LLR observation. We find that the Mercury constraint is not competitive with the LLR and Cassini constraints and the LLR observation imposes much more stringent bounds on the strength ratio on large scales than on small scales. Our results show that this theory is sufficiently close to GR for a small enough fifth force strength and can reduce to GR with a minimally coupled scalar field in the absence of fifth force.

Observational tests of asymptotically flat R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} spacetimes

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.

Multi-scalar theories of gravity with direct matter couplings and their parametrized post-Newtonian parameters

We study theories of gravity including, in addition to the metric, several scalar fields in the gravitational sector. The particularity of this work is that we allow for direct couplings between these gravitating scalars and the matter sector, which can generally be different for the source and the probe of gravity, in addition to the universal interactions generated by the Jordan frame metric. The weak gravity regime of this theory, which would describe solar-system experiments, is studied using the parametrized post-Newtonian (PPN) formalism. We derive the expression of the ten parameters of this formalism. Among them, ζ 3 and ζ 4 are modified with respect to their values in the theories without direct couplings. This fact holds even after eliminating the direct couplings between the gravitating scalars and the energy density of the source, by redefinition of the Jordan frame. All other PPN parameters are insensitive to the direct couplings once in the correctly identified Jordan frame. When direct couplings are different for the source and the probe of gravity, they make non-relativistic probes deviate from the geodesics of the PPN metric in this frame, already at Newtonian order. Such couplings would thus be directlydetectable and would have been excluded by experiments.This shows that, contrary to the claims in the recent literature, it is impossible to screen the presence of gravitating scalars relying only on a curved target space and direct couplings to matter.

Solving nonlinear Klein-Gordon equations on unbounded domains via the finite element method

A large class of scalar-tensor theories of gravity exhibit a screening mechanism that dynamically suppresses fifth forces in the Solar system and local laboratory experiments. Technically, at the scalar field equation level, this usually translates into nonlinearities which strongly limit the scope of analytical approaches. This article presents $femtoscope$ $-$ a Python numerical tool based on the Finite Element Method (FEM) and Newton method for solving Klein-Gordon-like equations that arise in particular in the symmetron or chameleon models. Regarding the latter, the scalar field behavior is generally only known infinitely far away from the its sources. We thus investigate existing and new FEM-based techniques for dealing with asymptotic boundary conditions on finite-memory computers, whose convergence are assessed. Finally, $femtoscope$ is showcased with a study of the chameleon fifth force in Earth orbit.

I-Love-Q relations in Hořava-Lifshitz gravity

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars.

Solar system constraints of a polymer black hole in loop quantum gravity

A new polymer black hole solution in loop quantum gravity was proposed recently. The difference between the polymer black hole and Schwarzschild black hole is captured by a quantum parameter $A$. In order to get the constraints on parameter $A$, we consider the observational constraints imposed on $A$ by using the Solar System experiments and calculate the deflection of light, Shapiro time delay, perihelion precession and obtain the effects associated with parameter $A$. Moreover, the parameterized post-Newtonian approach of this loop quantum gravity black hole was also carried out. It turns out the tightest constraint on $A$ can be improved to $0<A<4.0\times10^{-6}$.

Solar system tests for massive conformal gravity

We find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity and test it with some solar system experiments. The result is that the theory agrees with the general relativistic observations in the solar system for a determined lower bound on the graviton mass.

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.

Neutron Stars in the Symmetron Model

Screening mechanisms are often deployed by dark energy models to conceal the effects of their new degrees of freedom from the scrutiny of terrestrial and solar system experiments. However, the extreme properties of nuclear matter may lead to a partial failure of screening mechanisms inside the most massive neutron stars observed in nature, opening up the possibility of probing these theories with neutron star observations. In this work, we explore equilibrium and stability properties of neutron stars in two variants of the symmetron model. We show that around sufficiently compact neutron stars, the symmetron is amplified with respect to its background (cosmological) value by several orders of magnitude, and that the properties of such unscreened stars are sensitive to corrections to the leading linear coupling between the symmetron and matter.

Erratum: Neutron star sensitivities in Hořava gravity after GW170817 [Phys. Rev. D 100 , 084053 (2019)

Hořava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters α, β and λ. The first two of these parameters are tightly bound by Solar System and gravitational-wave propagation experiments, but λ remains relatively unconstrained (0≤λ≲0.01–0.1). We restrict here to the parameter-space region defined by α=β=0 (with λ kept generic), which in a previous paper we showed to be the only one where black hole solutions are nonpathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star “sensitivities,” which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for α=β=0 and generic λ≠0. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational-wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain λ.

Relation between general relativity and a class of Hořava gravity theories

Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Ho\v{r}ava, but are increasingly constrained in the infrared. At low energies, Ho\v{r}ava gravity is characterized by three dimensionless couplings, $\alpha$, $\beta$ and $\lambda$, which vanish in the general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings ($\alpha$ and $\beta$) to tiny values, but the third remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). Moreover, demanding that (slowly moving) black-hole solutions are regular away from the central singularity requires $\alpha$ and $\beta$ to vanish {\it exactly}. Although a canonical constraint analysis shows that the class of khronometric theories resulting from these constraints ($\alpha=\beta=0$ and $\lambda\neq0$) cannot be equivalent to General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary pulsars and gravitational-wave generation show perfect agreement with General Relativity. Here, we analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave {\it exactly} as in General Relativity, as far as {\it observational} predictions are concerned. Nevertheless, we find that spherical collapse leads to the formation of a regular {\it universal} horizon, i.e. a causal boundary for signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons. Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2 graviton of General Relativity remains strongly coupled at low energies, even on curved backgrounds. These puzzling results suggest that any further bounds on Ho\v{r}ava gravity will probably come from cosmology.

Observational tests of the generalized uncertainty principle: Shapiro time delay, gravitational redshift, and geodetic precession

This paper is based on the study of the paper of Scardigli and Casadio (2015) [56] where the authors computed the light deflection and perihelion precession for the Generalized Uncertainty Principle (GUP) modified Schwarzschild metric. In the present work, we computed the gravitational tests such as Shapiro time delay, gravitational redshift, and geodetic precession for the GUP modified Schwarzschild metric. Using the results of Solar system experiments and observations, we obtain upper bounds for the GUP parameter β. Finally, we compare our bounds with other bounds in the literature.

A planet's gravity assist as a powerful amplifier of small physical effects in the Solar system

A planetary model simulating the Sun, Venus, and Earth is constructed with the possibility of “Venus” to render a gravity assist to a ballistic space probe sent from the Earth's orbit. Thorough analytical and numerical analysis shows that a shift of the probe's impact parameter (IP) entails a noticeable deflection of the probe at the final point back on the Earth's orbit. For a relatively short IP, the “Venus-GA” acts as a powerful amplifier (up to 105 times), making it possible to detect changes in the probe's IP that are caused by different physical reasons. This finding prompted Solar system experiments to measure very small physical effects, e.g., to check the actuality of gravity theories.

Observational tests of the self-dual spacetime in loop quantum gravity

The self-dual spacetime was derived from the mini-superspace approach, based on the polymerization quantization procedure in loop quantum gravity (LQG). Its deviation from the Schwarzschild spacetime is characterized by the polymeric function $P$, purely due to the geometric quantum effects from LQG. In this paper, we consider the observational constraints imposed on $P$ by using the solar system experiments and observations. For this purpose, we calculate in detail the effects of $P$ on astronomical observations conducted in the Solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, and geodetic precession. The observational constraints are derived by confronting the theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the measurement of the gravitational time delay by the Cassini mission, which yields $0<P<5.5\times 10^{-6}$. In addition, we also discuss the potential constraint that can be obtained in the near future by the joint European-Japanese BepiColombo project and show that it could significantly improve the current constraints.

PPN rotation curves in static distributions with spherical symmetry

From a parametrized post-Newtonian (PPN) perspective, we address the question of whether or not the new degrees of freedom represented by the PPN potentials can lead to significant modifications in the dynamics of galaxies in the direction of rendering dark matter obsolete. Here, we focus on the study of rotation curves associated with spherically symmetric configurations. The values for the post-Newtonian parameters, which help us to classify the different metric theories of gravity, are tightly constrained, mainly by Solar System experiments. Such restrictions render the modifications of gravitational effects, with respect to general relativity (GR), to be insignificant, making attempts to find alternative metrical theories rather fruitless. However, in recent years, metric theories characterized by screening mechanisms have become popular, due to the fact that they lead to the possibility of modifications in larger scales than the Solar System while retaining the success of GR on it, allowing for violations of the constraints of the post-Newtonian parameters. In such a context, we consider here two kinds of solutions for field equations: (i) Vacuum solutions (i.e., when no matter fields are present) and (ii) fields in the presence of a polytropic distribution of matter. For case (i), we find that the post-Newtonian corrections do not lead to modifications significant enough to be considered an alternative to the dark matter hypothesis. In case (ii), we find that for a wide range of values for the PPN parameters $\ensuremath{\gamma}$, $\ensuremath{\beta}\ensuremath{\le}1$, $\ensuremath{\xi}\ensuremath{\ge}0$, ${\ensuremath{\alpha}}_{3}$, ${\ensuremath{\zeta}}_{1}$, and ${\ensuremath{\zeta}}_{2}$, the need for dark matter is unavoidable in order to find flat rotation curves. It is only for theories in which ${\ensuremath{\zeta}}_{3}g0$, or $\ensuremath{\beta}g1$, or $\ensuremath{\xi}l0$ that some resemblance of flat rotation curves is found. But the latter two require some direct fine-tuning of the screening radius ${r}_{c}$, while ${\ensuremath{\zeta}}_{3}g0$ implies the most sound modifications. The latter suggests, at least for the models considered, that these are the only theories (consistent with the usual PPN approach) capable of replacing dark matter as a possible explanation for the dynamics of galaxies.

Solar system tests in modified teleparallel gravity

In this paper, we study different Solar System tests in a modified Teleparallel gravity theory based on an arbitrary function f(T,B) which depends on the scalar torsion T and the boundary term B. To do this, we first find new perturbed spherically symmetric solutions around Schwarzschild for different power-law forms of the arbitrary Lagrangian. Then, for each model we calculated the photon sphere, perihelion shift, deflection of light, Cassini experiment, Shapiro delay and the gravitational redshift. Finally, we confront these computations with different known experiments from these Solar System tests to put different bounds on the mentioned models. We then conclude that f(T,B) is compatible with these Solar System experiments with a wide range of parameters which are relevant for cosmology.

Neutron star sensitivities in Hořava gravity after GW170817

Ho\v{r}ava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters $\alpha$, $\beta$ and $\lambda$. The first two of these parameters are tightly bound by solar system and gravitational wave propagation experiments, but $\lambda$ remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). We restrict here to the parameter space region defined by $\alpha=\beta=0$ (with $\lambda$ kept generic), which in a previous paper we showed to be the only one where black hole solutions are non-pathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star 'sensitivities', which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for $\alpha=\beta=0$ and generic $\lambda\neq0$. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain $\lambda$.

Selected topics in scalar–tensor theories and beyond

Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time, these escaped detection until 2012 when the Higgs boson was observed for the first time. Since then, alternatives to the general theory of relativity like the Brans–Dicke (BD) theory, scalar–tensor theories of gravity and their higher derivative generalizations — collectively known as Horndeski theories — have acquired renewed interest. In the present review, we discuss several selected topics regarding these theories, mainly from the theoretical perspective but with due mention of the observational aspect. Among the topics covered in this review, we pay special attention to the following: (1) the asymptotic dynamics of cosmological models based on the BD, scalar–tensor and Horndeski theories, (2) inflationary models, extended quintessence and the Galileons, with emphasis in causality and stability issues, (3) the chameleon and Vainshtein screening mechanisms that may allow the elusive scalar field to evade the tight observational constraints implied by the solar system experiments, (4) the conformal frames conundrum with a brief discussion on the disformal transformations and (5) the role of Weyl symmetry and scale invariance in the gravitation theories. The review is aimed at specialists as well as at nonspecialists in the subject, including postgraduate students.

Testing general relativity with black hole-pulsar binaries

Binary pulsars allow us to carry out precision tests of gravity and have placed stringent bounds on a broad class of theories beyond general relativity. Current and future radio telescopes, such as FAST, SKA, and MeerKAT, may find a new astrophysical system, a pulsar orbiting around a black hole, which will provide us a new source for probing gravity. In this paper, we systematically study the prospects of testing general relativity with such black hole-pulsar binaries. We begin by finding a mapping between generic non-Einsteinian parameters in the orbital decay rate and theoretical constants in various modified theories of gravity and then summarize this mapping with a ready-to-use list. Theories we study here include scalar-tensor theories, varying $G$ theories, massive gravity theories, generic screening gravity and quadratic curvature-corrected theories. We next use simulated measurement accuracy of the orbital decay rate with FAST/SKA to derive projected upper bounds on the generic non-Einsteinian parameters. We find that such bounds from black hole-pulsars can be stronger than those from neutron star-pulsar and neutron star-white dwarf binaries by a few orders of magnitude when the correction enters at negative post-Newtonian orders. By mapping such bounds on generic parameters to those on various modified theories of gravity, we find that one can constrain the time variation in Newton's constant $G$ to be comparable and complementary to the current strongest bound from solar system experiments. We also study how well one can probe quadratic gravity from black hole quadrupole moment measurements of black hole-pulsars. We find that bounds on the parity-violating sector of quadratic gravity can be stronger than current bounds by six orders of magnitude. These results suggest that a new discovery of black hole-pulsars in the future will provide powerful ways to probe gravity further.

Monopolar and quadrupolar gravitational radiation from magnetically deformed neutron stars in modified gravity

Some modified theories of gravity are known to predict monopolar, in addition to the usual quadrupolar and beyond, gravitational radiation in the form of `breathing' modes. For the same reason that octupole and higher-multipole terms often contribute negligibly to the overall wave strain, monopole terms tend to dominate. We investigate both monopolar and quadrupolar continuous gravitational radiation from neutron stars deformed through internal magnetic stresses. We adopt the Parameterised-Post-Newtonian formalism to write down equations describing the leading-order stellar properties in a theory-independent way, and derive some exact solutions for stars with mixed poloidal-toroidal magnetic fields. We then turn to the specific case of scalar-tensor theories to demonstrate how observational upper limits on the gravitational-wave luminosity of certain neutron stars may be used to place constraints on modified gravity parameters, most notably the Eddington parameter $\gamma$. For conservative, purely poloidal models with characteristic field strength given by the spindown minimum, upper limits for the Vela pulsar yield $1-\gamma \lesssim 4.2 \times 10^{-3}$. For models containing a strong toroidal field housing $\sim 99\%$ of the internal magnetic energy, we obtain the bound $1- \gamma \lesssim 8.0 \times 10^{-7}$. This latter bound is an order of magnitude tighter than those obtained from current Solar system experiments, though applies to the strong-field regime.