Solar System Experiments Research Articles

Probing f(T) gravity with gravitational time advancement

The effects of a quadratic gravity on astronomical observations and solar system experiments were recently considered in previous works. Its deviation from Einstein’s general relativity is characterized by a model parameter α and the cosmological constant Λ whose constraints were respectively found as m2 and m−2 in the solar system. In this paper, a new test of the gravity by measuring the gravitational time advancement is presented and studied. The gravitational time advancement arises in a two-way light propagation between an observer and a distant spacecraft, where the light traveling time is recorded by the observer’s proper time. It is found that (1) relying on their signs, α and Λ can make the gravitational time advancement smaller or larger than the one of general relativity; (2) the configuration of the inferior conjunction between the observer and the spacecraft is more suitable for detecting the advancement, because its effect is almost 3.5 times larger than the one in the superior conjunction; (3) the time advancement could be effectively complementary to Shapiro time delay for gravitational experiments in practice; and (4) the implement of planetary laser ranging and optical clocks in the future will provide much more insight into the gravity.

Probing gravitational parity violation with gravitational waves from stellar-mass black hole binaries

The recent discovery of gravitational wave events has offered us unique testbeds of gravity in the strong and dynamical field regime. One possible modification to General Relativity is the gravitational parity violation that gives rise to the amplitude birefringence in gravitational waves, where one of the circularly-polarized mode is amplified while the other one is suppressed during their propagation. In this paper, we study how well one can measure gravitational parity violation via the amplitude birefringence of gravitational waves from stellar-mass black hole binaries. We choose Chern-Simons gravity as an example and work within an effective field theory formalism. We consider gravitational waves from both individual sources and stochastic gravitational wave backgrounds. Regarding bounds from individual sources, we estimate them using a Fisher analysis and carry out Monte Carlo simulations by randomly distributing sources over their sky location and binary orientation. We find that the bounds on the scalar field evolution in Chern-Simons gravity from GW150914 are too weak to satisfy the weak Chern-Simons approximation, while aLIGO with its design sensitivity can place meaningful bounds. Regarding bounds from stochastic gravitational wave backgrounds, we set the threshold signal-to-noise ratio for detection of the parity-violation mode as 5 and estimate projected bounds with future detectors assuming that signals are consistent with no parity violation. We find that a network of two third-generation detectors is able to place bounds that are slightly stronger than current binary pulsar bounds. Since gravitational wave observations probe either the difference in parity violation between the source and the detector or the line-of-sight integration of the scalar field, such bounds are complementary to local measurements from solar system experiments and binary pulsar observations.

Screening mechanisms in hybrid metric-Palatini gravity

We investigate the efficiency of screening mechanisms in the hybrid metric-Palatini gravity. The value of the field is computed around spherical bodies embedded in a background of constant density. We find a thin shell condition for the field depending on the background field value. In order to quantify how the thin shell effect is relevant, we analyze how it behaves in the neighborhood of different astrophysical objects (planets, moons or stars). We find that the condition is very well satisfied except only for some peculiar objects. Furthermore we establish bounds on the model using data from solar system experiments such as the spectral deviation measured by the Cassini mission and the stability of the Earth-Moon system, which gives the best constraint to date on $f(R)$ theories. These bounds contribute to fix the range of viable hybrid gravity models.

Chameleon mechanism in f(R) modified gravitation model of polynomial-exponential form

In this paper, we first present briefly to Chameleon mechanism in modified gravity of f(R), then we apply it to modified gravity of polynomial exponential form to find constraints from solar system experiments to parameters of α and β of the model. Results show that the Chameleon mechanism sets strict constraints on α and β parameters as follows: 0 < β < 7.67 × 10−15 and 0 < α < 9 × 10−75.

Stable cosmology in chameleon bigravity

The recently proposed chameleonic extension of bigravity theory, by including a scalar field dependence in the graviton potential, avoids several fine-tunings found to be necessary in usual massive bigravity. In particular it ensures that the Higuchi bound is satisfied at all scales, that no Vainshtein mechanism is needed to satisfy solar-system experiments, and that the strong coupling scale is always above the scale of cosmological interest all the way up to the early universe. This paper extends the previous work by presenting a stable example of cosmology in the chameleon bigravity model. We find a set of initial conditions and parameters such that the derived stability conditions on general flat Friedmann background are satisfied at all times. The evolution goes through radiation dominated, matter dominated, and de Sitter eras. We argue that the parameter space allowing for such a stable evolution may be large enough to encompass an observationally viable evolution. We also argue that our model satisfies all known constraints due to gravitational wave observations so far and thus can be considered as a unique testing ground of gravitational wave phenomenologies in bimetric theories of gravity.

Causal properties of nonlinear gravitational waves in modified gravity

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments.

Testing Brans-Dicke gravity using the Einstein telescope

Gravitational radiation is an excellent field for testing theories of gravity in strong gravitational fields. The current observations on the gravitational-wave (GW) bursts by LIGO have already placed various constraints on the alternative theories of gravity. In this paper, we investigate the possible bounds which could be placed on the Brans-Dicke gravity using GW detection from inspiralling compact binaries with the proposed Einstein Telescope, a third-generation GW detector. We first calculate in details the waveforms of gravitational radiation in the lowest post-Newtonian approximation, including the tensor and scalar fields, which can be divided into the three polarization modes, i.e. "plus mode", "cross mode" and "breathing mode". Applying the stationary phase approximation, we obtain their Fourier transforms, and derive the correction terms in amplitude, phase and polarization of GWs, relative to the corresponding results in General Relativity. Imposing the noise level of Einstein Telescope, we find that the GW detection from inspiralling compact binaries, composed of a neutron star and a black hole, can place stringent constraints on the Brans-Dicke gravity. The bound on the coupling constant $\omega_{\rm BD}$ depends on the mass, sky-position, orbital angle, polarization angle, luminosity distance, redshift distribution and total observed number $N_{\rm GW}$ of the binary systems. Taking into account all the burst events up to redshift $z=5$, we find that the bound could be $\omega_{\rm BD}\gtrsim 10^{6}\times(N_{\rm GW}/10^4)^{1/2}$. Even for the conservative estimation with $10^{4}$ observed events, the bound is still more than one order tighter than the current limit from Solar System experiments. So, we conclude that Einstein Telescope will provide a powerful platform to test alternative theories of gravity.

Black hole based tests of general relativity

General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the Universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is four-dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar–tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.

Constraining scalar-tensor theories of gravity from the most massive neutron stars

Scalar-tensor~(ST) theories of gravity are natural phenomenological extensions to general relativity. Although these theories are severely constrained both by solar system experiments and by binary pulsar observations, a large set of ST families remain consistent with these observations. Recent work has suggested probing the unconstrained region of the parameter space of ST theories based on the stability properties of highly compact neutron stars. Here, the dynamical evolution of very compact stars in a fully nonlinear code demonstrates that the stars do become unstable and that the instability, in some cases, drives the stars to collapse. We discuss the implications of these results in light of recent observations of the most massive neutron star yet observed. In particular, such observations suggest that such a star would be subject to the instability for a certain regime; its existence therefore supports a bound on the ST parameter space.

Improved upper bounds on Kaluza–Klein gravity with current Solar System experiments and observations

As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun.

Post-Newtonian approximation of teleparallel gravity coupled with a scalar field

We use the parameterized post-Newtonian (PPN) formalism to explore the weak field approximation of teleparallel gravity non-minimally coupling to a scalar field ϕ, with arbitrary coupling function ω(ϕ) and potential V(ϕ). We find that all the PPN parameters are identical to general relativity (GR), which makes this class of theories compatible with the Solar System experiments. This feature also makes the theories quite different from the scalar–tensor theories, which might be subject to stringent constraints on the parameter space, or need some screening mechanisms to pass the Solar System experimental constraints.

Possibility of setting a new constraint to scalar-tensor theories

Scalar-tensor theories (STTs) are a widely studied alternative to general relativity (GR) in which gravity is endowed with an additional scalar degree of freedom. Although severely constrained by solar system and pulsar timing experiments, there remains a large set of STTs which are consistent with all present day observations. In this paper, we investigate the possibility of probing a yet unconstrained region of the parameter space of STTs based on the fact that stability properties of highly compact neutron stars in these theories may radically differ from those in GR.

A perturbative approach for the study of compatibility between nonminimally coupled gravity and Solar System experiments

We develop a framework for constraining a certain class of theories of nonminimally coupled (NMC) gravity with Solar System observations.

Constraints on the Brans-Dicke gravity theory with the Planck data

Based on the new cosmic CMB temperature data from the Planck satellite, the 9 year polarization data from the WMAP, the BAO distance ratio data from the SDSS and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt a parametrization $\zeta=\ln(1+1/\omega})$, where the general relativity (GR) limit corresponds to $\zeta = 0$. We find no evidence of deviation from general relativity. At 95% probability, $-0.00246 < \zeta < 0.00567$, correspondingly, the region $-407.0 < \omega <175.87$ is excluded. If we restrict ourselves to the $\zeta>0$ (i.e. $\omega >0$) case, then the 95% probability interval is $\zeta<0.00549$, corresponding to $\omega> 181.65$. We can also translate this result to a constraint on the variation of gravitational constant, and find the variation rate today as $\dot{G}=-1.42^{+2.48}_{-2.27} \times 10^{-13} $yr$^{-1} $ ($1\sigma$ error bar), the integrated change since the epoch of recombination is $\delta G/G = 0.0104^{+0.0186}_{-0.0067} $ ($1\sigma$ error bar). These limits on the variation of gravitational constant are comparable with the precision of solar system experiments.

F (T) gravity: effects on astronomical observations and Solar system experiments and upper bounds

The effects of the f (T) gravity have previously been investigated and constrained by using perihelion advances. As an extension of previous work and as an attempt to find more stringent constraints on its parameters, we investigate here its effects on astronomical observations and on experiments conducted in the Solar system. The expression for f (T) contains a quadratic correction of α*T2 (where α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, in addition to the light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. From these results, we find qualitatively that the light deflection provides a unique bound on α, without dependence on Λ, and that the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observations and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper bounds quantitatively: |α| ≤ 1.2 × 102 m2 and |Λ| ≤ 1.8 × 10−43 m−2, which are at least 10 times tighter than the previous results.

Neutron-star mergers in scalar-tensor theories of gravity

Scalar-tensor theories of gravity are natural phenomenological alternatives to General Relativity, where the gravitational interaction is mediated by a scalar degree of freedom, besides the usual tensor gravitons. In regions of the parameter space of these theories where constraints from both solar system experiments and binary-pulsar observations are satisfied, we show that binaries of neutron stars present marked differences from General Relativity in both the late-inspiral and merger phases. In particular, phenomena related to the spontaneous scalarization of isolated neutron stars take place in the late stages of the evolution of binary systems, with important effects in the ensuing dynamics. We comment on the relevance of our results for the upcoming Advanced LIGO/Virgo detectors.

New constraint on scalar Gauss-Bonnet gravity and a possible explanation for the excess of the orbital decay rate in a low-mass x-ray binary

It was recently shown that a black hole (BH) is the only compact object that can acquire a scalar charge in scalar Gauss-Bonnet (sGB) theory under the small coupling approximation. This leads to the fact that scalar radiation is emitted from a binary containing at least one BH. In this letter, we find the constraints on this theory from BH low-mass X-ray binaries (BH-LMXBs). The main result of this letter is that from the orbital decay rate of A0620-00, we obtained a conservative bound that is six orders of magnitude stronger than the solar system bound. In addition to this, we look at XTE J1118+480, whose orbital decay rate has been recently measured with an excess compared to the theoretical prediction in GR due to the radiation reaction. The cause of this excess is currently unknown. Although it is likely that the cause is of astrophysical origin, here we investigate the possibility of explaining this excess with the additional scalar radiation in sGB theory. We find that there still remains a parameter range where the excess can be explained while also satisfying the constraint obtained from A0620-00. The interesting point is that for most of other alternative theories of gravity, it seems difficult to explain this excess with the additional radiation. This is because it would be difficult to evade the constraints from binary pulsars or they have already been constrained rather strongly from other observations such as solar system experiments. We propose several ways to determine whether the excess is caused by the scalar radiation in sGB gravity including future gravitational wave observations with space-borne interferometers, which can give a constraint three orders of magnitude stronger than that from A0620-00.

Fab Four: When John and George Play Gravitation and Cosmology

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

Massless scalar field and solar-system experiments

The solution of Einstein's field equations with the energy-momentum tensor of a massless scalar field is known as the Fisher solution. It is well known that this solution has a naked singularity due to the ''charge''{Sigma} of the massless scalar field. Here I obtain the radial null geodesic of the Fisher solution and use it to confirm that there is no black hole. In addition, I use the parametrized post-Newtonian formalism to show that the Fisher spacetime predicts the same effects on solar-system experiments as the Schwarzschild one does, as long as we impose a limit on {Sigma}. I show that this limit is not a strong constraint and we can even take values of {Sigma} bigger than M. By using the exact formula of the redshift and some assumptions, I evaluate this limit for the experiment of Pound and Snider [Phys. Rev. 140, B788 (1965)]. It turns out that this limit is {Sigma}<5.8x10{sup 3} m.

Exact cosmological solution of a scalar-tensor gravity theory compatible with theΛCDMmodel

We consider the massive scalar-tensor theory in the Jordan frame $F(\ensuremath{\Phi})={K}^{2}{\ensuremath{\Phi}}^{2}$ and $U(\ensuremath{\Phi})=(1/2){m}^{2}{\ensuremath{\Phi}}^{2}$, where $F(\ensuremath{\Phi})$ corresponds to a constant Brans-Dicke parameter ${\ensuremath{\omega}}_{\mathrm{BD}}=1/4{K}^{2}$. The constraint of the Solar System experiments is ${K}^{2}&lt;(1/400{)}^{2}$. For dustlike matter in a spatially flat, homogeneous isotropic universe, we reduce the equations of motion to a system of two differential equations of first order which can be exactly solved. We obtain simple and explicit expressions for $\frac{\ensuremath{\Phi}(z)}{\ensuremath{\Phi}(0)}$ and $\frac{H(z)}{{H}_{0}}$ that depend only on two parameters, ${K}^{2}$ and ${\ensuremath{\Omega}}_{m,0}$. For $K\ensuremath{\le}1/400$, the expansion rate $H(z)$ can be practically superposed on the $\ensuremath{\Lambda}\mathrm{CDM}$ solution ${H}_{\ensuremath{\Lambda}}(z)$, up to high redshift $z$, but the equation of state ${w}_{\mathrm{DE}}(z)$ of the dark energy is not constant: it presents a very slight crossing of the phantom divide line $w=\ensuremath{-}1$ in the neighborhood of $z=0$ and becomes very slightly positive at high redshifts.