Tensor-vector-scalar Research Articles

Geometric interpretation of Tensor-Vector-Scalar theory in a Kaluza–Klein reference fluid

Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully–Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the cosmic microwave background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, a generalized TeVeS from Kaluza–Klein theory in one extra dimension is derived as a consequence of n = 0 Kaluza–Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D Arnowitt–Deser–Misner formalism enforced by a reference fluid as in the Isham-Kuchař method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza–Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles, the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza–Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it provides a symmetry breaking motivation for the interpolating function in MOND.

Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light

A number of theories of gravity have been proposed as proxies for dark matter in the regime of galaxies and cosmology. The recent observations of gravitational waves (GW170817) from the merger of two neutron stars, followed by an electromagnetic counterpart (GW170817a) have placed stringent constraints on the difference of the speed of gravity to the speed of light, severely restricting the phenomenological viability of such theories. We revisit the impact of these observations on the Tensor-Vector-Scalar (TeVeS) paradigm of relativistic Modified Newtonian Dynamics (MOND) and demonstrate the existence of a previously unknown class of this paradigm where the speed of gravity always equals the speed of light. We show that this holds without altering the usual (bimetric) MOND phenomenology in galaxies.

The Polarizations of Gravitational Waves

The gravitational wave provides a new method to examine General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyze the polarization contents of Horndeski theory and f(R) gravity. We find out that in addition to the familiar plus and cross polarizations, a massless Horndeski theory predicts an extra transverse polarization, and there is a mix of pure longitudinal and transverse breathing polarizations in the massive Horndeski theory and f(R) gravity. It is possible to use pulsar timing arrays to detect the extra polarizations in these theories. We also point out that the classification of polarizations using Newman–Penrose variables cannot be applied to massive modes. It cannot be used to classify polarizations in Einstein-æther theory or generalized Tensor-Vector-Scalar (TeVeS) theory, either.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

In this work, we discuss the polarization contents of Einstein-\ae ther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-\ae ther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-\ae ther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-\ae ther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Cosmology of the Galileon extension of Bekenstein’s theory of relativistic modified Newtonian dynamics

A generalization of Bekenstein's Tensor-Vector-Scalar (TeVeS) model of modified gravity has recently been proposed as an alternative to dark matter. This model -- which we will refer to as g-TeVeS -- utilizes a Galileon-induced Vainshtein mechanism to suppress modifications to General Relativity in strong gravity regimes and so avoids the need to introduce the baroque kinetic terms that typically exist in relativistic models of Modified Newtonian Dynamics (MOND). We explore the behavior of this model in spacetimes with exact Friedmann-Robertson-Walker (FRW) symmetry. The ability of the theory to recover MOND phenomenology places restrictions on the theory's parameter space and it is found that within an estimate of this area of parameter space the theory cannot successfully approximate the Friedmannian cosmological behavior of cold dark matter. It is found that much closer agreement may be recovered in other regions of the theory's parameter space and the reasons for this are discussed.

Testing the tensor-vector-scalar theory with the latest cosmological observations

The tensor-vector-scalar (TeVeS) model is considered a viable theory of gravity. It produces the Milgrom's modified Newtonian dynamics in the nonrelativistic weak field limit and is free from ghosts. This model has been tested against various cosmological observations. Here we investigate whether new observations such as the galaxy velocity power spectrum measured by 6dF and the kinetic Sunyaev Zel'dovich effect power spectrum measured by ACT/SPT can put further constraints on the TeVeS model. Furthermore, we perform the test of TeVeS cosmology with a sterile neutrino by confronting to Planck data, and find that it is ruled out by cosmic microwave background measurements from the Planck mission.

Can TeVeS be a viable theory of gravity?

Among modified gravitational theories, the Tensor–Vector–Scalar (TeVeS) occupies a special place – it is a covariant theory of gravity that produces the modified Newtonian dynamics (MOND) in the nonrelativistic weak field limit and explains the astrophysical data at scales larger than that of the Solar System, without the need of an excessive amount of invisible matter. We show that, in contrast to other modified theories, TeVeS is free from ghosts. These achievements make TeVeS (and its nonrelativistic limit) a viable theory of gravity. A speculative outlook on the emergence of TeVeS from a quantum theory is presented.

Testing Modified Newtonian Dynamics with LISA Pathfinder

We suggest that LISA Pathfinder, a technology demonstrator for the future gravitational wave observatory LISA, could be used to carry out a direct experimental test of Modified Newtonian Dynamics (MOND). The LISA Pathfinder spacecraft is currently being built and the launch date is just a few years away. No modifications of the spacecraft are required, nor any interference with its nominal mission. The basic concept is to fly LISA Pathfinder through the region around the Sun-Earth saddle point, in an extended mission phase, once the original mission goals are achieved. We examine various strategies to reach the saddle point, and find that the preferred strategy, yielding relatively short transfer times of just over 1year, probably involves a lunar fly-by. LISA Pathfinder will be able to probe the intermediate MOND regime, i.e. the transition between deep MOND and Newtonian gravity. We present robust estimates of the anomalous gravity gradients that LISA Pathfinder should be exposed to, based on MONDian effects as derived from the Tensor-Vector-Scalar (TeVeS) theory. The spacecraft speed and spatial scale of the MOND signal combine in a way that the spectral signature of the signal falls precisely into LISA Pathfinder’s measurement bandwidth. We find that if the gravity gradiometer on-board the spacecraft achieves its currently predicted sensitivity, these anomalous gradients could not just be detected, but measured in some detail.

Geometry of modified Newtonian dynamics

Modified Newtonian dynamics is an empirical modification to Poisson's equation which has had success in accounting for the ``gravitational field'' $\ensuremath{\Phi}$ in a variety of astrophysical systems. The field $\ensuremath{\Phi}$ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ensuremath{\Phi}\ensuremath{\rightarrow}0$. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.

TeVeS/MOND is in harmony with gravitational redshifts in galaxy clusters

ABSTRACT Wojtak, Hansen & Hjorth have recently claimed to confirm general relativity (GR) and to rule out the tensor–vector–scalar (TeVeS) gravitational theory based on an analysis of the gravitational redshifts of galaxies in 7800 clusters. However, their ubiquitous modelling of the sources of cluster gravitational fields with Navarro–Frenk–White mass profiles is neither empirically justified out to the necessary radii in clusters, nor germane in the case of TeVeS. Using MONDian (where MOND stands for MOdified Newtonian Dynamics) isothermal sphere models consistently constructed within MOND (equivalent to TeVeS models), we can fit the determined redshifts no worse than does GR with dark haloes. Moreover, Wojtak, Hansen & Hjorth have inappropriately used the simple MOND interpolating function for the μ function of the scalar field of TeVeS; the consequent MOND effective interpolating function turns out to enhance the gravitational potential, and so contributes to the discrepancy which forms the basis of their claims.

Slowly Rotating Relativistic Stars in TeVeS

In order to examine the rotational effect around neutron star in tensor-vector-scalar (TeVeS) theory, we consider the slowly rotating relativistic stars with a uniform angular velocity. As a result, we find that similar to the case in general relativity (GR), the angular momentum is proportional to the angular velocity and one could possibly distinguish the gravitational theory in the strong field regime even in the case that the value of the coupling constant K is quite small.

Improving relativistic modified Newtonian dynamics with Galileonk-mouflage

We propose a simple field theory reproducing the MOND phenomenology at galaxy scale, while predicting negligible deviations from general relativity at small scales thanks to an extended Vainshtein ("k-mouflage") mechanism induced by a covariant Galileon-type Lagrangian. The model passes solar-system tests at the post-Newtonian order, including those of local Lorentz invariance, and its anomalous forces in binary-pulsar systems are orders of magnitude smaller than the tightest experimental constraints. The large-distance behavior is obtained as in Bekenstein's tensor-vector-scalar (TeVeS) model, but with several simplifications. In particular, no fine-tuned function is needed to interpolate between the MOND and Newtonian regimes, and no dynamics needs to be defined for the vector field because preferred-frame effects are negligible at small distances. The field equations depend on second (and lower) derivatives, and avoid thus the generic instabilities related to higher derivatives. Their perturbative solution around a Schwarzschild background is remarkably simple to derive. We also underline why the proposed model is particularly efficient within the class of covariant Galileons.

Torsional oscillations in tensor-vector-scalar theory

With the Cowling approximation, the torsional oscillations on relativistic stars in tensor-vector-scalar (TeVeS) theory are examined. The spectrum features in TeVeS are very similar to those in general relativity (GR), but the torsional frequencies in TeVeS become larger than those expected in GR. We find that, compared with the fluid oscillations with polar parity, the torsional frequencies depend strongly on the gravitational theory. Since the dependences of fundamental frequencies on the gravitational theory and on the equation of state are different from those of overtone, it could be possible to distinguish TeVeS from GR in the strong-field regime via observations of this type of oscillations with the help of the observation of stellar mass.

Black Holes and Neutron Stars in Tensor-Vector-Scalar Theory

Bekenstein's Tensor-Vector-Scalar (TeVeS) theory has had considerable success as a relativistic theory of Modified Newtonian Dynamics. In the strong-field regime it makes many predictions that differ from General Relativity implying this regime provides an excellent testing ground for the theory using both current and future observations of neutron stars and black holes in both the electromagnetic and gravitational wave spectrum. I look at the current status of black hole and neutron star solutions in both the original TeVeS theory and its generalisation, including some key observational properties that differ from General Relativity.

Stability and quasinormal modes of black holes in tensor-vector-scalar theory: Scalar field perturbations

The imminent detection of gravitational waves will trigger precision tests of gravity through observations of quasinormal ringing of black holes. While general relativity predicts just two polarizations of gravitational waves, the so-called plus and cross polarizations, numerous alternative theories of gravity predict up to six different polarizations which will potentially be observed in current and future generations of gravitational wave detectors. Bekenstein's Tensor-Vector-Scalar (TeVeS) theory and its generalization fall into one such class of theory that predict the full gamut of six polarizations of gravitational waves. In this paper we begin the study of quasinormal modes (QNMs) in TeVeS by studying perturbations of the scalar field in a spherically symmetric background. We show that, at least in the case where superluminal propagation of perturbations is not present, black holes are generically stable to this kind of perturbation. We also make a unique prediction that, as the limit of the various coupling parameters of the theory tend to zero, the QNM spectrum tends to $1/\sqrt{2}$ times the QNM spectrum induced by scalar perturbations of a Schwarzschild black hole in general relativity due to the intrinsic presence of the background vector field. We further show that the QNM spectrum does not vary significantly from this value for small values of the theory's coupling parameters, however can vary by as much as a few percent for larger, but still physically relevant parameters.

Toroidal oscillations of a slowly rotating relativistic star in tensor-vector-scalar theory

We examine the toroidal oscillations on the slowly rotating relativistic stars in tensor-vector-scalar (TeVeS) theory with the Cowling approximation. As a result, we find that perturbation equations describing the toroidal oscillations are same equation form as in general relativity (GR). Although the frequencies of toroidal oscillations in TeVeS are not so different from those in GR, the momentum inertia depends strongly on the gravitational theory. Thus, observing the frequencies of toroidal oscillations and momentum inertia with high accuracy might reveal the gravitational theory in the strong-field regime.

Slowly rotating relativistic stars in tensor-vector-scalar theory

In order to examine the rotational effect around neutron star in tensor-vector-scalar (TeVeS) theory, we consider the slowly rotating relativistic stars with a uniform angular velocity. As a result, we find that similar to the case in general relativity (GR), the angular momentum is proportional to the angular velocity. Additionally, as the value of coupling constant $K$ becomes higher, the frame dragging in TeVeS becomes quite different distribution from that in GR, where we can also see the deviation even in the interior of star. While with smaller value of $K$, although the frame dragging approaches to that expected in GR, the induced vector field due to the rotation does not vanish and still exists. Thus, through the observations associated with relativistic object, one could be possible to distinguish the gravitational theory in strong field regime even in the case that the value of coupling constant $K$ is quite small.

Black holes and neutron stars in the generalized tensor-vector-scalar theory

Bekenstein's tensor-vector-scalar (TeVeS) theory has had considerable success as a relativistic theory of modified Newtonian dynamics. However, recent work suggests that the dynamics of the theory are fundamentally flawed and numerous authors have subsequently begun to consider a generalization of TeVeS where the vector field is given by an Einstein-\AE{}ther action. Herein, I develop strong-field solutions of the generalized TeVeS theory, in particular exploring neutron stars as well as neutral and charged black holes. I find that the solutions are identical to the neutron star and black hole solutions of the original TeVeS theory, given a mapping between the parameters of the two theories, and hence provide constraints on these values of the coupling constants. I discuss the consequences of these results in detail including the stability of such spacetimes as well as generalizations to more complicated geometries.

Probing tensor-vector-scalar theory with gravitational wave asteroseismology

In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime ($w$ modes), are independent from the perturbations of scalar field and the effects of scalar field can be mounted only via the background properties. Using two different equations of state, we calculate the complex eigenfrequencies of axial $w$ modes and find that the dependences of frequencies on the stellar compactness are almost independent from the adopted equation of state and the parameter in TeVeS. Additionally, these dependences of frequencies of axial $w$ modes in TeVeS is obviously different from those expected in the general relativity. Thus the direct observations of gravitational waves could reveal the gravitational theory in the strong-field regime.

Can the relativistic field theory version of modified Newtonian dynamics avoid dark matter on galactic scales?

A fully relativistic analysis of gravitational lensing in tensor-vector-scalar (TeVeS) theory is presented. By estimating the lensing masses for a set of six lenses from the CASTLES database, and then comparing them to the stellar mass, the deficit between the two is obtained and analyzed. Considering a parametrized range for the TeVeS function $\ensuremath{\mu}(y)$, which controls the strength of the modification to gravity, it is found that on galactic scales TeVeS requires additional dark matter with the commonly used $\ensuremath{\mu}(y)$. A soft dependence of the results on the cosmological framework and the TeVeS free parameters is discussed. For one particular form of $\ensuremath{\mu}(y)$, TeVeS is found to require very little dark matter. This choice is however ruled out by rotation curve data. The inability to simultaneously fit lensing and rotation curves for a single form of $\ensuremath{\mu}(y)$ is a challenge to a no dark matter TeVeS proposal.