General Scalar-tensor Theory Of Gravity Research Articles

Well-Posedness of the Four-Derivative Scalar-Tensor Theory of Gravity in Singularity Avoiding Coordinates.

We show that the most general scalar-tensor theory of gravity up to four derivatives in 3+1 dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practice by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling condition is order one, without instabilities developing. Our Letter provides the means for such simulations to be undertaken by the many numerical relativity codes that rely on the moving puncture gauge to evolve black hole singularities.

Warm inflation in general scalar-tensor theory of gravity

In this work, we investigate warm inflationary models in the context of a general scalar-tensor theory of gravity which is coupled to radiation through a dissipation term. We first derive the potential of exponential and hyperbolic tangent forms. We consider a dissipation parameter of the form $\Gamma = C_{1}T$ with $C_1$ being a coupling parameter and focus only on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We compute inflationary observables and constrain the parameters of our model using current Planck 2018 data. From our analysis, we discover that the weak coupling limit $\xi\ll 1$ is needed in order to have the derived $n_s$ and $r$ consistent with the Planck 2018 observational constraints. Particularly, we constrain the potential scale $V_{0}$ of the models.

Wave-like spatially homogeneous models of Stäckel spacetimes (2.1) type in the scalar-tensor theory of gravity

Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like spacetime models allow the existence of privileged coordinate systems where the eikonal equation and the Hamilton–Jacobi equation of test particles can be integrated by the method of complete separation of variables with the separation of isotropic (wave) variables on which the space metric depends (non-ignored variables). An explicit form of the scalar field and two functions of the scalar field that are part of the general scalar-tensor theory of gravity are found. The explicit form of the eikonal function and the action function for test particles in the considered models is given. The obtained solutions are of type III according to the Bianchi classification and type N according to the Petrov classification. Wave-like spatially homogeneous spacetime models can describe primordial gravitational waves of the Universe.

Sudden Brans–Dicke singularities

We show that cosmological sudden singularities that respect the energy conditions can occur at finite times in Brans–Dicke and more general scalar-tensor theories of gravity. We construct these explicitly in the Friedmann universes. Higher-order versions of these singularities are also possible, including those that arise with when scalar fields have a self-interaction potential of power-law form.

What if Newton’s Gravitational Constant Was Negative?

In this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, G. To this end, we consider general scalar-tensor gravity theories as they provide the field theory natural framework for the variation of the gravitational coupling. We find that models with a quadratic potential naturally stabilize the value of G into the positive branch of the evolution and further, that de Sitter inflation and a relaxation to General Relativity is easily attained.

Cosmological lorentzian wormholes via noether symmetry approach

Noether symmetry has been invoked to explore the forms of a couple of coupling parameters and the potential appearing in a general scalar-tensor theory of gravity in the background of Robertson-Walker space-time. Exact solutions of Einstein's field equations in the familiar Brans-Dicke, Induced gravity and a General non-minimally coupled scalar-tensor theories of gravity have been found using the conserved current and the energy equation, after being expressed in a set of new variables. Noticeably, the form of the scale factors remains unaltered in all the three cases and represents cosmological Lorentzian wormholes, analogous to the Euclidean ones. While classical Euclidean wormholes requires an imaginary scalar field, the Lorentzian wormhole do not, and the solutions satisfy the weak energy condition.

The polarizations of gravitational waves

The direct detection of gravitational waves opens a new window to probe the nature of gravity, and it brings us into the era of multi-messenger astronomy.Gravitational wave has no effect on the geodesics of a test particle, but it affects the relative motion between two nearby test particles.To measure gravitational wave and its polarizations, we need to study the geodesic deviation equation for two nearby test particles.Since only the electric part of the Riemann tensor $R_{i0j0}$ appears in the geodesic deviation equation and it has six independent components,there are up to six possible polarization states in general metric theories of gravity.In terms of the electric part of the Riemann tensor, the six polarizations are defined as follows.$\\hat{P}_+=-R_{x0x0}+R_{y0y0}$ corresponds to the “+ mode, $\\hat{P}_\\times=2R_{x0y0}$ denotes the “$\\times$ mode,$\\hat{P}_b=R_{x0x0}+R_{y0y0}$ corresponds to the breathing mode, $\\hat{P}_x=R_{x0z0}$ corresponds to the vector-$x$ mode,$\\hat{P}_x=R_{y0z0}$ represents to the vector-$y$ mode, and $\\hat{P}_l=R_{z0z0}$ denotes the longitudinal mode.For weak, plane and null gravitational waves, these six polarizations can be classified based on their properties under the Lorentz transformation.In Einsteins general relativity, the gravitational waves are tensor waves and there are “+ and “$\\times$ modes of polarization.In Brans-Dicke theory, in addition to the “+ and “$\\times$ polarization states, the scalar breathing mode also appears, and all these threepolarizations are transverse modes. In the most general scalar-tensor theory of gravity, the Horndeski theory,the massive scalar field excites both the breathing and the longitudinal modes, so in addition to the “+ and “$\\times$ polarizations,there exists a single mix state consisting of both the breathing and the longitudinal modes. In the massless limit,the longitudinal mode disappears andthe mix state becomes the pure transverse breathing polarization as that in Brans-Dicke theory. The nonlinear $f$($R$) theory of gravitycan be written as a scalar-tensor theory of gravity, so the polarization states in $f$($R$) gravity are the sameas those in Horndeski theory except that there is no massless limit in $f$($R$) gravity.In Einstein-Aether theory, due to the existence of the unit timelike vector field,the local Lorentz invariance is violated. The gravitational waves propagate with speeds different from the speed of light,and there are five independent polarization states,the “+ state $\\hat{P}_+$, the “$\\times$ state $\\hat{P}_\\times$, the vector$-x$ state $\\hat{P}_x$, the vector$-y$ state $\\hat{P}_y$ and themix state consisting of both the breathing and the longitudinal modes excited by the scalar field.In TeVeS theory, the local Lorentz invariance is also broken,so the gravitational waves in TeVeS theory propagate with speeds different from the speed of light.There are six polarization states in TeVeS theory,$\\hat{P}_+$, $\\hat{P}_\\times$, $\\hat{P}_x$, $\\hat{P}_y$ and twomix states excited by the two scalar fields. Each of the mix states consists of both the breathing and the longitudinal modes.Because gravitational waves have different polarization states for different theories of gravity, the measurementof polarizations is a powerful tool in probing the nature of gravity.

Inflationary attractors from nonminimal coupling

We show explicitly how the E model attractor is obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. By using conformal transformations, any attractor with the observables ns and r can be obtained. The existence of attractors imposes a challenge to distinguish different models.

Nonminimal coupling and inflationary attractors

We show explicitly how the T model, E model, and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $\xi$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.

Towards the most general scalar-tensor theories of gravity: A unified approach in the language of differential forms

We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under Local Lorentz Transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second order equations, which can be associated with Horndeski's theory. In this process, we identify a new second order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step we focus on theories with second order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories.

Disformally self-tuning gravity

We extend a previous self-tuning analysis of the most general scalar-tensor theory of gravity in four dimensions with second order field equations by considering a generalized coupling to the matter sector. Through allowing a disformal coupling to matter we are able to extend the Fab Four model and construct a new class of theories that are able to tune away the cosmological constant on Friedmann-Lemaitre-Robertson-Walker backgrounds.

Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation.

Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Parametrized post-Newtonian limit of Horndeski’s gravity theory

We discuss the parametrized post-Newtonian (PPN) limit of Horndeski's theory of gravity, also known under the name generalized G-inflation or ${\mathrm{G}}^{2}$-inflation, which is the most general scalar-tensor theory of gravity with at most second-order field equations in four dimensions. We derive conditions on the action for the validity of the post-Newtonian limit. For the most general class of theories consistent with these conditions we calculate the PPN parameters $\ensuremath{\gamma}(r)$ and $\ensuremath{\beta}(r)$, which in general depend on the interaction distance $r$ between the gravitating mass and the test mass. For a more restricted class of theories, in which the scalar field is massless, we calculate the full set of PPN parameters. It turns out that in this restricted case all parameters are constants and that the only parameters potentially deviating from observations are $\ensuremath{\gamma}$ and $\ensuremath{\beta}$. We finally apply our results to a number of example theories, including Galileons and different models of Higgs inflation.

The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier

We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called “mimetic” dark matter theory recently introduced by Chamsedinne and Mukhanov. These conclusions hold true irrespective of whether the scalar field in the action of the assumed scalar-tensor theory of gravity is the same or different than the scalar field involved in the transformation. The new equations of motion for our general mimetic theory can also be derived from an action containing an additional Lagrange multiplier field. The general mimetic scalar-tensor theory has the same number of derivatives in the equations of motion as the original scalar-tensor theory. As an application we show that the simplest mimetic scalar-tensor model is able to mimic the cosmological background of a flat FLRW model with a barotropic perfect fluid with any constant equation of state.

Parametrizations in scalar-tensor theories of gravity and the limit of general relativity

We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and the parametrized post-Newtonian parameters coincide with those of general relativity. We demonstrate that these so-called limits of general relativity are independent of the parametrization of the scalar field, although the transformation between scalar fields may be singular at the corresponding value of the scalar field. In particular, the limit of general relativity can equivalently be determined and investigated in the commonly used Jordan and Einstein frames.

Fab 5: noncanonical kinetic gravity, self tuning, and cosmic acceleration

We investigate circumstances under which one can generalize Horndeski'smost general scalar-tensor theory of gravity. Specifically we demonstratethat a nonlinear combination of purely kinetic gravity terms can give riseto an accelerating universe without the addition of extra propagatingdegrees of freedom on cosmological backgrounds, and exhibit self tuning tobring a large cosmologicalconstant under control. This nonlinear approach leads to new propertiesthat may be instructive for exploring the behaviors of gravity.

The relativistic pulsar-white dwarf binary PSR J1738+0333 - II. The most stringent test of scalar-tensor gravity

(abridged) We report the results of a 10-year timing campaign on PSR J1738+0333, a 5.85-ms pulsar in a low-eccentricity 8.5-hour orbit with a low-mass white dwarf companion (...) The measurements of proper motion and parallax allow for a precise subtraction of the kinematic contribution to the observed orbital decay; this results in a significant measurement of the intrinsic orbital decay: (-25.9 +/- 3.2) \times 10^{-15} s/s. This is consistent with the orbital decay from the emission of gravitational waves predicted by general relativity, (-27.7 +1.5/-1.9) \times 10^{-15} s/s (...). This agreement introduces a tight upper limit on dipolar gravitational wave emission, a prediction of most alternative theories of gravity for asymmetric binary systems such as this. We use this limit to derive the most stringent constraints ever on a wide class of gravity theories, where gravity involves a scalar field contribution. When considering general scalar-tensor theories of gravity, our new bounds are more stringent than the best current solar-system limits over most of the parameter space, and constrain the matter-scalar coupling constant {\alpha}_0^2 to be below the 10^{-5} level. For the special case of the Jordan-Fierz-Brans-Dicke, we obtain the one-sigma bound {\alpha}_0^2 < 2 \times 10^{-5}, which is within a factor two of the Cassini limit. We also use our limit on dipolar gravitational wave emission to constrain a wide class of theories of gravity which are based on a generalization of Bekenstein's Tensor-Vector-Scalar gravity (TeVeS), a relativistic formulation of Modified Newtonian Dynamics (MOND).

Scalar-tensor cosmologies with dust matter in the general relativity limit

We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmological time. This allows us to distinguish the theories with solutions that asymptotically converge to general relativity and draw some implications about the cosmological dynamics near this limit.

Evolution of homogeneous and isotropic scalar-tensor cosmological models

Homogeneous and isotropic cosmological models are considered in the framework of general scalar-tensor theories of gravity with arbitrary coupling function and scalar potential. Nonlinear approximate equations are derived for the regime close to the so-called limit of general relativity where the local observational constraints are satisfied. Approximate solutions in cosmological time are presented for the potential dominated era and for the era when the energy density of ordinary matter dominates over the energy density of scalar potential.