Metin Arik, Tarik Tok
We consider the scalar mode of gravity as expressed by a conformal factor of the metric and present a model motivated by the Jordan-Brans-Dicke action. The reduced action provides a Lagrangian density in Minkowski space which exhibits a massive particle and an expanding space-time through a mechanism which is similar to the Higgs mechanism.
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We study static black hole solutions in scalar tensor gravity. We present exact solutions in hiperextended models with a quadratic scalar potential.
Note About Born-Infeld Inspired Gravity Coupled Non-Minimally to Scalar Fields and Eddington Gravity with Matter
本文研究非最小耦合标量场的 Born-Infeld 启发引力正则结构，并构造多标量场耦合的 Eddington 引力，使其哈密顿量等价于最小耦合标量场的广义相对论。
Stationary, asymptotically flat black holes in scalar-tensor theories of gravity are studied. It is shown that such black holes have no scalar hair and are the same as in General Relativity.
We discuss a class of teleparallel scalar-torsion theories of gravity, which is parametrized by five free functions of the scalar field. The theories are formulated covariantly using a flat, but non-vanishing spin connection. We show how the actions of different theories within this class are related via conformal transformations of the tetrad and redefinitions of the scalar field, and derive the corresponding transformation laws for the free function in the action. From these we construct a number of quantities which are invariant under these transformations, and use them to write the action …
We discuss a generic form of the scalar potential appearing in the geometric scalar theory of gravity. We find the conditions on the potential by considering weak and strong gravity. The modified black hole solutions are obtained for generic potentials and the inverse problems on a black hole and on a spherical body (`pseudo-gravastar') are investigated.
The analysis of certain singularities in scalar-tensor gravity contained in a recent paper is completed, and situations are pointed out in which these singularities cannot occur.
A role of the scalar-matter direct coupling in the evolution of scalar-tensor gravity was studied. If the coupling functions in the generalized scalar-tensor gravity satisfy a definite equation the scalar-tensor gravity is reduced to Einstein's tensor gravity. We consider the issue in Jordan frame and then Einstein frame. It is shown that the coupling strength in the right hand side of the master equation obtained in Damour and Nordtvedt(1993) must be added by a coupling strength $\hatβ$ which characterizes the scalar-matter direct coupling. If a minimum of potential $\ln C(φ)$ does not coinci…
We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities…
Critical collapse in tensor-multi-scalar gravity theories is studied, and found that for any given target space all the theories conformally related belong to the same universal class. When only one scalar field is present, the universality is extended to include a class of non-linear gravity theories.
The scalar-tensor representation of nonlocally corrected gravity is considered. Some special solutions of the vacuum background equations were obtained that indicate to the nonequivalence of the initial theory and its scalar-tensor representation.
Wehus and Ravndal have argued that in d + 1 dimensions the general solution for gravity minimally coupled to a scalar field can not be explicitly written in Schwarzschild coordinates. We contest these objections.
A combined variable theory of gravity and scalar field is developed under ADM formulation by redefining new canonical conjugate variables (Φ, Π). It is a dynamical theory of the space-matter with implicit time dependence. Quantizing this new field theory results in quantization of geometry and scalar field combined.
In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction potential V, with a direct link to the semiclassical limit below the Planck scale. Additionally, we compute the Hamilton's equations of motion for this model, performing various consistency checks on the quantum theory.
Nordstrom's theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a 'Nordstrom-Katz' superpotential.
The canonical theory of gravity together with the scalar field is written as a combined variable theory in ADM form, in the classical and quantum theory. FLRW $κ= 0$ cosmology is rewritten in the combined variable theory.
We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.
We reformulate the recently proposed regularized version of Lovelock gravity in four dimensions as a scalar-tensor theory. By promoting the warp factor of the internal space to a scalar degree of freedom by means of Kaluza-Klein reduction, we show that regularized Lovelock gravity can be described effectively by a certain subclass of the Horndeski theory. Cosmological aspects of this particular scalar-tensor theory are studied. It is found that the background with a scalar charge is generically allowed. The consequences of this scalar charge are briefly discussed.
Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry
本文利用共形耦合标量场的精确几何测试标量-张量引力一阶热力学，发现有效引力温度呈现非单调行为，表明修正引力热行为比先前认为的更丰富。
A stochastic background of relic gravitational waves is achieved by the so called adiabatically-amplified zero-point fluctuations process derived from early inflation. In principle, it provides a distinctive spectrum of relic gravitational waves. In the framework of scalar-tensor gravity, we discuss the scalar modes of gravitational waves and the primordial production of this scalar component which is generated beside tensorial one. We discuss also the upper limit for such a relic scalar component with respect to the WMAP constraints.
The modified gravity with 1/R term (R being scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown the current inflation obtained in the modified gravity is affected by the existence the phantom field.
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and the matrix elements of the resulting operator between basis states are analytic coefficients. These achievements open the way for a consistent analysis of the Quantum Gravity corrections to the classical dynamics of gravity in the presence of a scalar field in a cosmological setting.
We present a geometric scalar theory of gravity. Our proposal will be described using the "background field method" introduced by Gupta, Feynman and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor - which is one of the main difficult…
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman expansion. We also analyze a number of variations of the same model, the corresponding discrete gravity path integrals, its generalization to the coupling of multiple scalar fields and discuss its possible applications to the extraction of effective cosmological dynamics from the full quantum gravity formalism, in the context of group field theory condensate cosmol…
Thermal stability of stealth and de Sitter spacetimes in scalar-tensor gravity
本文在标量-张量引力的一阶热力学框架下，分析了隐身解与德西特时空作为非零温度热平衡态的可能性，发现不存在稳定平衡态，进一步验证了广义相对论作为引力理论平衡态的特殊地位。
Modified inflationary models based on scalar-torsion gravity
本文在标量-挠率引力框架下，通过幂律参数化远平行引力与标量-挠率引力的偏差，研究其对不同暴胀模型的宇宙学动力学、标量场势和扰动参数的影响。
A generalization of the Hawking-Hayward quasilocal mass to scalar-tensor gravity is compared, in vacuo and for asymptotically flat stationary geometries, with a recent multipole expansion of the gravitational field. The quasilocal mass seen at spatial infinity coincides with the monopole term, lending credibility to this construct.
The main results are reviewed of relating the scalar field of noncompactified Kaluza-Klein gravity to the Higgs field of particle physics. The embedding of 4D spacetime in a 5D manifold can result in a variable cosmological 'constant' and particle masses tiny compared to the Planck value.
We study some aspects of three-dimensional gravity by extending Jackiw's scalar theory to (2+1)-dimensions and find a black hole solution. We show that in in general this teory does not possess a Newtonian limit except for special metric configurations.
We consider modified $f(R)$ gravity with a kinetic curvature scalar as a chiral self-gravitating model in a spherically symmetric spacetime. Most attention devoted to finding solutions for special case of scaling transformation when modified gravity transforms to Einstein frame from Jordan one. We proposed the method of determination of kinetic function for given scalar field dependence on space coordinate. New classes of solutions are found for special choice of $f(R)$ function.
Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry negative energy. A gauge-invariant analysis shows that the background Minkowski space is stable at the classical level with respect to linear scalar and tensor inhomogeneous perturbations.
We examine the compatibility of the Einstein minimally coupled self-interacting scalar field theory with the local tests of gravity. We find that apart from the trivial case of the Schwarzschild-de Sitter solution with constant scalar field the theory does not admit any other static solution, which is consistent with the solar system tests of gravity.
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity
该研究针对$F(R)$修改引力中的引力波标量模四极辐射展开，推导了相关显式表达式，以双星、反弹星为源计算了两类模的辐射，估算了标量模质量，指出未来引力波观测或可探测到该标量模。
We derive a family of exact solutions for bi-metric gravity with an exchange symmetry between the two metrics. In this two-parameter family of solutions the gravitational field is sourced by a time-independent massless scalar field. We find that the only limit in which the scalar field entirely vanishes is flat space. The regular Schwarzschild-solution is left with a scalar field hidden in the second metric's sector.
Within the scope of $f(R,\,T)$ gravity we have studied the interacting scalar and electromagnetic fields in a Bianchi type I universe. It was found that if the study is confined to the case $f(R,\,T) = R + λf(T)$, the system is completely given by the equations similar to Einstein gravity. Moreover, the present study imposes some severe restrictions on the field equations as well.
A short overview of black hole entropy in alternative gravitational theories is presented. Motivated by the recent attempts to explain the cosmic acceleration without dark energy, we focus on metric and Palatini f(R) gravity and on scalar-tensor theories.
We consider an approach to Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that differs from the original Brans-Dicke theory in many aspects and presents some new features.
We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous Letter [Phys. Rev. D 103, L121501 (2021)], upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart's first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, "temperature of gravity", viscosities, entropy density, plus an equation describing the "diffusion" to Einstein gravity. These quantities, still missing in the usual thermo…
We study our non-perturbative formalism to describe scalar gauge-invariant metric fluctuations by extending the Ponce de Leon metric.
Scalar perturbation represented by the Klein-Gordon field equation of the system of black holes in 2+1 dimensional Static charged dilaton gravity proposed by Chan and Mann is investigated analytically. The radial equation is analyzed near horizon and at the asymptotic region to show the absence of superradiance instability.
In the present paper we construct novel non-topological, spontaneously scalarized neutron stars in multi-scalar Gauss-Bonnet gravity with maximally symmetric target space, and nontrivial map $φ:spacetime \rightarrow target\ space$. The theory is characterized by the fact that for some classes of coupling functions the field equations allow solutions with trivial scalar field, which coincide with the general relativistic ones. For a certain range of parameters those solutions lose stability and new branches of solutions with nontrivial scalar field bifurcate from the trivial branch. For a given…
The notions of mass and range of a Brans-Dicke-like scalar field in scalar-tensor and f(R) gravity are subject to an ambiguity that hides a potential trap. We spell out this ambiguity and identify a physically meaningful and practical definition for these quantities. This is relevant when giving a mass to this scalar in order to circumvent experimental limits on the PPN parameters coming from Solar System experiments.
We present a reconstruction technique for models of $f(R)$ gravity from the Chaplygin scalar field in flat de Sitter spacetimes. Exploiting the equivalence between $f(R)$ gravity and scalar-tensor theories, and treating the Chaplygin gas as a scalar field model in a universe without conventional matter forms, the Lagrangian densities for the $f(R)$ action are derived. Exact $f(R)$ models and corresponding scalar field potentials are obtained for asymptotically de Sitter spacetimes in early and late cosmological expansion histories. It is shown that the reconstructed $f(R)$ models all have Gene…
Extended Gravity Theories and the Einstein-Hilbert Action
我讨论任意高阶引力理论和标量张量引力场方程和作用量的水平之间的关系。证明了$(2n+4)$阶引力与Brans-Dicke引力在动力学上是等价的，其中Brans-Dicke引力场和$n$进一步的标量场具有相互作用势.这个标量-张量作用量于是共形地等价于具有$n+1$标量场的爱因斯坦-希尔伯特作用量。这阐明了在许多标量场下，广义引力理论和广义相对论之间共形等价的性质和程度。
General relativity characterizes gravity as a geometric property exhibited on spacetime by massive objects while teleparallel gravity achieves the same results, at the level of equations, by taking a torsional perspective of gravity. Similar to f (R) theory, teleparallel gravity can also be generalized to f (T ), with the resulting field equations being inherently distinct from f (R) gravity in that they are second order, while in the former case they turn out to be fourth order. In the present case, a minimally coupled scalar field is investigated in the f (T ) gravity context for several for…
We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such…
We investigate the Cartan formalism in $F(R)$ gravity. $F(R)$ gravity has been introduced as a theory to explain cosmological accelerated expansion by replacing the Ricci scalar $R$ in the Einstein-Hilbert action with a function of $R$. As is well-known, $F(R)$ gravity is rewritten as a scalar-tensor theory by using the conformal transformation. Cartan $F(R)$ gravity is described based on the Riemann-Cartan geometry formulated by the vierbein. In the Cartan formalism, the Ricci scalar $R$ is divided into two parts, one derived from the Levi-Civita connection and the other from the torsion. Ass…
We study the Hamiltonian structure of the general parity-invariant model of three-dimensional gravity with propagating torsion, with eight parameters in the Lagrangian. In the scalar sector, containing scalar or pseudoscalar modes with respect to maximally symmetric background, the phenomenon of constraint bifurcation is observed and analyzed. The stability of the Hamiltonian structure under linearization is used to identify dynamically acceptable values of parameters.
It is shown that, when f'' is non-vanishing, metric f(R) gravity is completely equivalent to a scalar-tensor theory (with zero Brans-Dicke parameter) with respect to perturbations of de Sitter space, contrary to previous expectations. Moreover, the stability conditions of de Sitter space with respect to homogeneous and inhomogeneous perturbations coincide in most scalar-tensor theories, as is the case in metric f(R) gravity.
Scalar-tensor theories offer the prospect of explaining the cosmological evolution of the Universe through an effective description of dark energy as a quantity with a non-trivial evolution. In this work, we investigate this feature of scalar-tensor theories in the teleparallel gravity context. Teleparallel gravity is a novel description of geometric gravity as a torsional-rather than curvature-based quantity which presents a new foundational base for gravity. Our investigation is centered on the impact of a nontrivial input from the kinetic term of the scalar field. We consider a number of mo…
We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that in the ADM formalism Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.
Motivated by statements in the literature which contradict two general theorems, the static and spherically symmetric Brans solutions of scalar-tensor gravity are analyzed explicitly in both the Jordan and the Einstein conformal frames. Depending on the parameter range, these solutions describe wormholes or naked singularities but not black holes.
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such a broken symmetry state.
In the present note we show that the thin-wall approximation is not an assumption rather a necessary condition for satisfying Boucher's criteria for gravitational stability of the scalar potential.
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
Scalar induced gravitational waves in chiral scalar-tensor theory of gravity
研究手性标量-张量引力理论中标量诱导引力波，通过含CS项的PV拉格朗日量推导半解析表达式，发现其在峰值频率前后表现不同于GR并产生高度圆偏振。
The Tolman-Ehrenfest criterion of thermal equilibrium in scalar-tensor gravity
本文将Tolman-Ehrenfest热平衡判据推广到标量-张量引力，发现引力标量场不影响热平衡，表明热量不会在更强引力场中更多地沉降。
The explicit derivation for the orbital precession of the S2 star in the Galactic Center in the Scalar-Tensor-Vector Gravity is discussed and compared with previous research. The two different predictions are validated by numerically integrating the geodesic equations for a test particle.
Torsion and Nonmetricity in Scalar-Tensor Theories of Gravity
我们证明了由i）标量曲率和其他标量场的任意函数加上ii）与连接无关的动力学项和源项组成的作用量所导出的引力场方程，无论我们选择非度量性为零且具有非零挠率，还是相反，都是相同的.
In this paper we consider the cosmological inflation within scalar-tensor gravity and compare it with standard inflation based on general relativity. The difference is determined by the value of the parameter $Δ$. This approach is associated with using the special ansatz which links a function that defines a type of gravity with a scale factor of the universe.
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