我们考虑一个非旋转的，大质量的测试粒子的“压力”型，非测地线加速度所产生的某种一般类的引力理论与非最小耦合之间的物质和度量。由此产生的两体系统的轨道摄动的分析和数值研究。在其他长期效应中，两体相对距离的长期增加发生。原则上，它可能产生一个物理机制，地球从太阳的稳定衰退最近提出的解释在太古代的微弱的年轻的太阳Parasites。目前，理论家们还没有推导出模型的一些关键参数的显式表达式，例如依赖于系统物质分布的积分“电荷”$ξ$，以及与非最小函数$F$相连的4-矢量$K^μ=\{K^0,\boldsymbol{K}\}$。因此，我们唯象地将它们视为自由参数，并根据最新的太阳系行星历表初步推断出它们的容许值的一些指示。从修正$Δ\dot\varpi$到标准近日点岁差的最新测定中，我们初步获得了火星的$|ξK|\lesssim 0.1$ kg s $^{-1}$。根据对行星半长轴长期变化率的当前界限的猜测，我们得到了火星的$|ξK^0|\lesssim 1249$ kg s $^{-1}$。更有效的约束，可以通过重新处理相同的行星数据集与专用的动力学模型，包括在这里研究的影响，并明确估计相关的参数。COBE和GP-B地面卫星产生$|ξK|\lesssim 2\times 10^{-4}$ kg s $^{-1}$和$|ξK_0|\lesssim 2\times 10^{-10}$ kg s $^{-1}$。
英文摘要：
We consider a non-rotating, massive test particle acted upon by a "pressure"-type, non-geodesic acceleration arising from a certain general class of gravitational theories with nonminimal coupling between the matter and the metric. The resulting orbital perturbations for a two-body system are investigated both analytically and numerically. Among the other long-term effects, a secular increase of the two-body relative distance occurs. In principle, it may yield a physical mechanism for the steady recession of the Earth from the Sun recently proposed to explain the Faint Young Sun Paradox in the Archean eon. At present, the theorists have not yet derived explicit expressions for some of the key parameters of the model, such as the integrated "charge" $ξ$, depending on the matter distribution of the system, and the 4-vector $K^μ=\{K^0,\boldsymbol{K}\}$ connected with the nonminimal function $F$. Thus, we phenomenologically treat them as free parameters, and preliminarily infer some indications on their admissible values according to the most recent Solar System's planetary ephemerides. From the latest determinations of the corrections $Δ\dot\varpi$ to the standard perihelion precessions, estimated by the astronomers who produced the EPM2011 ephemerides without modeling the theory considered here, we preliminarily obtain $|ξK|\lesssim 0.1$ kg s$^{-1}$ for Mars. From guesses on what could be the current bounds on the secular rates of change of the planetary semimajor axes, we get $|ξK^0|\lesssim 1249$ kg s$^{-1}$ for Mars. More effective constraints could be posed by reprocessing the same planetary data sets with dedicated dynamical models including the effects studied here, and explicitly estimating the associated parameters. COBE and GP-B terrestrial satellites yield $|ξK|\lesssim 2\times 10^{-4}$ kg s$^{-1}$ and $|ξK_0|\lesssim 2\times 10^{-10}$ kg s$^{-1}$.
We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context, different choices of Lagrangian density will apparently result in different phases of the Universe. By carefully choosing the variables, we prove that there is an attractor solution to describe the late time accelerating universe when the modified gravity is chosen in a simple power-law form of the curvature scalar. We further examine the temperature evolutio…
It is well known that one cannot apply a conformal transformation to $f(T)$ gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for $f(T)$ gravity. Furthermore nonminimally coupled "teleparallel dark energy models" are not conformally equivalent to $f(T)$ gravity. However, it can be shown that $f(T)$ gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as $f(T,B)$ gravity, wh…
We construct gravitational modifications that go beyond Horndeski, namely theories with extended nonminimal derivative couplings, in which the coefficient functions depend not only on the scalar field but also on its kinetic energy. Such theories prove to be ghost-free in a cosmological background. We investigate the early-time cosmology and show that a de Sitter inflationary phase can be realized as a pure result of the novel gravitational couplings. Additionally, we study the late-time evolution, where we obtain an effective dark energy sector which arises from the scalar field and its exten…
In the present work we show that the second law of thermodynamics does not generally hold if the matter and gravitational fields are nonminimally coupled. We demonstrate this result by explicitly computing the evolution of the entropy of the matter fields in the case of a closed homogeneous and isotropic universe filled with dust and radiation, showing that, in this case, the sign of the entropy variation is determined by the evolution of the universe. The preservation of the second law of thermodynamics in these modified theories would require its generalization to account for a gravitational…
We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is nonminimally coupled to the matter Lagrangian. More specifically, we consider a Lagrangian of the form $L \sim f_1(Q) + f_2(Q) L_M$, where $f_1$ and $f_2$ are generic functions of $Q$, and $L_M$ is the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. The motivati…
We generalize the mechanism for gravitational baryogensis in the context of $f(R)$ theories of gravity, including a nonminimal coupling between curvature and matter. In these models, the baryon asymmetry is generated through an effective coupling between the Ricci scalar curvature and the net baryon current that dynamically breaks Charge Conjugation, Parity and Time Reversal (CPT) invariance. We study the combinations of characteristic mass scales and exponents for both non-trivial functions present in the modified action functional and establish the allowed region for these parameters: we fin…
Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
Istituto per le Applicazioni del Calcolo, CNR（意大利国家研究委员会计算应用研究所）；INFN - Laboratori Nazionali di Frascati (LNF)（意大利国家核物理研究所弗拉斯卡蒂国家实验室）；Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto（波尔图大学理学院物理与天文系）；Centro de Física das Universidades do Minho e do Porto（米尼奥大学和波尔图大学物理中心）；Universitá di Camerino（卡梅里诺大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；ICRANet（国际相对论天体物理中心网络）
Four-dimensional homogeneous static and rotating black strings in dynamical Chern-Simons modified gravity, with and without torsion, are presented. Each solution is supported by a scalar field that depends linearly on the coordinate that span the string. The solutions are locally $\mbox{AdS}_3 \times \mathbb{R}$ and they represent the continuation of the Bañados-Teitelboim-Zanelli black hole. Moreover, they belong to the so-called Chern-Simons sector of the space of solutions of the theory, since the Cotton tensor contributes nontrivially to the field equations. The case with nonvanishing tors…
We study a single field inflationary model modified by a non-minimal coupling term between the Ricci scalar $R$ and the scalar field $φ$ in the context of constant-roll inflation. The first-order formalism is used to analyse the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, $W=W(φ)$ and $Z=Z(φ)$, which lead to the reduction of the equations of motion to first-order differential equations. The approach can be applied to a wide range of cosmological situations since it directly relates the …
Within $F\left( B^2\right)$ modified Weyl gravity, we consider a model of a spin-$1/2$ electric charge consisting of interior and exterior regions. The interior region is determined by quantum gravitational effects whose approximate description is carried out using Weyl gravity nonminimally coupled to a massless Dirac spinor field. The interior region is embedded in exterior Minkowski spacetime, and the joining surface is a two-dimensional torus. It is shown that mass, electric charge, and spin of the object suggested may be the same as those for a real electron.
The Brans-Dicke-like field of scalar-tensor gravity can be described as an imperfect fluid in an approach in which the field equations are regarded as effective Einstein equations. After completing this approach we recover, as a special case, the known effective fluid for a scalar coupled nonminimally to the Ricci curvature and we describe the imperfect fluid equivalent of f(R) gravity. A symmetry of electrovacuum Brans-Dicke gravity is translated into a symmetry of the corresponding effective fluid. The discussion is valid for any spacetime geometry.
Gauss-Bonnet-dilatonic coupling in four dimension plays an important role to explain late time cosmic evolution. However, this term is an outcome of low energy string effective action and thus ought to be important in the early universe too. Unfortunately, phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to higher order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation wit…
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a massless vector field, nonperturbative effects can arise in compact stars. We find solutions describing stars with nontrivial vector field configurations, some of which are associated to an instability, while others are not. The vector field can be interpreted either as the electromagnetic field, or as a hidden vector field weakly coupled with the standard mo…
Black hole shadows in nonminimally coupled Weyl connection gravity
Universidade dos Açores（亚速尔群岛大学）；Centro de Física das Universidades do Minho e do Porto（米尼奥与波尔图大学物理中心）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院空间天体物理与空间科学研究所）
We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration…
We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coo…
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a nonminimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and…
The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean's criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.
The extended scalar-tensor and vector-tensor theories admit black hole solutions with the nontrivial profiles of the scalar and vector fields, respectively. The disformal transformation maps a solution in a class of the scalar-tensor or vector-tensor theories to that in another class, and hence it can be a useful tool to construct a new nontrivial solution from the known one. First, we investigate how the stationary and axisymmetric solutions in the vector-tensor theories without and with the $U(1)$ gauge symmetry are disformally transformed. We start from a stationary and axisymmetric solutio…
In this proceeding, we review modified theories of gravity with a curvature-matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a non-vanishing covariant derivative of the energy-momentum tensor, that implies non-geodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy-momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter crea…
As a first step towards the calculation of waveform of Extreme Mass Ratio Inspirals for Modified Gravity theories, we calculate the orbital frequencies of a Small Compact Object inspiralling into a super massive blackhole for a Nonlocal gravity model. The small compact object moves along an orbit which can be approximated to a geodesic of the background spacetime due to large mass ratio of central blackhole to Small Compact Object. In General Relativity, the fundamental orbital frequencies $Ω_r,\;Ω_θ$ and $Ω_ϕ$ can be calculated by solving geodesic equations of the Kerr metric. If we formulate…
Unified dynamical system formulations for $f(R,ϕ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation
Institute of Research and Development, Duy Tan University（延大大学研发研究所）；Faculty of Natural Sciences, Duy Tan University（延大大学自然科学学院）；Center for Space Research, North-West University（西北大学太空研究中心）；Department of Applied Mathematics, University of Campinas（坎皮纳斯大学应用数学系）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）
A previous work found that a nonminimally coupled theory of gravity can, under appropriate conditions, give rise to an additional contribution to the field equations interpreted as dark matter [1]: in particular, the density of this dark matter component was found to scale as a power of the density of visible matter. However, no explicit solution for the modified field equations was provided, so that a direct computation of the specific density profile followed by visible matter is missing. This question is now addressed: analytical solutions to the modified field equations are derived in the …
Gravitational wave (GW) observations provide insight into the gravity regime. These observations relies on the comparison of the data to the GWs model, which depends on the orbital evolution of the binary systems. In this paper, we study the orbital evolution of eccentric compact binaries within screened modified gravity, which is a kind of scalar-tensor theory with screening mechanisms. According to the Noether's theorem, from the theory's GW action, we compute the angular momentum flux both as a function of the fields in the theory and as a function of the multipole moments of a N-body syste…
Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting theory and compute an effective $\frac{1}{c^2}$\,-Hamiltonian and leading post-Newtonian corrections to the trajectory and spin. Gravimagnetic moment causes the same precession of spin ${\bf S}$ as a fictitious rotation of the central body with angular momentum ${\bf J}=\frac{M}{m}{\bf S}$. So the modified equations imply a number of qualitatively new effects, t…
For many classes of astronomical and astrophysical binary systems, long observational records of their radial velocity $V$, which is their directly observable quantity, are available. For exoplanets close to their parent stars, they cover several full orbital revolutions, while for wide binaries like, e.g., the Proxima/$α$ Centauri AB system, only relatively short orbital arcs are sampled by existing radial velocity measurements. Here, the changes $ΔV$ induced on a binary's radial velocity by some long-range modified models of gravity are analytically calculated. In particular, extra-potential…
