Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a minimally coupled scalar field has been performed. To the leading order, vacuum Einstein's equation along with the functional Schrodinger equation for the matter field, propagating in the background of classical curved space are obtained. The Schrodinger equation is solved for a quartic potential. It is observed that the wave-functional admits the wormhole boundary condition even for large negative values of the coupling constant epsilon. For conformal coupling epsilon = 1/6, the Hawking-Page wormhole solution is recovered.
In this work we study how nonminimally coupled theories of gravity modify the usual Friedmann equation, and develop two methods to treat these. The ambiguity in the form of the Lagrangian density of a perfect fluid is emphasized, and the impact of different dominant matter species is assessed. The Cosmological Constant problem is also discussed.
Weyl gravity in the presence of a non-minimal matter-curvature coupling is presented. Some properties arising from the non-metricity give rise to a second order theory whose vacuum is compatible with a cosmological constant, under conditions on the vector field.
In this work we explore the viability of nonminimally coupled matter- curvature gravity theories, namely the conditions required for the absence of tachyon instabilities and ghost degrees of freedom. We contrast our finds with recent claims of a pathological behaviour of this class of models, which resorted to, in our view, an incorrect analogy with k-essence.
We study the possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity. From an E^3-invariant Robertson-Walker metric we propose an Ansatz for the vector field, allowing us to study the evolution of the system. We study the behaviour of the equations of motion using the methods of the theory of dynamical systems and find exponential inflationary regimes.
We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the theory in the sense that the resulting equations of motion depend on the choice of a tetrad. For the assumed static spherically symmetric spacetime, we find a tetrad which leads to a self-consistent set of equations, and we construct the self-gravitating configurations of the scalar field---boson stars. The resulting configurations develop anisotropic principal pressures and satisfy the dominant ener…
We extend the analysis of Chiba, Smith and Erickcek \cite{CSE} of Solar System constraints on $f(R)$ gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize $f(R)$ theories by replacing the action functional of General Relativity (GR) with a more general form involving two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. While the function $f^1(R)$ is a nonlinear term in the action, analogous to $f(R)$ gravity, the function $f^2(R)$ yields a NMC between the matter Lagrangian density $\LL_m$ and the scalar curvature. The developed method allows f…
We consider a nonminimally coupled curvature-matter gravity theory at the Solar System scale. Both a fifth force of Yukawa type and a further non-Newtonian extra force that arises from the nonminimal coupling are present in the solar interior and in the solar atmosphere up to interplanetary space. The extra force depends on the spatial gradient of space-time curvature R. The conditions under which the effects of such forces can be screened by the chameleon mechanism and be made consistent with Cassini measurement of PPN parameter $γ$ are examined. This consistency analysis requires a specific …
A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes non-polynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the c…
A field-theoretic model for a highly compact object that mimicks a black hole is found for the gravitationally interacting system of a boson star and a global monopole which are nonminimally coupled to gravity. According to the strength of the nonlinear gravitational effects and the gravitational backreaction, three distinct coupling regimes are featured: weak, mild and strong. In the strong coupling regime we show that a repulsive monopole stabilizes an attractive boson star and the resulting configuration exhibits large energy density, large (and negative) principal pressures, large compactn…
Analytical solutions of nonminimally coupled scalar field cosmology corresponding to critical scalar field values constitute a potential challenge to the recent first-order thermodynamics of scalar-tensor gravity (a formalism picturing general relativity as the zero-temperature equilibrium state for modified gravity). The critical solutions are unstable with respect to homogeneous perturbations, hence unphysical.
We perform a LQC-quantization of the FRW cosmological model with nonminimally coupled scalar field. Making use of a canonical transformation, we recast the theory in the minimally coupled form (Einstein frame), for which standard LQC techniques can be applied to find the physical Hilbert space and the dynamics. We then focus on the semiclassical sector, obtaining a classical effective Hamiltonian, which can be used to study the dynamics. We show that the classical singularity is replaced by a "mexican hat"-shaped bounce, joining the contracting and expanding branches. The model accommodates Hi…
In this work we have studied a cosmological model based on a quintom dark energy model non-minimally coupled with gravity, endowed with a specfic potential energy of the exponential squared type. For this specific type of potential energy and non-minimal coupling, the dynamical properties are analyzed and the corresponding cosmological effects are discussed. Considering the linear stability method, we have investigated the dynamical properties of the phase space structure, determining the physically acceptable solutions. The analysis showed that in this model we can have various cosmological e…
In this note we comment on remarks about our recent effort to understand the specificities of the Boltzmann equation in the context of the alternative theories of gravity with non-minimal coupling between curvature and matter.
In this work we show the existence of traversable wormhole and time-machine solutions in a modified theory of gravity where matter and curvature are nonminimally coupled. Those solutions present a nontrivial redshift function and exist even in the presence of ordinary matter which satisfies the dominant energy condition.
In a recent paper, Hod proved that spherically symmetric Dirichlet reflecting compact stars cannot support static nonminimally coupled scalar fields. In the present paper, we study the validity of no hair theorems for compact stars with Neumann surface boundary conditions. We find that Neumann compact stars cannot support static massive scalar field hairs with a generic dimensionless nonminimal coupling parameter.
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 discuss constraints to some nonminimally (NMC) coupled curvature-matter models of gravity by means of Solar System experiments. First we discuss a NMC gravity model which constitutes a natural extension of $1/R^n$ gravity to the nonminimally coupled case. Such a NMC gravity model is able to predict the observed accelerated expansion of the Universe. Differently from the $f(R)=1/R^n$ gravity case, which is not compatible with Solar System observations, it turns out that this NMC model is a viable theory of gravity. Then we consider a further NMC gravity model which admits Minkowski spacetime…
When the Higgs field is nonminimally coupled to gravity, there exists a family of spherically symmetric particlelike solutions to the field equations. These monopoles are the only globally regular and asymptotically flat distributions with finite energy of the Higgs field around compact objects. Moreover, spontaneous scalarization is strongly amplified for specific values of their mass and compactness.
We consider the spatially flat Friedmann-Lemaitre-Robertson-Walker space time in the teleparallel model of gravity and assume that the universe is filled nearly by cold dark matter and a nonminimally coupled scalar field with a power-law potential as dark energy. We investigate the possibility that the universe undergoes a transition from quintessence to phantom phase. An analytical solution for the scalar field is obtained and necessary conditions required for such a transition are discussed.
In the framework of Higgs inflation, we consider the electromagnetic field nonminimally coupled to gravity via the parity-preserving $\propto RF^{2}$ and parity-violating $\propto RF\tilde{F}$ terms. Using the perturbation theory to the leading order in these couplings, we study the generation of the electromagnetic field during the inflation stage. We derive the effective kinetic and axial coupling functions arising in the Einstein frame in the usual metric as well as Palatini formulations of gravity. For both formulations, we determine the power spectrum, energy density, and helicality of th…
The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. This work expands upon previous results, extending the framework developed there to compute corrections up to order $O(1/c^4)$ of the $00$ component of the metric tensor. It is shown that additional contributions arise due to both the non-linear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including exponential contributions that cannot be expressed as an e…
In three dimensions, we consider the Einstein-Maxwell Lagrangian dressed by a nonminimally coupled scalar field in New Massive Gravity. For this theory, we provide two families of electrically charged Lifshitz black holes where their metric functions depend only on an integration constant. We calculate their masses using the quasilocal approach, as well as their entropy and electric charge. These charged configurations are interpreted as extremal in the sense that the mass vanishes identically while the entropy and electric charge are non zero thermodynamic quantities. Using these examples, we…
By using Bianchi I type of homogenous and anisotropic background metric having cylindrical symmetry in $x$ direction of a local cartesian coordinates system, we solve metric field equations for a non-minimally coupled Einstein-Maxwell gravity. To do so we choose long wavelength EM waves where spatial dependence of the waves are negligible at the expansion duration. Motivation of this work is study directional effects of the EM vector potential on anisotropy trajectory of the space time expansion scale factor. This problem is checked just for de Sitter inflationary epoch because of its importan…
We study dynamics of a dark energy component nonminimally coupled to gravity on a moving domain wall. We use this setup to explain late-time accelerated expansion and crossing of the phantom divide line by the equation of state parameter of this non-minimally coupled dark energy component. By analyzing parameter space of the model, we show that this model accounts for accelerated expansion and crossing of the phantom divide line with a suitable fine-tuning of the nonminimal coupling. Then we study the issue of bouncing solutions in this framework.
In extended models of gravity a nonminimal coupling to matter has been assumed to lead to irreversible particle creation. In this paper we challenge this assumption. We argue that a non-minimal coupling of the matter and gravitational sectors results in a change in particle-momentum on a cosmological timescale, irrespective of particle creation or decay. We further argue that particle creation or decay associated with a non-minimal coupling to gravity could only happen as a result of significant deviations from a homogeneous Friedmann-Robertson-Walker geometry on microscopic scales, and provid…
In this paper, a new generalised gravity-matter coupled theory of gravity is presented. This theory is constructed by assuming an action with an arbitrary function $f(T,B,L_m)$ which depends on the scalar torsion $T$, the boundary term $B=\nabla_μT^μ$ and the matter Lagrangian $L_m$. Since the function depends on $B$ which appears in $R=-T+B$, it is possible to also reproduce curvature-matter coupled models such as $f(R,L_m)$ gravity. Additionally, the full theory also contains some interesting new teleparallel gravity-matter coupled theories of gravities such as $f(T,L_m)$ or $C_1 T+ f(B,L_m)…
We investigate homogeneous and isotropic cosmological models in scalar-tensor theories of gravity where two scalar fields are nonminimally coupled to the geometry. Exact solutions are found, by Noether symmetries, depending on the form of couplings and self-interaction potentials. An interesting feature is that we deal with the Brans-Dicke field and the inflaton on the same ground since both are nonminimally coupled and not distinguished {\it a priori} as in earlier models. This fact allows to improve dynamics to get successful extended inflationary scenarios. Double inflationary solutions are…
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）
Here, we report pp waves configurations of three-dimensional gravity for which a scalar field nonminimally coupled to them acts as a source. In absence of self-interaction the solutions are gravitational plane waves with a profile fixed in terms of the scalar wave. In the self-interacting case, only power-law potentials parameterized by the nonminimal coupling constant are allowed by the field equations. In contrast with the free case the self-interacting scalar field does not behave like a wave since it depends only on the wave-front coordinate. We address the same problem when gravitation is…
The four laws of black hole mechanics have been put forward for a long time. However, the zeroth law, which states that the surface gravity of a stationary black hole is a constant on the event horizon, still lacks universal proof in various modified gravitational theories. In this paper, we study the zeroth law {in a special Horndeski gravity}, which is an interesting gravitational theory with a nonminimally coupled scalar field. After assuming that {the nonminimally coupled scalar field has the same symmetries with the spacetime,} the minimally coupled matter fields satisfy the dominant ener…
We consider the non-Gaussianity of the nonlinear density perturbations in a single-field inflationary model when a scalar field couples nonminimally with gravity. Gravity theories with a nonminimal coupling can be transformed into the Einstein gravity with canonical kinetic terms by using a suitable conformal transformation. We find that a nonlinear generalization of the gauge invariant quantity $ζ_i$ is invariant under the conformal transformation. With the help of this conformal invariant property, we calculate the non-Gaussianity, which is characterized by a nonlinear parameter $f_{NL}$, in…
In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the Loop Quantum Gravity. From our results, we can check that the Self-Dual Black Hole is stable under the scalar perturbations when assuming small values for the …
I study a fresh inflationary model with a scalar field nonminimally coupled to gravity. An example is examined. I find that, as larger is the value of $p$ (the power of the scale factor), smaller (but larger in its absolute value) is the necessary value of the coupling $ξ$ to the inflaton field fluctuations can satisfy a scale invariant power spectrum.
A static, spherically symmetric, asymptotically flat spacetime may allow for circular, closed null-geodesics which are said to belong to a photon sphere. In the context of gravitational lensing in the strong deflection regime, the presence of a photon sphere leads to an unbounded angle of deflection of light (multiple turns) and formation of relativistic images. In this paper, we show that photon spheres may form in some configurations of boson stars constructed with a free massive complex scalar field nonminimally coupled to gravity. Assuming that the boson star is transparent to light, photo…
In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant $ξ$ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant $ξ$. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral ferm…
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…
In the paper we investigate observational constraints on coupling to gravity constant parameter $ξ$ using distant supernovae SNIa data, baryon oscillation peak (BOP), the cosmic microwave background radiation (CMBR) shift parameter, and $H(z)$ data set. We estimate the value of this parameter to constrain the extended quintessence models with nonminimally coupled to gravity phantom scalar field. The combined analysis of observational data favors a value of $ξ$ which lies in close neighborhood of the conformal coupling. While our estimations are model dependent they give rise to a indirect boun…
A nonminimally coupled quintessence dark energy in teleparallel model of gravity is considered. It is clarified how a matter dominated universe with initial negligible dark energy density can evolve to a late time de Sitter space-time via the $Z_2$ symmetry breaking.
We examine the constraints on the Yukawa regime from the non-minimally coupled curvature-matter gravity theory arising from deep underwater ocean experiments. We consider the geophysical experiment of Zumberge et al. of 1991 for searching deviations of Newton's inverse square law in ocean. In the context of non-minimally coupled curvature-matter theory of gravity the results of Zumberge et al. can be used to obtain an upper bound both on the strength $α$ and range $λ$ of the Yukawa potential arising from the non-relativistic limit of the non-minimally coupled theory. The existence of an upper …
We investigate the stability of a free scalar field nonminimally coupled to gravity under linear perturbations in the spacetime of a charged spherical shell. Our analysis is performed in the context of quantum field theory in curved spacetimes. This paper completes previous analyses which considered the exponential enhancement of vacuum fluctuations in the spacetime of massive shells.
Self-gravitating scalar fields with nonminimal coupling to gravity and having a quartic self-interaction are considered in the domain of outer communications of a static black hole. It is shown that there is no value of the nonminimal coupling parameter $ζ$ for which nontrivial static black hole solutions exist. This result establishes the correctness of Bekenstein ``no-scalar-hair'' conjecture for quartic self-interactions.
We derive the Boltzmann equation in the context of a gravity theory with non-minimal coupling between matter and curvature. We show that as the energy-momentum tensor is not conserved in these theories, it follows a condition on the normalisation of an homogeneous distribution function. The Boltzmann H-theorem is preserved such that the entropy vector flux is still a non-decreasing function in these theories. The case of an homogeneous and isotropic Universe is analysed.
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）
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…
It is proved that spherically symmetric asymptotically flat neutral black holes cannot support spatially regular static configurations made of massive scalar fields with non-minimal coupling to gravity. Interestingly, our compact no-hair theorem is valid for generic values of the dimensionless physical parameter $ξ$ which quantifies the strength of coupling between the scalar field and the spacetime curvature.
It has recently been proved that horizonless compact stars with reflecting boundary conditions {\it cannot} support spatially regular matter configurations made of minimally coupled scalar fields, vector fields, and tensor fields. In the present paper we extend this intriguing no-hair property to the physically interesting regime of scalar fields with {\it nonminimal} coupling to gravity. In particular, we prove that static spherically symmetric configurations made of nonminimally coupled massless scalar fields cannot be supported by compact reflecting stars.
In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by ${\mathcal L}_m=T$, where $T$ is the trace of the energy-momentum tensor. We show that our results have profound implications for theories of gravity where the m…
