We show a curvaton model, in which the curvaton has a nonminimal derivative coupling to gravity. Thanks to such a coupling, we find that the scale-invariance of the perturbations can be achieved for arbitrary values of the equation-of-state of background, provided that it is nearly a constant. We also discussed about tensor perturbations, the local non-Gaussianities generated by the nonminimal derivative coupling curvaton model, as well as the adiabatic perturbations which are transferred from the field perturbations during the curvaton decay.
We investigate two-field inflationary models in which scalar cosmological pertubations are generated via a spectator field nonminimally coupled to gravity, with the particular emphasis on curvaton scenarios. The principal advantage of these models is in the possibility to tune the spectator spectral index via the nonminimal coupling. Our models naturally yield red spectrum of the adiabatic perturbation demanded by observations. We study how the nonminimal coupling affects the spectrum of the curvature perturbation generated in the curvaton scenarios. In particular we find that for small, negat…
In this paper, we continue our study on the curvaton model with nonminimal derivative coupling (NDC) to Einstein gravity proposed in our previous work, focusing on the reheating mechanism. We found that according to whether the curvaton has dominated the background after the end of inflation, it will have two different behaviors of evolution, which should be the general property of curvaton with nonminimal couplings. This will cause diffferent rates of particle creation, which goes on via the parametric resonance process. The reheating temperature is estimated for both cases in which reheating…
In our previous work \cite{Feng:2013pba}, we have shown a curvaton model where the curvaton has a nonminimal derivative coupling to gravity. Such a coupling could bring us scale-invariance of the perturbations for wide range constant values of the equation-of-state of the cosmic background at the early time. In this paper, we continue our study by fully analyzing its perturbations up to the third order. Apart from the usual 2-point correlation function that has already been calculated in \cite{Feng:2013pba}, we have also taken into account the 3-point correlation functions including pure scala…
We consider a model with nonminimal derivative coupling of inflaton to gravity. The reheating process during rapid oscillation of the inflaton is studied and the reheating temperature is obtained. Behaviors of the inflaton and produced radiation in this era are discussed.
An exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison-Zel'dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model pr…
We investigate the existence of scalar hair in the background of a reflecting star. The kinetic part of the scalar field is nonminimally coupled to the Einstein tensor. For both the Dirichlet and the Neumann boundary conditions, we study the no-hair theorem. For the massless case, we show that there is no scalar hair, and in the massive case conditions leading to the no-hair theorem are specified.
We consider static spherically symmetric wormhole configurations in a gravitational theory of a scalar field with a potential $V(ϕ)$ and nonminimal derivative coupling to the curvature describing by the term $(εg_{μν} + κG_{μν}) ϕ^{,μ}ϕ^{,ν}$ in the action. We show that the flare-out conditions providing the geometry of a wormhole throat could fulfilled both if $ε=-1$ (phantom scalar) and $ε=+1$ (ordinary scalar). Supposing additionally a traversability, we construct numerical solutions describing traversable wormholes in the model with arbitrary $κ$, $ε=-1$ and $V(ϕ)=0$ (no potential). The tr…
We investigate the slow-roll inflation in the nonminimal derivative coupling (NDC) model with exponential, quadric, and quartic potentials. It was known that this model provides an enhanced slow-roll inflation induced by gravitationally enhanced friction even for a steep exponential potential. In the phase portrait, the inflationary attractor is described by the slow-roll equation. Introducing the autonomous form, the inflation is regarded as an emergence from the saddle point and it leaves this fixed point along the slow-roll equation. We show explicitly that if one uses the NDC with potentia…
We revisit the reheating mechanism after the end of inflation in the non-minimal derivative coupling (NDC) to gravity with quadratic potential. This is because the inflaton of the NDC should describe the slow-roll inflation as well as the preheating stage after the end of inflation. We point out that the non-periodic inflaton solution implies the absence of parametric resonance, compared to the periodic oscillating inflaton for the canonical coupling (CC) to gravity. Furthermore, it is demonstrated that narrow and broad parametric resonances do not appear after the end of inflation in the NDC …
In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry- based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the Renormalization Group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonmin…
We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity. Since cosmological constant is taken into account it allowed us not only derive static black hole with spherical horizon but also to obtain topological solutions with non-spherical horizons. The obtained metrics are thoroughly analyzed, namely for different distances and types of topology of horizon. To investigate singularities of the metrics Kretschmann scalar is used and it is shown that the character of singularity depends on the type of topolog…
We study a nonminimal derivative coupling (NMDC) of scalar field, where the scalar field is coupled to curvature tensor in the five dimensional universal extra dimension model. We apply the Einstein equation and find its solution. First, we consider a special case of pure free scalar field without NMDC and we find that for static extradimension, the solution is equivalent to the standard cosmology with stiff matter. For a general case of pure free scalar field with NMDC, we find that the de Sitter solution is the solution of our model. For this solution, the scalar field evolves linearly in ti…
We investigate the inflaton decay and reheating period after the end of inflation in the non-minimal derivative coupling (NDC) model with chaotic potential. In general, this model is known to provide an enhanced slow-roll inflation caused by gravitationally enhanced friction. We find violent oscillations of Hubble parameter which induces oscillations of the sound speed squared, implying the Lagrangian instability of curvature perturbation $ζ$ under the comoving gauge $φ=0$. Also, it is shown that the curvature perturbation blows up at $\dotϕ=0$, leading to the breakdown of the comoving gauge a…
We show that the primordial gravitational wave with scale-invariant spectrum might emerge from a nearly Minkowski space, in which the gravity is asymptotic-past free. We illustrate it with a model, in which the derivative of background scalar field nonminimally couples to gravity. We also show that since here the tensor perturbation is dominated by its growing mode, mathematically our slowly expanding background is conformally dual to the matter contraction, but there is no the anisotropy problem.
The nonminimal coupling of the kinetic term to Einstein's tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parametrized post-Newtonian (PPN) parameters for the scalar--tensor theory of gravity with nonminimally derivative coupling. We find that under experimental constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein's general relativity in the order of $10^{-20}$, and the effect of the nonminimal coupling is negligible if we take the scalar field as dynamical dark energy. With the …
We have obtained an exact solution for a static black hole in the theory with nonminimal derivative coupling of a scalar field and gravity with a power-law Maxwell field minimally coupled to gravity. Supposing that the black hole might be topological we examined the obtained solution. We also investigated black hole thermodynamics using Wald procedure for calculation of entropy of the black hole.
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift an…
We study the dynamics of a generalized inflationary model in which both the scalar field and its derivatives are coupled to the gravity. We consider a general form of the nonminimal derivative coupling in order to have a complete treatment of the model. By expanding the action up to the second order in perturbation, we study the spectrum of the primordial modes of the perturbations. Also, by expanding the action up to the third order and considering the three point correlation functions, the amplitude of the non-Gaussianity of the primordial perturbations is studied both in equilateral and ort…
We obtain topological black hole solutions in scalar-tensor gravity with nonminimal derivative coupling between scalar and tensor components of gravity and power-law Maxwell field minimally coupled to gravity. The obtained solutions can be treated as a generalization of previously derived charged solutions with standard Maxwell action \cite{Feng_PRD16}. We examine the behaviour of obtained metric functions for some asymptotic values of distance and coupling. To obtain information about singularities of the metrics we calculate Kretschmann scalar. We also examine the behaviour of gauge potentia…
For a theory in which a scalar field $ϕ$ has a nonminimal derivative coupling to the Einstein tensor $G_{μν}$ of the form $ϕ\,G_{μν}\nabla^μ\nabla^ν ϕ$, it is known that there exists a branch of static and spherically-symmetric relativistic stars endowed with a scalar hair in their interiors. We study the stability of such hairy solutions with a radial field dependence $ϕ(r)$ against odd- and even-parity perturbations. We show that, for the star compactness ${\cal C}$ smaller than $1/3$, they are prone to Laplacian instabilities of the even-parity perturbation associated with the scalar-field …
We propose an inflationary scenario based on the concurrent presence of non-minimal coupling (NMC) and generalized non-minimal derivative coupling (GNMDC), in the context of Higgs inflation. The combined construction maintains the advantages of the individual scenarios without sharing their disadvantages. In particular, a long inflationary phase can be easily achieved due to the gravitational friction effect owed to the GNMDC, without leading to trans-Planckian values and unitarity violation. Additionally, the tensor-to-scalar ratio remains to low values due to the NMC contribution. Finally, t…
We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd- parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solu…
The cubic scalar field theory admits the bell-shaped solitary wave solutions which can be interpreted as massive Bose particles. We rule out the nonminimal p-brane action for such a solution as the point particle with curvature. When quantizing it as the theory with higher derivatives, it is shown that the corresponding quantum equation has SU(2) dynamical symmetry group realizing the exact spin-coordinate correspondence. Finally, we calculate the quantum corrections to the mass of the bell boson which can not be obtained by means of the perturbation theory starting from the vacuum sector.
We study the possibility of the Primordial Black Holes (PBHs) formation with the aim of finding a considerable fraction of Dark Matter (DM), using the gravitationally enhanced friction mechanism which arises from a nonminimal derivative coupling between the scalar field and the gravity. Assuming the nonminimal coupling parameter as a special function of the scalar field and considering the potential of natural inflation, we find three parameter sets that produce a period of ultra slow-roll inflation. This leads to sufficiently large enhancement in the curvature power spectra to form PBHs. We s…
We study static non-critical hairy black holes of four dimensional gravitational model with nonminimal derivative coupling and a scalar potential turned on. By taking an ansatz, namely, the first derivative of the scalar field is proportional to square root of a metric function, we reduce the Einstein field equation and the scalar field equation of motions into a single highly nonlinear differential equation. This setup implies that the hair is secondary-like since the scalar charge-like depends on the non-constant mass-like quantity in the asymptotic limit. Then, we show that near boundaries …
Scalar-tensor theory of gravity with nonlinear electromagnetic field, minimally coupled to gravity is considered and static black hole solutions are obtained. Namely, power-law and Born-Infeld nonlinear Lagrangians for the electromagnetic field are examined. Since the cosmological constant is taken into account, it allowed us to investigate so-called topological black holes. Black hole thermodynamics is studied, in particular temperature of the black holes is calculated and examined and the first law of thermodynamics is obtained with help of Wald's approach.
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…
We consider a gravitational theory of a scalar field $ϕ$ with nonminimal derivative coupling to curvature. The coupling terms have the form $κ_1 Rϕ_{,μ}ϕ^{,μ}$ and $κ_2 R_{μν}ϕ^{,μ}ϕ^{,ν}$ where $κ_1$ and $κ_2$ are coupling parameters with dimensions of length-squared. In general, field equations of the theory contain third derivatives of $g_{μν}$ and $ϕ$. However, in the case $-2κ_1=κ_2\equivκ$ the derivative coupling term reads $κG_{μν}ϕ^{,mu}ϕ^{,ν}$ and the order of corresponding field equations is reduced up to second one. Assuming $-2κ_1=κ_2$, we study the spatially-flat Friedman-Robertso…
We obtain a slowly rotating black hole solution in the scalar-tensor theory of gravity with nonminimal derivative coupling to the Einstein tensor. Properties of the obtained solution have been examined carefully. We also investigate the thermodynamics of the given black hole. To obtain thermodynamic functions, namely its entropy we use the Wald procedure which is suitable for quite general diffeomorphism-invariant theories. The applied approach allowed us to obtain the expression for entropy and the first law of black hole thermodynamics. Having introduced thermodynamic pressure which is relat…
By starting with a two-fields model in which the fields and their derivatives are nonminimally coupled to gravity, and then by using a conformal gauge, we obtain a model in which the derivatives of the canonically normalized field are nonminimally coupled to gravity. By adopting some appropriate functions, we study two cases with constant and E-model nonminimal derivative coupling, while the potential in both cases is chosen to be E-model one. We show that in contrary to the single field $α$-attractor model that there is an attractor \textit{point} in the large $N$ and small $α$ limits, in our…
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 investigate the generation of Primordial Black Holes (PBHs) with the aid of gravitationally increased friction mechanism originated from the NonMinimal field Derivative Coupling (NMDC) to gravity framework, with the quartic potential. Applying the coupling parameter as a two-parted function of inflaton field and fine-tuning of five parameter assortments we can acquire ultra slow-roll phase to slow down the inflaton field due to high friction. This enables us to achieve enough enhancement in the amplitude of curvature perturbations power spectra to generate PBHs with different masses. The re…
The coupling of gravity to a scalar field raises a number of interesting questions of principle since the usual minimal coupling obtained by replacing ordinary derivatives with covariant derivatives is not available -- they are the same operation on scalar fields. Conformal couplings in the Lagrangian proportional to $ϕ^2 R$ have been suggested before, usually to maintain conformal invariance for massless scalar fields, but at the cost of breaking the equivalence principle. Here we give intuitive arguments for the appearance of such a term due to fluctuations of scalar particles about their cl…
In this work we study a nonlinear gauged O(3)-sigma model with both minimal and nonminimal coupling in the covariant derivative. Using an asymmetric scalar potential, the model is found to exhibit both topological and non-topological soliton solutions in the Bogomol'nyi limit.
Recently, exact solutions of wormhole geometries supported by a nonminimal curvature-matter coupling were found, where the nonminimal coupling minimizes the violation of the null energy condition of normal matter at the throat. In this brief report, we present a solution where normal matter satisfies the energy conditions at the throat and it is the higher order curvature derivatives of the nonminimal coupling that is responsible for the null energy condition violation, and consequently for supporting the respective wormhole geometries. For simplicity, we consider a linear R nonmiminal curvatu…
This paper is dedicated to the study of interactions between external sources for the electromagnetic field in a Lorentz symmetry breaking scenario. We focus on a particular higher derivative, Lorentz violating interaction that arises from a specific model that was argued to lead to interesting effects in the low energy phenomenology of light pseudoscalars interacting with photons. The kind of higher derivative Lorentz violating interaction we discuss do not appear in the well known Standard Model Extension, therefore they are called nonminimal. They are usually expected to be relevant only at…
We have studied the contributions of Lorentz-violating CPT-odd and CPT-even nonminimal couplings to the energy spectrum of the mesonic hydrogen and the higher-order radiative corrections to the effective action of the photon sector of a Lorentz-violating version of the scalar electrodynamics. By considering the complex scalar field describes charged mesons (pion or kaon), the non-relativistic limit of the model allows to attain upper-bounds by analyzing its contribution to the mesonic hydrogen energy. By using the experimental data for the $1S$ strong correction shift and the pure QED transiti…
The spectral index is studied at the point where scalar fields deviate from slow-roll during inflation. Considering the deviation that may cause a significant difference to the time derivative of the Hubble parameter and also to the terms in the evolution equation, we show how the deviation affects the spectral index of the curvature perturbations. Considering conventional inflation, curvatons and other inhomogeneous scenarios as mechanisms for generating the cosmological perturbation, we examine whether the spectral index induced by the deviation from the standard slow-roll can explain the sp…
Here, Primordial Black Holes (PBHs) creation from exponential potential has been inquired, through gravitationally raised friction emanated from the nonminimal coupling between gravity and field derivative setup. Setting a two-parted exponential function of inflaton field as coupling parameter, and fine-tuning of four parameter cases of our model, we could sufficiently slow down the inflaton owing to high friction during an ultra slow-roll phase. This empowers us to achieve enough enhancement in the amplitude of curvature perturbations power spectra, via numerical solving of Mukhanov-Sasaki eq…
We study a class of models in which the inflaton is minimally coupled to gravity with a term $f(R)\vp^2$. We focus in particular on the case when $f\sim R^2$, the expansion of the scale factor is driven by the usual potential energy, while the rolling of the inflaton is driven by the nonminial coupling. We show that the power spectrum is in general blue, and the problem of getting a running spectral index is eased. However, the inflaton potential must have a large second derivative in order to get a large running.
We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six coupling parameters. First three parameters relate to the nonminimal coupling of non-Abelian gauge field and gravity field, two parameters describe the so-called derivative nonminimal coupling of scalar multiplet with gravity field, and the sixth parameter introduces the standard coupling of scalar field with Ricci scalar. The formulated six-parameter nonminimal Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special c…
We have studied the existence of topological self-dual configurations in a nonminimal CPT-odd and Lorentz-violating (LV) Maxwell-Higgs model, where the LV interaction is introduced by modifying the minimal covariant derivative. The Bogomol'nyi-Prasad-Sommerfield formalism has been implemented, revealing that the scalar self-interaction implying self-dual equations contains a derivative coupling. The CPT-odd self-dual equations describe electrically neutral configurations with finite total energy proportional to the total magnetic flux, which differ from the charged solutions of other CPT-odd a…
In this letter we show for the first time that the usual CPT-even gauge term of the standard model extension (SME) can be radiatively generated, in a gauge invariant level, in the context of a modified QED endowed with a dimension-five nonminimal coupling term recently proposed in the literature. As a consequence, the existing upper bounds on the coefficients of the tensor $(K_{F}) $ can be used improve the bounds on the magnitude of the nonminimal coupling, $λ(K_{F}),$ by the factors $10^{5}$ or $10^{25}.$ The nonminimal coupling also generates higher-order derivative contributions to the gau…
We examine a new class of CPT-even and dimension-five nonminimal interactions between fermions and photons, deprived of higher-order derivatives, yielding electric dipole moment and magnetic dipole moment in the context of the Dirac equation. These couplings are Lorentz-violating nonminimal structures, composed of a rank-2 tensor, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial hermitian versions. We use the electron's anomalous magnetic and electric dipole moment measurements to reach upper bounds of $1$ part in $10^{11}$ and $10^{16}$ GeV$^{-1}$.
Wormhole geometries in curvature-matter coupled modified gravity are explored, by considering an explicit nonminimal coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter. It is the effective stress-energy tensor containing the coupling between matter and the higher order curvature derivatives that is responsible for the null energy condition violation, and consequently for supporting the respective wormhole geometries. The general restrictions imposed by the null energy condition violation are presented in the presence of a nonminimal R-matter…
We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler-DeWitt equation of second order, showing that a Bohm-de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion…
We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent of that of Born-Infeld Lagrangians. We study the s…
In this letter, we examine a new class of CPT-even nonminimal interactions, between fermions and photons, deprived of higher order derivatives, that yields electric dipole moment (EDM) and magnetic dipole moment (MDM) in the context of the Dirac equation. The couplings are dimension-five CPT-even and Lorentz-violating nonminimal structures, composed of a rank-2 tensor, $T_{μν}$, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial Hermitian versions, and also comprising general possibilities. We then use the electron's anomalous magnetic dipole moment and …
We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We derive the explicit form of the equations of motion for massi…
In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables suc…
This paper is concerned with the construction and analysis of boson stars in the context of nonminimal derivative coupling theories. In particular we embed our model in the biscalar extension of Horndeski gravity, considering a scalar field theory displaying a nonminimally coupled kinetic term given by the Einstein tensor. We focus on the case where the potential is given by a mass term only, and when a six order self-interaction is included. In the latter case we consider specific couplings in the self-interacting terms in such a way that our self-interaction is given by a positive definite p…
We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function reproduces the well-known result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension $D$ up to the first…
The rapid oscillating scalar field is considered as the quintessence in the framework of nonminimal kinetic coupling model. The scalar field behaves like a perfect fluid with a variable equation of state parameter which can be expressed as a function of the Hubble parameter. This feature enables us to study its evolution via continuity equation. The scalar field may behave as dark energy in the present epoch, while it behaves like dark matter in the future. This characteristic allows the occurrence of a decelerated expansion after the present acceleration, without invoking any interaction. The…
