Non-minimal Kinetic Coupling Research Articles

Comparing potential-driven DBI-inspired non-minimal kinetic coupling (Dinkic) inflation with observational data**Supported by NSFC (11405069, 11653002, 11735007, 111375070)

In our previous work [], a new kind of inflation model was proposed, which has the interesting property that its perturbation equation of motion gets a correction of k4, due to the non-linearity of the kinetic term. Nonetheless, the scale-invariance of the power spectrum remains valid, both in large-k and small-k limits. In this paper, we investigate in detail the spectral index, the index running and the tensor/scalar ratio in this model, especially in the potential-driven case, and compare the results with the current PLANCK/BICEP observational data. We also discuss the tensor spectrum in this case, which is expected to be tested by future observations of primordial gravitational waves.

Dynamical analysis for a scalar–tensor model with kinetic and nonminimal couplings

We study the autonomous system for a scalar–tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

A note on ‘gaugings’ in four spacetime dimensions and electric-magnetic duality

The variety of consistent ‘gauging’ deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper nv abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to ns uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by . The symplectic group mixes its electric and magnetic potentials. The model admits a global duality symmetry subgroup G which acts also on the scalars. We recall first how the general second order Lagrangian, its local deformations and those of its abelian gauge group will depend on the choice of 2nv directions (choice of ‘Darboux frame’). We start from a general frame defined by the symplectic transformation relating it to a fixed ‘reference’ one. Combinations of symplectic matrix coefficients appear then as constant parameters in the second order Lagrangians. Another gauging method uses an ‘embedding tensor’ that characterizes the realization of the gauge group via the global duality group. It involves additional 2-form gauge fields. A suitable zero charge limit of this realization has abelian gauge group and the ‘gauging’ can be viewed as a consistent deformation of that limit. We show that the two methods applied to the corresponding ungauged models have equivalent local deformations—and more generally, have isomorphic local BRST cohomology at all ghost numbers. We finally consider manifestly duality invariant first order actions with abelian gauge group. We point out that obstructions to non-abelian deformations of the Yang–Mills type exhibited in a previous work remain present when couplings to scalar fields are included.

General dynamical properties of cosmological models with nonminimal kinetic coupling

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as η Gμνϕ,μϕ,ν, where η is an arbitrary coupling parameter, and the scalar potential V(ϕ) which assumed to be as general as possible. With an appropriate dimensionless parametrization we represent the field equations as an autonomous dynamical system which contains ultimately only one arbitrary function χ (x)= 8 π | η | V(x/√8 π) with x=√8 πϕ. Then, assuming the rather general properties of χ(x), we analyze stationary points and their stability, as well as all possible asymptotical regimes of the dynamical system. It has been shown that for a broad class of χ(x) there exist attractors representing three accelerated regimes of the Universe evolution, including de Sitter expansion (or late-time inflation), the Little Rip scenario, and the Big Rip scenario. As the specific examples, we consider a power-law potential V(ϕ)=M4(ϕ/ϕ0)σ, Higgs-like potential V(ϕ)=λ/4(ϕ2−ϕ02)2, and exponential potential V(ϕ)=M4 e−ϕ/ϕ0.

КРОТОВЫЕ НОРЫ В ТЕОРИИ ГРАВИТАЦИИ С НЕМИНИМАЛЬНОЙ КИНЕТИЧЕСКОЙ СВЯЗЬЮ И КОСМОЛОГИЧЕСКОЙ ПОСТОЯННОЙ

КРОТОВЫЕ НОРЫ В ТЕОРИИ ГРАВИТАЦИИ С НЕМИНИМАЛЬНОЙ КИНЕТИЧЕСКОЙ СВЯЗЬЮ И КОСМОЛОГИЧЕСКОЙ ПОСТОЯННОЙ

Observational manifestations of black holes in the Horndeski gravity model

The geodesic equations for black hole solutions in the scalar–tensor Horndeski gravity model with non-minimal kinetic coupling have been investigated. The ranges of model parameters admitting the existence of bounded orbits have been determined. Constraints on the model parameters providing agreement of the model with the observational data on the accretion and motion of bodies in the Solar system have been obtained.

Warm inflation with an oscillatory inflaton in the non-minimal kinetic coupling model

In the cold inflation scenario, the slow roll inflation and reheating via coherent rapid oscillation, are usually considered as two distinct eras. When the slow roll ends, a rapid oscillation phase begins and the inflaton decays to relativistic particles reheating the Universe. In another model dubbed warm inflation, the rapid oscillation phase is suppressed, and we are left with only a slow roll period during which the reheating occurs. Instead, in this paper, we propose a new picture for inflation in which the slow roll era is suppressed and only the rapid oscillation phase exists. Radiation generation during this era is taken into account, so we have warm inflation with an oscillatory inflaton. To provide enough e-folds, we employ the non-minimal derivative coupling model. We study the cosmological perturbations and compute the temperature at the end of warm oscillatory inflation.

Thermodynamics of Horndeski black holes with non-minimal derivative coupling

We explore thermodynamic properties of a new class of Horndeski black holes whose action contains a non-minimal kinetic coupling of a massless real scalar and the Einstein tensor. Our treatment is based on the well-accepted consideration, where the cosmological constant is dealt with as thermodynamic pressure and the mass of black holes as thermodynamic enthalpy. We resort to a newly introduced intensive thermodynamic variable, i.e., the coupling strength of the scalar and tensor whose dimension is length square, and thus yield both the generalized first law of thermodynamics and the generalized Smarr relation. Our result indicates that this class of Horndeski black holes presents rich thermodynamic behaviors and critical phenomena. Especially in the case of the presence of an electric field, these black holes undergo two phase transitions. Once the charge parameter exceeds its critical value, or the cosmological parameter does not exceed its critical value, no phase transitions happen and the black holes are stable. As a by-product, we point out that the coupling strength acts as the thermodynamic pressure in the behavior of thermodynamics.

Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings

We study the phase space for a scalar-tensor string inspired model of dark energy with nonminimal kinetic and Gauss-Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which gives rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from a matter or radiation dominated universe to a dark energy dominated universe. Trajectories were found in the phase space departing from unstable or saddle fixed points and arriving at the stable scalar field dominated point corresponding to late-time accelerated expansion.

Dirac-Born-Infeld inflation model with kinetic coupling to Einstein gravity

In this paper we study a new class of inflation models which generalize the Dirac-Born-Infeld (DBI) action with the addition of a nonminimal kinetic coupling (NKC) term. We dubbed this model as the {\it new DBI inflation model}. The NKC term does not bring new dynamical degree of freedom, so the equations of motion remain of second order. However, with such a coupling, the action is no longer linear with respect to the Einstein curvature term ($R$ or $G^{\mu\nu}$), which leads to a correction term of $k^4$ in the perturbations. The new DBI inflation model can be viewed as theories beyond Horndeski. Without violating nearly scale-invariance, such a correction may lead to new effects on the inflationary spectra that could be tested by future observations.

Tachyon Cosmology with Gauss–Bonnet and Non-Minimal Kinetic Couplings

We consider a tachyonic model of dark energy in which scalar field non-minimally coupled with curvature and kinetic part of its Lagrangian density. Additionally the model contains the Gauss–Bonnet coupling to the scalar field through an arbitrary function. The non-minimal Gauss–Bonnet coupling function and scalar field potential have been obtained for power-law solution and then for a dynamically varying equation of state. We have extracted the required condition for the so-called phantom divide line crossing in the model and represented such a crossing numerically.

The non-minimal ekpyrotic trispectrum

Employing the covariant formalism, we derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory. These equations can be used to derive predictions for local bi- and trispectra of multi-field cosmological models. Our main application is to ekpyrotic models in which the primordial curvature perturbations are generated via the non-minimal entropic mechanism. In these models, nearly scale-invariant entropy perturbations are generated first due to a non-minimal kinetic coupling between two scalar fields, and subsequently these perturbations are converted into curvature perturbations. Remarkably, the entropy perturbations have vanishing bi- and trispectra during the ekpyrotic phase. However, as we show, the conversion process to curvature perturbations induces local non-Gaussianity parameters fNL and gNL at levels that should be detectable by near-future observations. In fact, in order to obtain a large enough amplitude and small enough bispectrum of the curvature perturbations, as seen in current measurements, the conversion process must be very efficient. Interestingly, for such efficient conversions the trispectrum parameter gNL remains negative and typically of a magnitude \U0001d4aa(102)–\U0001d4aa(103), resulting in a distinguishing feature of non-minimally coupled ekpyrotic models.

Cosmology with nonminimal kinetic coupling and a Higgs-like potential

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as κGμνϕ,μϕ,ν, and the Higgs-like potential . Using the dynamical system method, we analyze stationary points, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) The late-time de Sitter epoch when the Hubble parameter tends to the constant value, as t → ∞, while the scalar field tends to zero, 0ϕ(t)→ , so that the Higgs potential reaches its local maximum . (ii) The Big Rip when H(t)∼(t*−t)−1 → ∞ and ϕ(t)∼(t*−t)−2 → ∞ as t → t*. (iii) The Little Rip when H(t)∼ t1/2 → ∞ and ϕ(t)∼ t1/4 → ∞ as t → ∞. Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.

Dynamical stability of Minkowski space in higher order gravity

We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space is proposed. This method was applied for some modified gravity theories, such as f(R) gravity, f(R)+αR□R gravity and scalar–tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of f(R) gravity Minkowski solution is asymptotically stable in ghost-free (f′ > 0) and tachyon-free (f″ > 0) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of higher order gravity with αR□R correction conditions of Minkowski stability with respect to isotropic perturbations are significantly different: f′(0) < 0, f″(0) < 0 and 3f′(0) + f″(0)2/α > 0. And in the case of scalar-tensor gravity with non-minimal kinetic coupling Minkowski solution is asymptotically stable in expanding Universe with respect to isotropic perturbations of metric. Moreover, the developed method may be used for finding additional restrictions on parameters of different modified gravity theories.

Temperature in warm inflation in non-minimal kinetic coupling model

Warm inflation in the non minimal derivative coupling model with a general dissipation coefficient is considered. We investigate conditions for the existence of the slow roll approximation and study cosmological perturbations. The spectral index, and the power spectrum are calculated and the temperature of the universe at the end of the slow roll warm inflation is obtained.

Cosmology and stability in scalar tensor bigravity with non-minimal kinetic coupling gravity

We generalize the scalar tensor bigravity models to the non-minimal kinetic coupling scalar tensor bigravity models with two scalar fields whose kinetic terms are non-minimally coupled to two Einstein tensors constructed by two metrics. We show that a broad class of expanding universes can be explained by some solutions of this model. Then, we study the stability issue of the solutions by means of imposing homogeneous perturbation on the equations of motion and extract the stable solutions.

Exact wormhole solutions with nonminimal kinetic coupling

We consider static spherically symmetric solutions in the scalar-tensor theory of gravity with a scalar field possessing the nonminimal kinetic coupling to the curvature. The lagrangian of the theory contains the term $(\varepsilon g^{\mu\nu}+\eta G^{\mu \nu})\phi_{,\mu}\phi_{,\nu}$ and represents a particular case of the general Horndeski lagrangian, which leads to second-order equations of motion. We use the Rinaldi approach to construct analytical solutions describing wormholes with nonminimal kinetic coupling. It is shown that wormholes exist only if $\varepsilon=-1$ (phantom case) and $\eta>0$. The wormhole throat connects two anti-de Sitter spacetimes. The wormhole metric has a coordinate singularity at the throat. However, since all curvature invariants are regular, there is no curvature singularity there.

Rapid oscillatory quintessence with variable equation of state parameter in non minimal derivative coupling model

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 model is also studied in the presence of an interaction between dark sectors alleviating the coincidence problem. The stability of the model is investigated and the stable attractor solutions are studied.

Exponential potential for an inflaton with nonminimal kinetic coupling and its supergravity embedding

In the light of new observational results, we discuss the status of the exponential potentials driving inflation. We depart from the minimal scenario and study an inflaton kinetically coupled to the Einstein tensor. We find that in this case, the exponential potentials are well compatible with observations. Their predictions coincide with those of the chaotic-type quadratic potential for an inflaton minimally coupled to gravity. We show that there exists a simple mapping between the two models. Moreover, a novel aspect of our model is that it features a natural exit from the inflationary phase even in the absence of a minimum. We also turn to supergravity and motivate this sort of potential and the nonminimal kinetic coupling as possible effective dilaton theories.

Implications of the primordial anisotropy for a scalar field with nonminimal kinetic coupling

We consider a scalar field with a kinetic term non-minimally coupled to gravity in an anisotropic background. Various potentials for the scalar field are considered. By explicit examples, we show that how the anisotropy can change the dynamics of the scalar field compared with the isotropic background.