Non-minimal Coupling Function Research Articles

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

A thermodynamic study of (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {(2+1)}}$$\\end{document}-dimensional analytic charged hairy black holes with Born–Infeld electrodynamics

This work presents analytical black hole solutions for a coupled Einstein–Born–Infeld–Scalar gravity system in AdS spacetime with two different non-minimal coupling functions f(z). For both solutions, we establish the regularity of the scalar field and curvature scalars outside the horizon. For one of the considered coupling cases, thermodynamic analysis in the canonical ensemble reveals stability across all temperatures, while the other case exhibits the Hawking/Page phase transition between the stable large phase of the black hole and thermal-AdS. We investigate the effect of the scalar hair parameter and black hole charge on the phase transition temperature and observe that the critical values of the scalar hair and the charge parameters constrain the feasibility of Hawking/Page phase transition.

Study on Kalb–Ramond field localization in f(T) gravity theory with a noncanonical scalar field

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of [Formula: see text] gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the [Formula: see text] branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential.

Dynamical analysis in regularized 4D Einstein–Gauss–Bonnet gravity with non-minimal coupling

We investigate the regularized four-dimensional Einstein–Gauss–Bonnet (4DEGB) gravity with a non-minimal scalar coupling function, which is an extension of the regularized 4DEGB theory. By introducing non-minimal coupling to the Gauss-Bonnet term, we demonstrate the additional contribution to the dynamical equations which is otherwise absent in the dimensionally regularized theory. Furthermore, we analyze the stability of the system by using the dynamical system approach based on fixed points. Then, we consider time evolution to investigate the history of the universe and to constrain observational data to obtain the cosmological parameters of the model.

Arbitrary Static, Spherically Symmetric Space-Times as Solutions of Scalar-Tensor Gravity

It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar field in this representation can change its nature from canonical to phantom on certain coordinate spheres. This representation, however, is valid in general not in the full range of the radial coordinate but only piecewise. Two examples of STT representations are discussed: for the Reissner-Nordstr\"om metric and for the Simpson-Visser regularization of the Schwarzschild metric (the so-called black bounce space-time).

The alteration of the Schwinger effect on radiatively corrected Higgs inflationary magneto-genesis by axial coupling

We study the alteration of the Schwinger effect on radiatively corrected Higgs inflationary magneto-genesis by axial coupling function. The conformal invariance of Maxwell action should be broken by axial coupling with the inflaton field. We use the potential of [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0; M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] with the simplest coupling function [Formula: see text] in which [Formula: see text] is a dimensionless coupling parameter. In comparison to our previous work (in which we used curvature-based coupling or so-called nonminimal coupling function to gravity to break conformal invariance of action) of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we find that the Schwinger effect does alter magneto-genesis and is considerable. In fact, in comparison to our previous work of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we obtain that for some certain values of coupling parameter [Formula: see text] the Schwinger effect does alter magneto-genesis (see [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0]) and the energy density of created charged particles during the Schwinger effect becomes considerable and of course comparable to the energy density of inflaton field. Therefore, the Schwinger effect decreases the value of the electric field, so that it helps to finish the inflation stage. Then the universe enters the stage of preheating. The Schwinger effect produces charged particles, imposing the Schwinger reheating framework even before the ending of last oscillations of the inflaton field.

Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology

The Hamiltonian constraint of scalar-tensor theories (STTs) in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The corresponding effective equations of motion derived from these effective Hamiltonian constraints turn out to be drastically different. The implications of each set of effective equations of motion are discussed in detail. In the latter half of this paper, as a concrete example, we study the effective dynamics of a specific model of STTs with the non-minimal coupling function and self-interacting quartic potential. Using numerical results, we find different features for different effective dynamics. Moreover, it is also found that the spacetime singularity is absent and the cosmological bounce exists in each effective dynamics of this model.

Isocurvature modes and non-Gaussianity in affine inflation

Inflationary dynamics driven by multiple fields, especially with nonminimal couplings, allow for highly interesting features such as isocurvature, non-Gaussianity, and preheating. In this paper, we study two-field inflation in the context of purely affine gravity, where the metrical structure results from the dynamics of the spacetime affine connection. We introduce a covariant formulation in the new framework and show that it leads to a curved field space which can produce conspicuous departure from the purely metric gravity. In the case where the fields are canonical, the field manifold gains a conformally flat shape. Interestingly, while the manifold is generally curved, it is possible to be flattened by allowing specific non-canonical field kinetic terms. This in turn simplifies the inflationary dynamics significantly while allowing for new predictions due to the effects of the nonminimal coupling function on the potential solely. We use this new feature in studying two-field inflation driven by quartic potentials for given parameter constants. We perform a numerical solution of the slow-roll dynamics and track the possible non-Gaussianity. We focus on field parameters that allow for spectral indices within the favored region of the Planck results. These are associated to tiny tensor-to-scalar ratios, $r \sim 10^{-6}$ for single field and $r \sim 10^{-4}$ for two-fields. We also show that two-field Higgs inflation may favor a curved field manifold.

Chaotic inflation and reheating in generalized scalar-tensor gravity

In the present work, we study slow-roll inflation in scalar-tensor gravity theories in the presence of both the non-minimal coupling between the scalar field and curvature, and the Galileon self-interaction of the scalar field. Furthermore, we give predictions for the duration of reheating as well as for the reheating temperature after inflation. After working out the expressions for the power spectra of scalar and tensor perturbations in the case of a general non-minimal coupling function that depends solely on the scalar field and a general scalar potential, we focus on the special cases of the power-law coupling function and chaotic quadratic inflation. Thus, under the slow-roll approximation we confront the predictions of the model with the current PLANCK constraints on the spectral index n s and the tensor-to-scalar ratio r using the n s-r plane. We found that the combination of the non-minimal coupling and Galileon self-interaction effects allows us to obtain better results for r than in the case in which each effect is considered separately. Particularly, we obtained that the predictions of the model are in agreement with the current observational bounds on n s and r within the 95 % C.L region and also slightly inside the 68 % C.L region. Also, we investigate the oscillatory regime after the end of inflation by solving the full background equations, and then we determine the upper bound for the Galileon and non-minimal coupling parameters under the condition that the scalar field oscillates coherently during reheating. Finally, after approximating reheating by a constant equation of state, we derive the relations between the reheating duration, the temperature at the end of reheating, its equation of state, and the number of e-folds of inflation and then we relate them all to the inflationary observables.

Reconstructing inflation in scalar-torsion f(T,phi ) gravity

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function f(T,phi ) of the torsion scalar T of teleparallel gravity and the inflaton phi . For the class of theories with Lagrangian density f(T,phi )=-M_{pl}^{2} T/2 - G(T) F(phi ) - V(phi ), with G(T)sim T^{s+1} and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function F(phi ) and the scalar potential V(phi ) through the parametrization (or attractor) of the scalar spectral index n_{s}(N) and the tensor-to-scalar ratio r(N) as functions of the number of e-folds N. As specific examples, we analyze the attractors n_{s}-1 propto 1/N and rpropto 1/N, as well as the case rpropto 1/N (N+gamma ) with gamma a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function F(phi ) and the potential V(phi ), as also the constraints on the parameters present in our model and its reconstruction.

Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

In the presence of appropriate non-minimal couplings between a scalar field and the curvature squared Gauss–Bonnet (GB) term, compact objects such as neutron stars and black holes (BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The non-minimal coupling functions that allow this mechanism are, however, always postulated ad hoc. Here, we point out that families of such functions naturally emerge in the context of Higgs–Chern–Simons gravity models, which are found as dimensionally descents of higher dimensional, purely topological, Chern–Pontryagin non-Abelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions in a particular Einstein-GB-scalar field model, whose coupling is obtained from this construction, pointing out novel features and caveats thereof. The possibility of vectorization is also discussed, since this construction also originates vector fields non-minimally coupled to the GB invariant.

Quasinormal modes of hot, cold and bald Einstein\u2013Maxwell-scalar black holes

Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function f(phi ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, f(phi )=1+alpha phi ^4 (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

Dynamical System Study of Nonminimal Tachyon Field within Holographic Cosmology

We use the dynamical system method in order to investigate the dynamics of a non-minimally coupled tachyon field within induced gravity on the brane in a holographic cosmological context. Assuming an exponential potential and a monomial form of the nonminimal coupling function, we construct the phase space of the model. Two possible cases, namely, the minimal and nonminimal coupling, are investigated. Using dynamical systems tools, it is found that the model can describe an attractor solution which corresponds to the inflationary era in the non-minimal coupling case.

Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking

In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function f(T,ϕ) of the torsion scalar T and a scalar field ϕ, plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lorentz rotation of the tetrad field. After integrating out all the auxiliary modes, we obtain a second order action for the scalar and tensor propagating modes and their power spectrum generated during inflation. It is found that an explicit mass term emerges in the second order action for curvature perturbation, describing the imprints of local Lorentz violation at first-order of slow-roll. We show that only inflationary models with nonminimal coupling functions f(T,ϕ) which are non-linear in T, including the case of f(T) gravity with minimally coupled scalar field, can generate primordial fluctuations. For a concrete model of inflation, we study the power-law potential by using the latest Planck data.

Boltzmann's H-theorem, entropy and the strength of gravity in theories with a nonminimal coupling between matter and geometry

In this paper we demonstrate that Boltzmann's H-theorem does not necessarily hold in the context of theories of gravity with nonminimally coupled matter fields. We find sufficient conditions for the violation of Boltzmann's H-theorem and derive an expression for the evolution of Boltzmann's H in terms of the nonminimal coupling function, valid in the case of a collisionless gas in a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universe. We highlight the implications of this result for the evolution of the entropy of the matter fields, briefly discussing the role played by collisions between particles whenever they are relevant. We also suggest a possible link between the high entropy of the Universe and the weakness of gravity in the context of these theories.

Non-minimally coupled Einstein–Gauss–Bonnet inflation phenomenology in view of GW170817

We study the inflationary phenomenology of a non-minimally coupled Einstein–Gauss–Bonnet gravity theory, in the presence of a scalar potential, under the condition that the gravitational wave speed of the primordial gravitational waves is equal to unity, that is cT2=1, in natural units. The equations of motion, which are derived directly from the gravitational action, form a system of differential equations with respect to Hubble’s parameter and the inflaton field which are very complicated and cannot be solved analytically, even in the minimal coupling case. In this paper, we present a variety of different approximations which could be used, along with the constraint cT2=1, in order to produce an inflationary phenomenology compatible with recent observations. All the different approaches are able to lead to viable results if the model coupling functions obey simple relations, however, different approaches contain different approximations which must be obeyed during the first horizon crossing, in order for the model to be rendered correct. Models which may lead to a non-viable phenomenology are presented as well in order to understand better the inner framework of this theory. Furthermore, since the velocity of the gravitational waves is set equal to cT2=1, as stated by the striking event of GW170817 recently, the non-minimal coupling function, the Gauss–Bonnet scalar coupling and the scalar potential are related to each other. Here, we shall assume no particular form of the scalar potential and we choose freely the scalar functions coupled to the Ricci scalar and the Gauss–Bonnet invariant. Certain models are also studied in order to assess the phenomenological validity of the theory, but we need to note that all approximations must hold true in order for a particular model to be valid. Finally, even though each possible approach assumes different approximations, we summarize them in the last section for the sake of completeness.

Electromagnetic dual Einstein-Maxwell-scalar models

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions f(ϕ) and g(ϕ), depending on a real scalar field ϕ. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the SO(2) electromagnetic duality rotations of Maxwell’s theory, defines 1-parameter, closed duality orbits in the space of EMS models, connecting different electromagnetic fields in “dual” models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to S-duality.

Einstein-Maxwell-scalar black holes: The hot, the cold and the bald

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function f(ϕ), between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: f(Φ)=1+αΦ4. The domain of existence of the scalarised BHs, for fixed α, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myers-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.

Generalized scalar\u2013tensor theory of gravity reconstruction from physical potentials of a scalar field

We describe how to reconstruct generalized scalar–tensor gravity (GSTG) theory, which admits exact solutions for a physical type of potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is an a priori specified relation between the Hubble parameter H and a function of a non-minimal coupling F=1+delta F, Hpropto sqrt{F}. Deviations from Einstein gravity delta F induce corresponding deviations of the potential delta V from a constant value and modify the dynamics from a pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such a consideration allows us to substitute the physical potential into the obtained equations and then to calculate the non-minimal coupling function and kinetic term that define the GSTG parameters. With this method, we reconstruct GSTG for the polynomial, exponential, Higgs, Higgs–Starobinsky and Coleman–Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove the correspondence of the obtained solutions to observational data from Planck.