Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We also write down the solution for the Bianchi-I Universe in the induced gravity cosmology.
We study the minimally and non-minimally coupled scalar field models as possible alternatives for dark energy, the mysterious energy component that is driving the accelerated expansion of the universe. After discussing the dynamics at both the background and perturbation level, we confront the two models with the latest cosmological data. After obtaining updated constraints on their parameters we perform model selection using the basic information criteria. We found that the $Λ$CDM model is strongly favored when the local determination of the Hubble constant is not considered and that this sta…
We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensib…
Dynamical systems methods are used to study the evolution of the Bianchi I model with a scalar field. We show that inclusion of the non-minimal coupling term between the scalar field and the curvature changes evolution of the model compared with the minimally coupled case. In the model with the non-minimally coupled scalar field there is a new type of singularity dominated by the non-minimal coupling term. We examine the impact of the non-minimal coupling on the anisotropy evolution and demonstrate the existence of its minimal value in the generic case.
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble param…
We, in the first part, contemplate a massless minimally coupled scalar which is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background of an inflating spacetime. We compute the scalar's quantum corrected mode function, power spectrum, spectral index and the running of the spectral index at one-loop order. We find that the spectrum is slightly blue-tilted; hence, the amplitudes of fluctuations grow slightly toward the smaller scales. Then, in the second part, we apply the computation method used in the first part to a massless minimally coupled scalar with a quartic self-i…
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $…
We study the integrable model with minimally and non-minimally coupled scalar fields and the correspondence of their general solutions. Using the model with a minimally coupled scalar field and a the constant potential as an example we demonstrate the difference between the general solutions of the corresponding models in the Jordan and the Einstein frames.
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first l…
Properties of soliton stars that could be expected to naturally arise out of a first order phase transition in non-minimally coupled scalar-field-induced gravity theories are investigated. Of particular interest are configurations, similar to Lee-Wick stars, with vanishing effective gravitational constant in the interiors.
We extend here the result of Bekenstein [1,2] proving the non-existence of minimally coupled scalar black hole hair in general relativity to the Lanczos-Lovelock gravity in arbitrary dimension with non-negative coupling constants. The only physical requirement on the multiplet of minimally coupled scalar fields is that it fulfills the weak energy condition. We also assume, similarly to Bekenstein, spherical symmetry and asymptotic flatness.
Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.
Using the generalized Schwinger-DeWitt technique, we calculate the divergent part of the one-loop effective action for gravity non-minimally coupled to a multiplet of scalar fields. All the calculations are consistently done in the Jordan frame.
We study the existence of scalar fields outside neutral reflecting shells. We consider static massive scalar fields non-minimally coupled to the Gauss-Bonnet invariant. We analytically investigated properties of scalar fields through the scalar field equation. In the small scalar field mass regime, we derive a compact resonance formula for the allowed masses of scalar fields in the composed scalar field and shell configurations.
We discuss the two-dimensional dilaton gravity with a scalar field as the source matter. The coupling between the gravity and the scalar, massless, field is presented in an unusual form. We work out two examples of these couplings, and solutions with black-hole behaviour are discussed and compared with those found in the literature.
In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term $ξR ψ^{2}$ in the scalar field action. The quadratic potential function $V(ψ)\propto ψ^{2}$ is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling $ξ$ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field c…
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results se…
We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.
The isolated horizon framework is extended to include non-minimally coupled scalar fields. As expected from the analysis based on Killing horizons, entropy is no longer given just by (a quarter of) the horizon area but also depends on the scalar field. In a subsequent paper these results will serve as a point of departure for a statistical mechanical derivation of entropy using quantum geometry.
The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation to the non- minimally coupled Holst action. In the first part of the paper, we introduce the non- minimal scalar coupling of the Holst action and construct the covariant phase space of the theory. Using the covariant phase space, we prove the laws of black hole mechanics and show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern-Simons theory. The level of the Chern- Simons theory is shown to depend on the non-minimally coupled scalar field.
We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the $N$ degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n<N$, $N<n<2N$ and $n>2N$ cases…
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model wi…
An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfied on and outside the event horizon. The thermodynamical analysis shows the existence of a critical temperature, below which a black hole in vacuum undergoes a spontaneous dressing up with a nontrivial s…
We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configur…
We look for necessary conditions such that minimally coupled scalar-tensor theory with a massive scalar field and a perfect fluid in the Bianchi type I model isotropises. Then we derive the dynamical asymptotical properties of the Universe.
We show that Einstein's gravity coupled to a non-minimally coupled scalar field is stable even for high values of the scalar field, when the sign of the Einstein-Hilbert action is reversed. We also discuss inflationary solutions and a possible new mechanism of reheating.
In previous works, we studied the isotropisation of Bianchi class A models with a minimally coupled scalar field. In this paper, we extend these results to the case of a non minimally coupled one. We first make the calculations in the Einstein frame where the scalar field is minimally coupled to the curvature but non minimally coupled to the perfect fluid. Then, we use a conformal transformation to generalise our results to a scalar field non minimally coupled to the curvature. Universe isotropisation for the Brans-Dicke and low energy string theories are studied.
The solution to the current extending Universe problem, and the description of all stages of evolution compels scientists to consider various cosmological models. Scalar - tensor models are rather simple and also allow us to clearly define the separate stages of evolution. Furthermore, other cosmological models are reduced. Our work takes into consideration the non-minimally interacted scalar field and the spinor field. The spinor field has been considered to establish a better understanding of the stages of evolution in our Universe.
In this work a new non-minimally coupled model is presented, where a generic function $f(R)$ of the scalar curvature factors the usual Einstein-Hilbert action functional, motivated by relevant results obtained from similar models. Its cosmological dynamics are derived and the possibility of attaining a phase of accelerated expansion is assessed. To further probe the possible implications of the model, a dynamical system formulation is established, and used to assess the scenarios where $f(R)$ assumes a power-law or exponential form.
We present the four-dimensional equations on a brane with a scalar field non-minimally coupled to the induced Ricci curvature, embedded in a five-dimensional bulk with a cosmological constant. This is a natural extension to a brane-world context of scalar-tensor (Brans-Dicke) gravity. In particular we consider the cosmological evolution of a homogeneous and isotropic (FRW) brane. We identify low-energy and strong-coupling limits in which we recover effectively four-dimensional evolution. We find de Sitter brane solutions with both constant and evolving scalar field. We also consider the specia…
Several results related to flat Friedmann-Lema\^ıtre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling functions are considered. Mild assumptions under such functions (differentiable class, number of singular points, asymptotes, etc) are introduced in a straightforward manner in order to characterize the asymptotic structure on a phase space. We pay special attention to the possible scaling solutions. Numerical evidence confirming our results is presented.
We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singula…
Previous studies showed that, in the presence of a simple and well-motivated self-interaction scalar potential, asymptotically flat and spherical black holes can carry minimally coupled and charged scalar cloud/hair in Einstein-Maxwell gravity. We extend these studies to Einstein-Born-Infeld gravity to consider the effect of nonlinearity of the electromagnetic field. Series of spherical cloudy/hairy black hole solutions are constructed numerically. Results show that increasing the Born-Infeld coupling constant $b$ will make the domain of existence of the solution shrink or even disappear when …
We consider a non-minimally coupled curvature-matter gravity model (NMC) with a Weyl connection, a theory referred to as non-minimally coupled Weyl connection gravity (NMCWCG). The Weyl connection is an affine connection that is not compatible with the metric, and involves a vector field. Assuming a vacuum expectation value for the vector field and a matter Lagrangian that only contains the contributions of the vacuum energy, we show that the model admits solutions in the space-form with a reference curvature that can be fine-tuned to much smaller values than the contribution of the matter fie…
The interaction of massless minimally coupled scalar field and spinor field $ \left( Ψ+ Φ_m \rightarrow Ψ+ Φ_m \right) $ is investigated and the behavior of interaction and scattering matrix in Minkowski limit is studied. It is seen that the massless minimally coupled scalar field operator, the interaction Lagrangian and the scattering matrix become zero. Also the incoming and outgoing spinor fields, which in de Sitter space-time are different and are interacted with massless minimally coupled scalar field, in null curvature limit are the same and no interaction seen. In other word, the massle…
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame.
Motivated by the structure of one-loop vacuum polarization effects in curved spacetime we discuss a non-minimal extension of the Einstein-Maxwell equations. This formalism is applied to Bianchi I models with magnetic field. We obtain several exact solutions of the non-minimal system including those which describe an isotropization process. We show that there are inflationary solutions in which the cosmological constant is determined by the non-minimal coupling parameters. Furthermore, we find an isotropic de Sitter solution characterized by a "screening" of the magnetic field as a consequence …
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar fiel…
We study {\it analytically} the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum $\{R_{\text{s}}(Q,α,l;n)\}^{n=\infty}_{n=1}$ of charged shell radii that can support the non-minimally coupled mas…
We look for the necessary conditions allowing the Universe isotropisation in presence of a minimally coupled and massive scalar field with a perfect fluid. We conclude that it arises only when the Universe is scalar field dominated, leading to flat spacelike sections and accelerated expansion, and examine the case of a SUGRA theory.
We consider cosmological dynamics of a canonical bulk scalar field, which is coupled non-minimally to 5-dimensional Ricci scalar in a DGP setup. We show that presence of this non-minimally coupled bulk scalar field affects the jump conditions of the original DGP model significantly. Within a superpotential approach, we perform some numerical analysis of the model parameter space and consider bulk-brane energy exchange in this setup. Also we show that the normal, ghost-free branch of the DGP solutions in this case has the potential to realize a self-consistent phantom-like behavior and therefor…
In this work we check the validity of the no scalar hair theorem in charged axisymmetric stationary black holes for a wide class of scalar tensor theories.
We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de-Sitter attractor exists, and the dark matter solution is unstable.
We study the existence and stability of cosmological scaling solutions of a non-minimally coupled scalar field evolving in either an exponential or inverse power law potential. We show that for inverse power law potentials there exist scaling solutions the stability of which does not depend on the coupling constant $ξ$. We then study the more involved case of exponential potentials and show that the scalar field will assymptotically behaves as a barotropic fluid when $ξ\ll 1$. The general case $ξ\not\ll 1$ is then discussed an we illustrate these results by some numerical examples.
We examine Friedmann-Robertson-Walker models in three spacetime dimensions. The matter content of the models is composed of a perfect fluid, with a $γ$-law equation of state, and a homogeneous scalar field minimally coupled to gravity with a self-interacting potential whose energy density red-shifts as $a^{-2 ν}$, where a denotes the scale factor. Cosmological solutions are presented for different range of values of $γ$ and $ν$. The potential required to agree with the above red-shift for the scalar field energy density is also calculated.
We derive an exact solution belonging to Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations.
In this paper, we investigate holographic superconductors dual to asymptotically anti-de Sitter black holes in an Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In the probe limit, it shows that the scalar condensate occurs below the critical temperature $T_{c}$, and decreases with the increase of the coupling constant $α$. On the other hand, the the critical temperature $T_{c}$ increases as the coupling constant $α$ grows. We also calculate the optical conductivity of the holographic superconductor, and observe that a gap forms below $T_{c}$. …
The purpose of this study is to describe a perfect fluid matter distribution that leads to a constant curvature region, thanks to the effect of a non-minimal coupling. This distribution exhibits a density profile within the range found in the interstellar medium and an adequate matching of the metric components at its boundary. By identifying this constant curvature with the value of the cosmological constant, and superimposing the spherical distributions arising from different matter sources throughout the universe, one is able to mimic a large-scale homogeneous cosmological constant solution…
Performing a relativistic approximation as the generalization to a curved spacetime of the flat space Klein-Gordon equation, an effective Hamiltonian which includes non-minimial coupling between gravity and scalar field and also quartic self-interaction of scalar field term is obtained.
We discuss black hole solutions in (2+1)-dimensions with a scalar field non-minimally coupled to Einstein's gravity in the presence of a cosmological constant and a self-interacting scalar potential. Without specifying the form of the potential, we find a general solution of the field equations, which includes all the known asymptotically anti-de Sitter (AdS) black hole solutions in (2+1)-dimensions as special cases once values of the coupling constants are chosen appropriately. In addition, we obtain numerically new black hole solutions and for some specific choices of the coupling constants …
We investigate first-order vacuum phase transitions in the presence of a non-minimally coupled scalar field starting with the coupling effect on the initial dynamics of phase transitions by defining an effective potential for the scalar field and then performing three dimensional numerical simulations to observe any possible distinction in gravitational wave power spectrum. Although we give a description of the model with the expanding background, in this particular paper, we exclude the scale factor contribution since we primarily focus on the immediate impact of the non-minimal coupling at i…
We examine the stability and the strong cosmic censorship in the Reissner-Nordstrom-de Sitter (RN-dS) black hole by investigating the evolution of a scalar field non-minimally coupled to the curvature. We find that when the coupling parameter is negative, the RN-dS black hole experiences instability. The instability disappears when the coupling parameter becomes non-negative. With the increase of the coupling parameter, the violation of the strong cosmic censorship occurs at a larger critical charge ratio. But such an increase of the critical charge is suppressed by the increase of the cosmolo…
