Constant Scalar Field Research Articles

Black hole thermodynamics in the Brans–Dicke–Maxwell theory

It has been shown that the exact solutions of four-dimensional (4D) Brans–Dicke–Maxwell (BDM) theory is nothing other than Reissner–Nordström (RN) black hole (BH)s coupled to a trivial constant scalar field (Cai and Myung in Phys Rev D 56:3466, 1997). Here, we show that it is the case only when the scalar potential is taken constant or equal to zero. Then, through obtaining the exact solutions, in the presence of a scalar potential, we show that this theory admits two classes of novel BH solutions which have been affected by a nontrivial scalar hair. Due to conformal invariance of Maxwell’s electrodynamics, multi-horizon BHs can occur which implies the anti-evaporation quantum effect. Inclusion of the scalar hair makes the asymptotic behavior of the solutions non-flat and non-AdS. Our novel solutions recover the RN-AdS BHs when the scalar field is turned off. Thermodynamic quantities of the 4D BDM BHs have been calculated by use of the appropriate methods and under the influence of scalar field. Then, by use of a Smarr-type mass formula, it has been found that the first law of BH thermodynamics is valid for our novel BHs. Thermal stability of the BDM BHs has been analyzed by use of the canonical ensemble and geometrical methods, comparatively.

On the constant roll complex scalar field inflationary models

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an appropriate form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, γ(t). We work with an arbitrary but constant function γ (where γ = 0 refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on γ function space solutions and found that dynamically stable trajectories in phase space are stable under γ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by N non-canonical fields, there will be N free parameters in the potential that can be attributed to the interaction between the fields.

Thermodynamics of Brans–Dicke–BTZ black holes coupled to conformal-invariant electrodynamics

Abstract The field equations of Brans–Dicke conformal-invariant theory in (2+1)-dimensions are highly nonlinear and difficult to solve directly. They are related to those of Einstein–dilaton theory, where the solutions can be obtained easily, by use of a mathematical tool known as the conformal transformation. The exact solutions of three-dimensional Brans–Dicke theory, which are obtained from their Einstein-dilaton counterparts, give two novel classes of conformal-invariant black holes. When the scalar potential is absent (or is considered constant) in the action, it has been shown that the exact solution of this theory is just the conformal-invariant BTZ black hole with a trivial constant scalar field. This issue corresponds to the four-dimensional Brans–Dicke–Maxwell theory discussed in Ref. [R.-G. Cai, Y. S. Myung, Phys. Rev. D 56, 3466 (1997)]. The Brans–Dicke conformal-invariant black holes’ thermodynamic quantities have been calculated by use of the appropriator methods, and it has been shown that they satisfy the first law of black hole thermodynamics in its standard form. The thermal stability of Brans–Dicke black holes has been studied by use of the canonical ensemble method and noting the signature of the black holes’ heat capacity.

On the stability of scale-invariant black holes

Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field configurations. We provide a complementary analysis of the same model in the static, spherically symmetric setting, obtaining two Schwarzschild-de Sitter solutions, which corresponds to the two fixed points existing in the cosmological scenario. The stability of such solutions is thoroughly investigated from two different perspectives. First, we study the system at the classical level by the analysis of linear perturbations. In particular, we provide both analytical and numerical results for the late-time behavior of the perturbations, proving the stable and unstable character of the two solutions. Then we perform a semi-classical, non-linear analysis based on the Euclidean path integral formulation. By studying the difference between the Euclidean on-shell actions evaluated on both solutions, we prove that the unstable one has a meta-stable character and is spontaneously decaying into the stable fixed point which is always favoured.

Asymptotic freedom and safety in quantum gravity

We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract β-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a scalar field. Quantum gravity can be asymptotically free, based on a flow trajectory from the corresponding ultraviolet fixed point to the infrared region. This flow can also be realized by a scaling solution for varying values of a scalar field. As an alternative possibility, quantum gravity can be realized by asymptotic safety at the other fixed point. There may exist a critical trajectory between the two fixed points, starting in the extreme ultraviolet from asymptotic freedom. We compute critical exponents and determine the number of relevant parameters for the two fixed points. Evaluating the flow equation for constant scalar fields yields the universal gravitational contribution to the effective potential for the scalars.

Quasinormal modes of the electric potential in the 4 dimensional anti de Sitter Reissner-Norstöm black hole spacetime with scalar hair

In this study, analytical calculations are performed to assess the quasinormal modes (qnm) of the perturbed electromagnetic potential within the a four-dimensional spacetime of the Reissner-Nordström (RN) anti-de Sitter (AdS) black holes which are dressed with scalar hair. The black holes serve as the solutions for the Einstein-Maxwell theory under a negative cosmological constant and conformally-coupled real self-interacting scalar field. When the strength of the scalar field is suitable, phase transition of the black holes occurs to create a new form of MTZ black holes. The electromagnetic field can then be perturbed and the qnm and their frequencies calculated in order to meet the boundary conditions both at the horizon and at the far distant region from the new MTZ black hole. In order to address a simplified version of this problem, this study investigates the case whereby the mass of the MTZ black hole is significantly less than the AdS radius.

On (non-)dynamical dark energy

The current Universe is composed by a mixture of relativistic species, baryonic matter, dark matter and dark energy which evolve in a non-trivial way at perturbative level. An advanced description of the cosmological dynamics should include non-standard features beyond the simplistic approach idealized by the standard cosmology in which cosmic components do not interact, are adiabatic and dissipationless. We promote a full perturbative analysis of linear scalar perturbations of a non-interacting cosmological model containing baryons, dark matter (both pressureless) and a scalar field allowing for the presence of relative entropic perturbations between the three fluids. Assuming an effective scalar-field sound speed equal to one and neglecting anisotropic stresses we establish a new set of equations for the scalar cosmological perturbations. As a consequence of this new approach, we show that tiny departures from a constant scalar field equation of state $w_S=-1$ damage structure formation in a non-acceptable manner. Hence, by strongly constraining $w_S$ our results provide compelling evidence in favor of the standard cosmological model and rule out a large class of dynamical dark energy models

On the component structure of one-loop effective actions in 6D, 𝒩 = (1,0) and 𝒩 = (1,1) supersymmetric gauge theories

We study the six-dimensional [Formula: see text] and [Formula: see text] supersymmetric Yang–Mills (SYM) theories in the component formulation. The one-loop divergencies of effective action are calculated. The leading one-loop low-energy contributions to bosonic sector of effective action are found. It is explicitly demonstrated that the contributions to effective potential for the constant background scalar fields are absent in the [Formula: see text] SYM theory.

Spontaneous scalarization of charged black holes in the scalar-vector-tensor theory

We present spontaneous scalarization of charged black holes (BHs) which is induced by the coupling of the scalar field to the electromagnetic field strength and the double-dual Riemann tensor $L^{\mu\nu\alpha\beta}F_{\mu\nu}F_{\alpha\beta}$ in a scalar-vector-tensor theory. In our model, the scalarization can be realized under the curved background with a non-trivial electromagnetic field, such as Reissner-Nordstr$\ddot{\rm o}$m Black Holes (RN BHs). Firstly, we investigate the stability of the constant scalar field around RN BHs in the model, and show that the scalar field can suffer a tachyonic instability. Secondly, the bound state solution of the test scalar field around a RN BH and its stability are discussed. Finally, we construct scalarized BH solutions, and investigate their stability.

Cosmology from multimeasure multifield model

We consider the cosmological application of a (variant of) relatively newly proposed model1 unifying inflation, dark energy, dark matter, and the Higgs mechanism. The model was originally defined using additional non-Riemannian measures, but it can be reformulated into effective quintessential model unifying inflation, dark energy and dark matter. Here, we demonstrate numerically that it is capable of describing the entire evolution of the Universe in a seamless way, but this requires some revision of the model setup. The main reason is that there is a strong effective friction in the model, a feature which has been neglected in the pioneer work. This improves the model potential for proper description of the evolution of the Universe, because the friction ensures a finite time inflation with dynamically maintained low-value slow-roll parameters in the realistic scenarios. In addition, the model predicts the existence of a constant scalar field in late Universe.

δ Gravity, δ Matter and the Accelerated Expansion of the Universe

Introducing an additional symmetry (δ symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (δ gravity) based on two symmetric tensors, gμv and gμv where an effective metric, given by gμv = gμv + gμv must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of δ gravity applied to cosmology was presented, where the δ symmetry was fixed in order to simplify the analysis of the model. The model predicts an accelerated expansion of the Universe without a cosmological constant or additional scalar fields, ending in a Big Rip. We present the full-fledged δ gravity, introducing a new kind of matter fields (δ matter) in order to preserve the δ symmetry. In this approach the prediction of the expansion of the Universe is preserved, but the value of the cosmological parameters improve greatly by the inclusion of δ matter. Additionally, δ matter gives us an excellent candidate for Dark Matter.

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

We analytically construct asymptotically AdS5 black string solutions starting from the four-dimensional domain wall black hole of [1]. It is shown that its uplift gives a black string in d = 5 minimal gauged supergravity, with momentum along the string. Applying instead the residual symmetries of N = 2, d = 4 Fayet-Iliopoulos-gauged super-gravity discovered in [2] to the domain wall seed leads, after uplifting, to a dyonic black string that interpolates between AdS5 and AdS3 × H2 at the horizon. A Kaluza-Klein reduction of the latter along an angular Killing direction ϕ followed by a duality transformation yields, after going back to five dimensions, a black string with both momentum along the string and rotation along ϕ. This is the first instance of using solution-generating techniques in gauged supergravity to add rotation to a given seed. These solutions all have constant scalar fields. As was shown in [3], the construction of supersymmetric static magnetic black strings in the FI-gauged stu model amounts to solving the SO(2, 1) spinning top equations, which descend from an inhomogeneous version of the Nahm equations. We are able to solve these in a particular case, which leads to a generalization of the Maldacena-Nuñez solution.

All static and electrically charged solutions with Einstein base manifold in the arbitrary-dimensional Einstein\u2013Maxwell system with a massless scalar field

We present a simple and complete classification of static solutions in the Einstein–Maxwell system with a massless scalar field in arbitrary n(ge 3) dimensions. We consider spacetimes which correspond to a warped product M^2 times K^{n-2}, where K^{n-2} is a (n-2)-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant real scalar field consists of nine solutions for nge 4 and three solutions for n=3. A complete geometric analysis of the solutions is presented and the global mass and electric charge are determined for asymptotically flat configurations. There are two remarkable features for the solutions with nge 4: (i) Unlike the case with a vanishing electromagnetic field or constant scalar field, asymptotically flat solution is not unique, and (ii) The solutions can asymptotically approach the Bertotti–Robinson spacetime depending on the integrations constants. In accordance with the no-hair theorem, none of the solutions are endowed of a Killing horizon.

Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.

Hybrid metric-Palatini stars

We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein condensate stars in the recently proposed hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms. It turns out that the theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. In this paper, we derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework of the scalar-tensor representation of the hybrid metric-Palatini theory, and we investigate their solutions numerically for different equations of state of neutron and quark matter, by adopting for the scalar field potential a Higgs-type form. It turns out that the scalar-tensor definition of the potential can be represented as an Clairaut differential equation, and provides an explicit form for $f(\mathcal{R})$ given by $f(\mathcal{R})\ensuremath{\sim}\mathcal{R}+{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{eff}}$, where ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{eff}}$ is an effective cosmological constant. Furthermore, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly constructed in both general relativity and hybrid metric-Palatini gravity, thus allowing an in-depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, hybrid gravity stars are more massive than their general relativistic counterparts. Furthermore, two classes of stellar models corresponding to two particular choices of the functional form of the scalar field (constant value, and logarithmic form, respectively) are also investigated. Interestingly enough, in the case of a constant scalar field the equation of state of the matter takes the form of the bag model equation of state describing quark matter. As a possible astrophysical application of the obtained results, we suggest that stellar mass black holes, with masses in the range of 3.8 and $6\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, respectively, could be in fact hybrid metric-Palatini gravity neutron or quark stars.

Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $\Lambda$ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\overline{\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\overline{\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating $\Lambda$ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

Non-existence of Brans-Dicke theory in higher dimensional FRW universe

In this paper, we have studied exact solutions of Brans-Dicke (BD) theory for higher dimensional generalized Friedmann-Robertson-Walker (FRW) universe in the presence of strange quark matter (SQM) attached to the string cloud and domain walls. We have obtained that string tension density does not survive in this model. This result agrees with Kiran and Reddy, Krori et al., Sahoo and Mishra and Reddy. Also we have obtained constant scalar field in the presence of string cloud and domain walls. Then BD theory does not observe for higher dimensional FRW universe with SQM attached to the string cloud and domain walls. Our BD solutions turn into general relativity (GR). Finally, some physical properties are discussed.

Horndeski: beyond, or not beyond?

Determining the most general, consistent scalar tensor theory of gravity is important for building models of inflation and dark energy. In this work we investigate the number of degrees of freedom present in the theory of beyond Horndeski. We discuss how to construct the theory from the extrinsic curvature of the constant scalar field hypersurface, and find a simple expression for the action which guarantees the existence of the primary constraint necessary to avoid the Ostrogradsky instability. Our analysis is completely gauge-invariant. However we confirm that, mixing together beyond Horndeski with a different order of Horndeski, obstructs the construction of this primary constraint. Instead, when the mixing is between actions of the same order, the theory can be mapped to Horndeski through a generalised disformal transformation. This mapping however is impossible with beyond Horndeski alone, since we find that the theory is invariant under such a transformation. The picture that emerges is that beyond Horndeski is a healthy but isolated theory: combined with Horndeski, it either becomes Horndeski, or likely propagates a ghost.

Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. I. Neutral gravitational collapse

There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One of the existing proposals is using the evolving matter as an intrinsic `clock' while investigating the dynamics of gravitational systems. The objective of our research was to check whether scalar fields can serve as time variables during a dynamical evolution of a coupled multi-component matter-geometry system. We concentrated on a neutral case, which means that the elaborated system was not charged electrically nor magnetically. For this purpose, we investigated a gravitational collapse of a self-interacting complex and real scalar fields in the Brans-Dicke theory using the 2+2 spacetime foliation. We focused mainly on the region of high curvature appearing nearby the emerging singularity, which is essential from the perspective of quantum gravity. We investigated several formulations of the theory for various values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke field and the matter sector of the theory. The obtained results indicated that the evolving scalar fields can be treated as time variables in close proximity of the singularity due to the following reasons. The constancy hypersurfaces of the Brans-Dicke field are spacelike in the vicinity of the singularity apart from the case, in which the equation of motion of the field reduces to the wave equation due to a specific choice of free evolution parameters. The hypersurfaces of constant complex and real scalar fields are spacelike in the regions nearby the singularities formed during the examined process. The values of the field functions change monotonically in the areas, in which the constancy hypersurfaces are spacelike.