Constant Scalar Field Research Articles

Scalar field as a time variable during gravitational evolution

Using a scalar field as an intrinsic 'clock' while investigating the dynamics of gravitational systems has been successfully pursued in various researches on the border between classical and quantum gravity. The objective of our research was to check explicitly whether the scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity. For this purpose, we analyzed a gravitational collapse of a self-interacting scalar field within the framework of general relativity. The obtained results indicated that the hypersurfaces of constant scalar field are spacelike in dynamical regions nearby the singularities formed during the investigated process. The scalar field values change monotonically in the areas, in which the constancy hypersurfaces are spacelike.

A natural cosmological constant from chameleons

We present a simple model where the effective cosmological constant appears from chameleon scalar fields. For a Kachru–Kallosh–Linde–Trivedi (KKLT)-inspired form of the potential and a particular chameleon coupling to the local density, patches of approximately constant scalar field potential cluster around regions of matter with density above a certain value, generating the effect of a cosmological constant on large scales. This construction addresses both the cosmological constant problem (why Λ is so small, yet nonzero) and the coincidence problem (why Λ is comparable to the matter density now).

Irreversible thermodynamic description of interacting dark energy-dark matter cosmological models

We investigate the interaction between dark energy and dark matter in the framework of irreversible thermodynamics of open systems with matter creation/annihilation. We consider dark energy and dark matter as an interacting two-component (scalar field and ``ordinary'' dark matter) cosmological fluid in a homogeneous spatially flat and isotropic Friedmann-Robertson-Walker Universe. The thermodynamics of open systems as applied together with the gravitational field equations to the two-component cosmological fluid leads to a generalization of the elementary dark energy-dark matter interaction theory, in which the decay (creation) pressures are explicitly considered as parts of the cosmological fluid stress-energy tensor. Specific models describing coherently oscillating scalar waves, leading to a high particle production at the beginning of the oscillatory period, and models with a constant potential energy scalar field are considered. Furthermore, exact and numerical solutions of the gravitational field equations with dark energy-dark matter interactions are also obtained.

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an <i>U</i>(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field

We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newtonʼs constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martínez–Zanelli solution of Einsteinʼs equations with a negative cosmological constant coupled to conformal scalar field.

Scalar field cosmology in phase space

Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field's origin or its potential, the results are independent of the high-energy model.

Superconformal $ \mathcal{N} = {3} $ SYM low-energy effective action

We construct a manifestly $ \mathcal{N} = {3} $ supersymmetric low-energy effective action of $ \mathcal{N} = {3} $ super Yang-Mills theory. The effective action is written in the $ \mathcal{N} = {3} $ harmonic superspace and respects the full $ \mathcal{N} = {3} $ superconformal symmetry. On mass shell this action is responsible for the four-derivative terms in the $ \mathcal{N} = {4} $ SYM effective action, such as F 4/X 4 and its supersymmetric completions, while off shell it involves also higher- derivative terms. For constant Maxwell and scalar fields its bosonic part coincides, up to the F 6/X 8 order, with the bosonic part of the D3 brane action in the AdS5 × S 5 background. We also argue that in the sector of scalar fields it involves the correctly normalized Wess-Zumino term with the implicit SU(3) symmetry.

String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action in the presence of a constant background scalar axion field C(τ, σ) and an U(1) gauge field Aα(τ, σ) is studied. The axion field C and the U(1) gauge field Aα, are seen to behave like the Wess–Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.

A new extension of Hořava-Lifshitz gravity and curing pathologies of the scalar graviton

We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.

An anisotropic cosmological model in a modified Brans–Dicke theory

Recently, it has been shown that a four-dimensional (4D) Brans–Dicke (BD) theory with an effective matter field and a self-interacting potential can be achieved from the vacuum 5D BD field equations, where we refer to as a modified Brans–Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing the obtained formalism, we derive the induced matter on any 4D hypersurface in the context of the MBDT. We illustrate that if the usual spatial scale factors are functions of the time while the scale factor of extra dimension is constant, and the scalar field depends on the time and the fifth coordinate, then, in general, one will encounter inconsistencies in the field equations. Then, we assume that the scale factors and the scalar field depend on the time and the extra coordinate as separated variables in the power-law forms. Hence, we find a few classes of solutions in 5D spacetime through which we probe the one which leads to a generalized Kasner relation among the Kasner parameters. The induced scalar potential is found to be in the power law or in the logarithmic form; however, for a constant scalar field and even when the scalar field only depends on the fifth coordinate, it vanishes. The conservation law is indeed valid in this MBDT approach for the derived induced energy–momentum tensor (EMT). We proceed our investigations for a few cosmological quantities, where for simplicity we assume that the metric and the scalar field are functions of the time. Hence, the EMT satisfies the barotropic equation of state, and the model indicates that the constant mean Hubble parameter is not allowed. Thus, by appealing to the variation of the Hubble parameter, we assume a fixed deceleration parameter, and set the evolution of the quantities with respect to the fixed deceleration, the BD coupling and the state parameters. The WEC allows a shrinking extra dimension for a decelerating expanding universe that, in the constant scalar field, evolves the same way as the flat FRW spacetime in GR. The quantities for the stiff fluid and the radiation-dominated universe indicate an expanding universe commenced with a big bang. There is a horizon for each of the fluids, and the rate of expansion slows down by the time. The allowed ranges of the deceleration and the BD coupling parameters have been obtained, and the model gives an empty universe when the time goes to infinity.

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow approach of induced matter theory for 5D vacuum BD, introduce induced matter and potential in 4D hypersurfaces, and employ generalized FRW type solution. We confine ourselves to scalar field and scale factors be functions of the time. This makes the induced potential, by its definition, vanishes. When the scale factor of fifth dimension and scalar field are not constants, 5D eqs for any geometry admit a power law relation between scalar field and scale factor of fifth dimension. Hence the procedure exhibits that 5D vacuum FRW like eqs are equivalent, in general, to corresponding 4D vacuum ones with the same spatial scale factor but new scalar field and coupling constant. We show that 5D vacuum FRW like eqs or its equivalent 4D vacuum ones admit accelerated solutions. For constant scalar field, eqs reduce to usual FRW eqs with typical radiation dominated universe. For this situation we obtain dynamics of scale factors for any geometry without any priori assumption. For nonconstant scalar fields and spatially flat geometries, solutions are found to be power law and exponential ones. We also employ weak energy condition for induced matter, that allows negative/positive pressures. All types of solutions fulfill WEC in different ranges. The power law solutions with negative/positive pressures admit both decelerating and accelerating ones. Some solutions accept shrinking extra dimension. By considering nonghost scalar fields and recent observational measurements, solutions are more restricted. We illustrate that accelerating power law solutions, which satisfy WEC and have nonghost fields, are compatible with recent observations in ranges -4/3 < \omega </- -1.3151 and 1.5208 </- n < 1.9583 for dependence of fifth dimension scale factor with usual scale factor. These ranges also fulfill condition nonghost fields in the equivalent 4D vacuum BD eqs.

Vacuum Energy Fluctuations, The Induced Cosmological Constant and Cosmological Reconstruction in Non-Minimal Modified Gravity Models~!2009-09-09~!2009-09-10~!2010-06-03~!

The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.

Vacuum Energy Fluctuations, The Induced Cosmological Constant and Cosmological Reconstruction in Non-Minimal Modified Gravity Models

The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.

Effective dynamics of the closed loop quantum cosmology

In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of Λ. If the value of Λ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of Λ exceedscritical value Λc = 31/2mPl2/2πγ3 ≃ 21mPl2 then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed.

Thermodynamics of charged Brans–Dicke AdS black holes

It is well known that in four dimensions, black hole solution of the Brans–Dicke–Maxwell equations is just the Reissner–Nordstrom solution with a constant scalar field. However, in n⩾4 dimensions, the solution is not yet the (n+1)-dimensional Reissner–Nordstrom solution and the scalar field is not a constant in general. In this Letter, by applying a conformal transformation to the dilaton gravity theory, we derive a class of black hole solutions in (n+1)-dimensional (n⩾4) Brans–Dicke–Maxwell theory in the background of anti-de Sitter universe. We obtain the conserved and thermodynamic quantities through the use of the Euclidean action method. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble. We find that the solution is thermally stable for small α, while for large α the system has an unstable phase, where α is a coupling constant between the scalar and matter field.

Compatibility of the Einstein minimally coupled self-interacting scalar field theory with the solar system tests of gravity

We examine the compatibility of the Einstein minimally coupled self-interacting scalar field theory with the local tests of gravity. We find that apart from the trivial case of the Schwarzschild–de Sitter solution with a constant scalar field the theory does not admit any other static solution, which is consistent with the solar system tests of gravity.

The Decay of Massive Scalar Field in Non-Static Gödel Type Universe with Viscous Fluid and Heat Flow

In this study, we have investigated the dynamics of non-static Godel type rotating universe with massive scalar field, viscous fluid and heat flow in the presence of cosmological constant. For various cosmic matter forms, the behavior of the cosmological constant (Λ), shear (η) and bulk (ξ) viscosity coefficients and other kinematic quantities have studied in the early universe. We have showed the decay of massive scalar field in the non-static rotating Godel type universe and we have obtained constant scalar field with and without source density. Also, we have investigated the effects of massive scalar field on the matter density and pressure. From solutions of the field equations, we have a cosmological model with non-zero expansion, shear, heat flux and rotation. Also some physical and geometrical aspects of the model discussed.

Resource Letter DEAU-1: Dark energy and the accelerating universe

This Resource Letter provides a guide to the literature on dark energy and the accelerating universe. It is intended to be of use to researchers, teachers, and students at several levels. Journal articles, books, and websites are cited for the following topics: Einstein’s cosmological constant, quintessence or dynamical scalar fields, modified cosmic gravity, relations to high-energy physics, cosmological probes and observations, terrestrial probes, calculational tools and parameter estimation, teaching strategies and educational resources, and the fate of the universe.

On wormholes and black holes solutions of Einstein gravity coupled to a K-massless scalar field

We investigate the nature of black holes and wormholes admitted by a K-essence model involving a massless scalar field ϕ, minimally coupled to gravity. Via Weyl's formalism, we show that any axial wormhole of the theory can be generated by a unique pair of harmonic functions: U(λ) = π/2 C + C arctan(λ/λ0), ϕ(λ) = π/2 D + D arctan(λ/λ0) where λ is one of the oblate coordinate, λ0 > 0 and (C, D) real parameters. The properties of the wormholes depends crucially upon the values of the parameters (C, D). Whenever (C, D) are chosen so that 2C2 − kD2 = −2 the wormhole is spherical, while for the case where 2C2 − kD2 = −4 or 2C2 − kD2 = −6 the wormhole throat possesses toroidal topology. Those two families of wormholes exhaust all regular static and axisymmetric wormholes admitted by this theory. For completeness we add that whenever (C, D) satisfy 2C2 − kD2 = −2l with l ⩾ 3/2 one still generates a spacetime possessing two asymptotically flat but the throat connecting the two ends contains a string like singularity. For the refined case where 2C2 − kD2 = −2l with l = 4,5, ... the resulting spacetime represents a multi-sheeted configuration which even though free of curvature singularities nevertheless the spacetime topology is distinct to so far accepted wormhole topology. Spacetimes generated by the pair (U(λ), ϕ(λ)) and parameters (C, D) subject to 2C2 − kD2 = −2l with l < 3/2 contain naked curvature singularities. For the classes of regular wormholes, the parameters (C, D) determine the ADM masses of the asymptotically flat ends and can be positive, negative or zero. Except for the cases of zero mass wormholes, the two ends possess ADM masses of opposite sign. In contrast to wormhole sector, the black hole sector of the theory is trivial. Any static, asymptotically flat solution of the theory that admits a IR × S2 bifurcating, regular Killing horizon necessary possesses a constant exterior scalar field. Under the assumption that the event horizon of any static black hole of this theory is a Killing horizon, the results show that the only static black hole admitted by this K-essence model, is the Schwarzschild black hole.