Dynamics Of Scalar Field Research Articles

Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields

We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field configurations, given by certain spaces of functionals which are studied here in depth. The analysis of such functionals is characterized by a combination of geometric, analytic and algebraic elements which (1) make our approach closer to quantum field theory, (2) allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and (3) provide a new pathway towards understanding dynamics. Particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and their linearizations.

An extended theory of gravity in a modified Riemann’s geometry

In this work, we study the evolution of an isotropic universe in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field [Formula: see text] as a complex vectorial function depending on a dynamical scalar field [Formula: see text]. By using the latest observational data, we observe that for [Formula: see text] the universe starts accelerating at the critical scale factor [Formula: see text] which corresponds to a redshift of [Formula: see text]. We also find that the dark energy fluid considered in this model is a generalized fluid with equation of state [Formula: see text].

Cosmic acceleration in the Randall-Sundrum II brane world

In this paper, we implement the dynamical system tools to study the dynamics of a self-interacting scalar field for suitable interactions of dark energy and dark matter in the Randall-Sundrum II brane scenario. Here we investigate three distinct forms of interaction strength namely, $I_{\phi}=\alpha\dot{\rho_{\phi}}$ , $I_{m1}=\delta \dot{\phi} \rho_{m}$ and $I_{m2}=\frac{\sigma\dot{\phi}^{2} \rho_{m}}{H}$ . We consider a homogeneous and isotropic Friedmann-Robertson-Walker brane model. The transformation equations are simplified to an autonomous system of ordinary differential equations by a suitable change of variables and hence a dynamical system analysis is performed for the respective interacting models in RS II brane cosmology. During the dynamical system analysis, we use the linear stability theory to study the stability of hyperbolic points, but these linearization techniques fail for non-hyperbolic points. So we apply the center manifold theory to determine the stability of non-hyperbolic points. For these specific interaction strengths, the 3D and 4D dynamical system analysis infers the existence of late-time attractors. These attractors are found for constant potential and inverse power law potential. The presence of these attractors results in late-time cosmic acceleration.

Superradiance and dynamical evolution of a charged scalar field in an asymptotically anti–de-Sitter dilatonic black hole

We study the dynamics of charged massless scalar fields in asymptotically anti–de Sitter (AdS) dilatonic black holes. The instability of the scalar field, which is triggered by the charged superradiant effect and Dirichlet boundary condition at AdS spatial infinity, can be notably described by exponential growth of the scalar field amplitude in time evolving and unstable quasinormal modes of scalar field perturbation. The numerical computation to demonstrate the superradiant instability of the charged scalar field are performed in the time domain and frequency domain, respectively. We confirm the mode that dominates long time behavior of scalar field matches with quasinormal mode obtained from frequency domain analysis quite well. It is well known the small Reissner-Nordstrom-anti–de Sitter (RN-AdS) black holes are superradiant unstable, while the large RN-AdS black holes are stable against the charged scalar perturbations. According to our numerical results, it is observed that the large dilatonic AdS black holes are also superradiant unstable. At last, we conclude that there exist rapid exponential growing superradiant modes in charged dilatonic AdS black holes, which is significant for the nonlinear dynamical evolution of charged superradiant instability.

Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant.

Gravitational Frames and Scalar Field Dynamics

Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and are found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough to remain conformal invariant. They should also be connected directly to the scalar curvature. Because of this characteristics, we investigated the structure and interactions of scalar fields under the conformal transformations. We show how to reduce the quadratic quantum contributions in the single scalar field theory. In the multi-scalar field theories, we analyzed interactions in certain limits. We suggest a new method for stabilizing Higgs bosons.

How the turbulent/non-turbulent interface is different from internal turbulence

The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20$^{\text{o}}$. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.

Varying constants driven baryogenesis

We study the spontaneous baryogenesis scenario in the early universe for three different frameworks of varying constants theories. We replace the constants by dynamical scalar fields playing the role of thermions. We first obtain the results for baryogenesis driven by the varying gravitational constant, G, as in the previous literature, then challenge the problem for varying fine structure constant alpha models as well as for varying speed of light c models. We show that in each of these frameworks the current observational value of the baryon to entropy ratio, eta _B sim 8.6 cdot 10^{-11}, can be obtained for large set of parameters of dynamical constants models as well as the decoupling temperature, and the characteristic cut-off length scale.

Constraints on Hořava gravity from binary black hole observations

Ho\v{r}ava gravity breaks Lorentz symmetry by introducing a preferred spacetime foliation, which is defined by a timelike dynamical scalar field, the khronon. The presence of this preferred foliation makes black hole solutions more complicated than in General Relativity, with the appearance of multiple distinct event horizons: a matter horizon for light/matter fields, a spin-0 horizon for the scalar excitations of the khronon, a spin-2 horizon for tensorial gravitational waves, and even, at least in spherical symmetry, a universal horizon for instantaneously propagating modes appearing in the ultraviolet. We study how black hole solutions in Ho\v{r}ava gravity change when the black hole is allowed to move with low velocity relative to the preferred foliation. These slowly moving solutions are a crucial ingredient to compute black hole "sensitivities" and predict gravitational wave emission (and in particular dipolar radiation) from the inspiral of binary black hole systems. We find that for generic values of the theory's three dimensionless coupling constants, slowly moving black holes present curvature singularities at the universal horizon. Singularities at the spin-0 horizon also arise unless one waives the requirement of asymptotic flatness at spatial infinity. Nevertheless, we have verified that at least in a one-dimensional subset of the (three-dimensional) parameter space of the theory's coupling constants, slowly moving black holes are regular everywhere, even though they coincide with the general relativistic ones (thus implying in particular the absence of dipolar gravitational radiation). Remarkably, this subset of the parameter space essentially coincides with the one selected by the recent constraints from GW170817 and by solar system tests.

Casimir effect in quadratic theories of gravity

In this paper, we study the Casimir effect in a curved spacetime described by gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and compute the corresponding mean vacuum energy density and pressure in the framework of quadratic theories of gravity. Since we are interested in the weak-field limit, as far as the gravitational sector is concerned we work in the linear regime. Remarkably, corrections to the flat spacetime result due to extended models of gravity (although very small) may appear at the first-order of our perturbative analysis, whereas general relativity contributions start appearing at the second order. Future experiments on the Casimir effect might represent a useful tool to test and constrain extended theories of gravity.

Cosmological Solutions and Quantum Measurements in Conformal Vacuum Analogue

In a quantum measurement with post selection condition for transient short range observations with weak values as statistical ensembles in a time reversed scenario, vacuum energy fluctuations with entangled entropy and with its qubits of information can show transitions to action potentials for energy flows of an anomalous nature, so that superfluid state of vacuum as a quantum condensate system is relativistically transformed as an idealized cosmological fluid system with ultra high temperatures and vorticity, like in Blackhole analogous non singular metric of Einstein vacuum solutions of field equations. This can also explain quark gluon plasmic fluids in such metrics corresponding to quantum fluid vortex systems in a highly thermalised state. For short range and short lived observers, vacuum is measured as a quantum entangled system, with energy fluctuations in a strongly correlated state. This can have analogies with a spin coupled many body system of quantum particles corresponding to a fermionic superfluid as a scalar field with boson excitation and higher amplitude phonon modes. There is conformance with a system of strongly correlated quantum harmonic oscillators where the motion can be approximated to a Fourier Transform of KG equation as a generalised Klein Gordon one describing a quantized complex scalar field dynamics with a self interaction potential. The de Sitter vacuum invariant can be shown to correspond to a Black hole like metric in a non singular solution of field equations, with negative energy domains due to torsion tensor and Dirac Spinor minimal coupling. The geometrical vorticity with space time fluid state angular momentum of a large order can correspond to 2D quantum vortex flows in superfluids. The initial conditions of the hydrodynamic reveal negative energy and negative temperature domains prior to onset of quantum turbulence as the idealized fluid system expands and decays due to entropic effects, naturally. This can show time reversal behaviour with short lived local violations of the second law of thermodynamics, given an entropic lowering effect. However there is entanglement entropy with high mutual information due to strongly correlated state that might even imply negative conditional information. A situation thus locally exists for a time interval of a transient nature when quantum weak measurements by a nearby short range observer can manipulate quantum fluctuations like a supersystem in nature, having analogies to a quantum Maxwell demon translating high mutual information of strongly correlated quantum entangled states of conformal vacuum to action potentials for energy dissipation and work. Quantum mechanical indeterminism permits imposing post selection condition in such time reversed, scenario, so that fast thermalization can take place in a transition from negative temperature state to ultrahigh positive absolute hot conditions, as if a thermodynamic engine with higher than Carnot efficiencies is operating, locally and transiently.

Scalar fields on λ-deformed cosets

We study dynamics of scalar fields on a large class of geometries described by integrable sigma models. Although equations of motion are not separable due to absence of isometries and Killing tensors, we completely determine the spectra using algebraic and group-theoretic methods.

Schwarzschild-de Sitter black hole in canonical quantization

We solve Wheeler-De Witt (WDW) metric probability wave equation on the apparent horizon hypersurface of the Schwarzschild de Sitter (SdS) black hole. To do so we choose radial dependent mass function M(r) for its internal regions in the presence of a dynamical massless quantum matter scalar field ψ(r) and calculate canonical supper hamiltonian constraint on t-constant hypersurface near the horizon r = M(r). In this case M(r) become geometrical degrees of freedom while ψ(r) is matter degrees of freedom of the apparent horizon. However our solution is obtained versus the quantum harmonic oscillator which defined against the well known hermit polynomials. In the latter case we obtain quantized mass of the SdS quantum black hole as in which Λ is the cosmological constant and n = 0,1, 2, ⋯ are quantum numbers of the hermit polynomials. This shows that a quantized SdS in its ground state has a nonzero value for the mass . Thus one can infer that the latter result satisfies Penrose hypotheses for cosmic censorship where a causal singularity may be covered by a horizon surface.

Zero modes, instantons and fluctuations in the Kraichnan model

Self-similar instanton solutions of the stochastic dynamics of the full passive scalar field in the Kraichnan model of turbulent advection are good candidates for describing the coherent motion of fluid particles leading to the production of strong gradients of the scalar and intermittency properties. By introducing a description of fluid particles in terms of quantum bosons, we show that instantons can be set in correspondence by a Legendre transformation with the so-called zero modes which are known, since the late 90s, to constitute the good mathematical framework for understanding and quantifying anomalous scaling in the Kraichnan model. Sticking to the classical level of approximation in the instanton approach leads clearly to an overestimation of scaling exponents of the structure functions of the scalar. To get further and incorporate the effect of fluctuations, we use the semiclassical instanton solutions as building blocks of more refined trial many-body wave functions for zero modes. One of the proposed approximation schemes gives surprisingly good estimates of scaling exponents even at low statistical orders and points towards a saturation of exponents at high statistical orders, as predicted by many authors either from numerics or analytic investigations in the large d limit.

D = 1 Supergravity and Quantum Cosmology

Using a D = 1 supergravity framework I construct a super-Friedmann equation for an isotropic and homogenous universe including dynamical scalar fields. In the context of quantum theory this becomes an equation for a wave-function of the universe of spinorial type, the Wheeler-DeWitt- Dirac equation. It is argued that a cosmological constant breaks a certain chiral symmetry of this equation, a symmetry in the Hilbert space of universe states, which could protect a small cosmological constant from being affected by large quantum corrections.

Open quantum cosmological system

We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of a cubic interaction term from the gravitational action and tracing out a set of longer wavelength modes, we find that the evolution of the system is non-Hamiltonian and non-Markovian. We find linear dissipation terms for a few modes with wavelength near the boundary between system and bath and nonlinear dissipation terms for all modes. The non-Hamiltonian terms persist to late times when the scalar field dynamics is such that the curvature perturbation continues to evolve on super-Hubble scales.

Cosmological implications of ultralight axionlike fields

Cosmological observations are used to test for imprints of an ultra-light axion-like field (ULA), with a range of potentials $V(\phi)\propto[1-\cos(\phi/f)]^n$ set by the axion-field value $\phi$ and decay constant $f$. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For $n\!=\!1$, once dynamical, the axion energy density dilutes as matter; for $n\!=\!2$ it dilutes as radiation and for $n\!=\!3$ it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual $n=1$ case. ULA models are parameterized by the redshift $z_c$ when the field becomes dynamical, the fractional energy density $f_{z_c} \equiv \Omega_a(z_c)/\Omega_{\rm tot}(z_c)$ in the axion field at $z_c$, and the effective sound speed $c_s^2$. Using Planck, BAO and JLA data, constraints on $f_{z_c}$ are obtained. ULAs are degenerate with dark energy for all three potentials if $1+z_c \lesssim 10$. When $3\times10^4 \gtrsim 1+z_c \gtrsim 10 $, $f_{z_c}$ is constrained to be $ \lesssim 0.004 $ for $n=1$ and $f_{z_c} \lesssim 0.02 $ for the other two potentials. The constraints then relax with increasing $z_c$. These results strongly constrain ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal.

The instability spectra of near-extremal Reissner–Nordström–de Sitter black holes

The linearized dynamics of charged massive scalar fields in the near-extremal charged Reissner–Nordström–de Sitter (RNdS) black-hole spacetime is studied analytically. Interestingly, it is proved that the non-asymptotically flat charged black-hole-field system is characterized by unstable (exponentially growing in time) complex resonant modes. Using a WKB analysis in the eikonal large-mass regime Mμ≫1, we provide a remarkably compact analytical formula for the quasinormal resonant spectrum {ωn(M,Q,Λ,μ,q)}n=0n=∞ which characterizes the unstable modes of the composed RNdS-black-hole-charged-massive-scalar-field system [here {M,Q,Λ} are respectively the mass, electric charge, and cosmological constant of the black-hole spacetime, and {μ,q} are the proper mass and charge coupling constant of the linearized field].

Functional renormalization group for stochastic inflation

We apply the functional renormalization group to Starobinsky's stochastic equation describing the local dynamics of a light scalar field in de Sitter. After elaborating on the over-damped regime of stochastic dynamics, we introduce an effective average action for the stochastic field, resulting by progressively integrating out frequencies, and study its flow equation in the local potential approximation (LPA). This effective action determines the approach to equilibrium and allows for the computation of unequal time correlators ⟨ϕ(t)ϕ(t+Δ t)⟩ for large values of Δ t. The stochastic RG flow in the LPA can be formulated in two ways, one that preserves the stochastic supersymmetry and one that breaks it. We show that both predict a characteristic decay time very close to that determined by the dynamical mass for a massless self-interacting scalar in de Sitter m2∼ √λH2. Furthermore, the temporal supersymmetric formulation remarkably recovers the flow for the effective potential found using Quantum Field Theory methods and a smoothing over spatial wavelengths. We also discuss how the stochastic framework generically predicts an infrared mass which is a few percent smaller than the dynamical mass obtained in the LPA. Our results further support the notion that stochastic inflation captures the correct IR dynamics of light scalar fields in inflation.

Stability analysis of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity has an interesting feature that the parity violating term exists, and the coupling is determined by a dynamical scalar field. When the spacetime has spherical symmetry, the parity violating term vanishes, and then the metric of the Schwarzschild spacetime with vanishing scalar field is an exact solution of dynamical Chern-Simons gravity. The effect of the Chern-Simons coupling appears in the study of perturbation around the Schwarzschild spacetime. Due to the parity violating term, the odd parity metric perturbation and the perturbed scalar field are coupled, and the perturbed field equations take the form of the coupled system of the Schr\"odinger equations. We prove linear mode stability for a generic massive scalar.