Initial Scalar Field Research Articles

Tadpole cosmology: Milne solution as a cosmological constant hideout

Dynamical cancellation frameworks present a potential means of mitigating the effect of a large vacuum energy, that would otherwise ruin the late-time, low energy dynamics of the Universe. Certain models in the literature, such as the Fab Four and Well Tempering, realize this idea by introducing some degeneracy in the dynamical equations. In this paper, we introduce a third potential route to self-tuning, and infer the existence of a new, exact Milne solution in the simplest tadpole plus cubic-Galileon scalar-tensor theory. We study the dynamics of the scalar field and metric in the vicinity of the Milne coordinate singularity, and find that the vacuum solution belongs to a more general family of Milne-like metrics. By numerically evolving the field equations for a range of initial conditions, we show that the Milne solution is not an attractor, and varying the initial scalar field data can lead to completely different asymptotic states; exponential growth of the scale factor, a static non-spatially flat metric or a severe finite-time instability in the scalar field and metric. We generalise the Milne solution to a class of FLRW spacetimes, finding that the tadpole-cubic Galileon model admits perfect-fluid-like solutions in the presence of matter. Finally, we present a second Horndeski model which also admits an exact Milne solution, hinting at the existence of a larger undiscovered model space containing vacuum-energy-screened solutions.

Chaotic inflationary universe in Rastall gravity

We study Linde’s chaotic inflation in Rastall gravity with a homogeneous scalar field. In Einstein’s general theory of relativity, Linde obtained chaotic scenario, which emerged from chaotic distribution of scalar field satisfying a limiting value of the initial scalar field ϕo > 3 MP that lies in the quantum gravity. The upper limit on the initial scalar field is obtained for a sufficient inflation to encompass the present universe. In the Rastall gravity, the upper limit is reduced depending on the Rastall parameter γ < 1. The upper limit on ϕo is found to increases for [Formula: see text]. In the later case, sufficient inflation is not permitted and the role of curvaton field is explored for an acceptable early chaotic inflation.

Zero-dimensional models for gravitational and scalar QED decoherence

We investigate the dynamics of two quantum mechanical oscillator system–bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar quantum electrodynamics (QED). The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence for initial scalar field system superposition states.

Primordial black hole formation from massless scalar isocurvature

We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated Universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wave number $k$; $\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{k}^{2}{R}^{2})$, where $R$ is the radial coordinate. We find that a PBH is formed for a sufficiently large amplitude of the scalar field profile. Nevertheless, we find that the late time behavior of the gravitational collapse is dominated by the dynamics of the fluid but not by the scalar field, which is analogous to the PBH formation from an adiabatic perturbation in the radiation-dominated Universe.

A conservative Eulerian-Lagrangian decomposition principle for the solution of multi-scale flow problems at high Schmidt or Prandtl numbers

The simulation of turbulent flow that involves scalar transport at high Schmidt or Prandtl numbers is a major challenge. Enhanced Schmidt and Prandtl numbers demand an excessive increase in numerical resolution. Otherwise, the accuracy of transport would suffer substantially through unresolved information and numerical diffusion. With the aim of providing an efficient alternative for such applications, this paper presents a simulation method that is based on a novel Eulerian-Lagrangian decomposition principle (ELD) of the transported quantity. Low-pass filtering of the initial scalar quantity field separates it into a smooth low-frequency component and a fine-structured high-frequency component. The low-frequency component is represented and transported according to the Eulerian description by applying the Finite Volume Method (FVM) with a numerical resolution according to the Kolmogorov scale. The high-frequency component is translated into the Lagrangian description by the formation of particles, which are transported in parallel. By exchanging information between the two components, a re-initialisation mechanism ensures that the frequency-based decomposition is maintained throughout the simulation. Such ELD approach combines the efficiency of the FVM with the numerical stability of Lagrangian particles. As a result of the frequency-separation, the latter are by principle limited to zones of small scales and thus effectively complement the FVM. Furthermore, the particle information allows details of the scalar quantity field to be reconstructed that extend into the sub-grid level. By using a mixing layer setup, the proposed method is tested for a range of Schmidt numbers, and the numerical costs are considered and discussed.

Instability of spherical naked singularities of a scalar field under gravitational perturbations

In this paper, we initiate the study of the instability of naked singularities beyond spherical symmetry. In a series of papers, Christodoulou proved that naked singularities are not stable in the context of the spherically symmetric Einstein equations coupled with a massless scalar field. We study in this paper the next simplest case: a characteristic initial value problem of this coupled system with the initial data given on two intersecting null cones, the incoming one of which is assumed to be spherically symmetric and singular at its vertex, and the outgoing one of which has no symmetries. It is shown that, arbitrarily fixing the initial scalar field, the set of the initial conformal metrics on the outgoing null cone such that the maximal future development does not have any sequences of closed trapped surfaces approaching the singularity, is of first category in the whole space in which the shear tensors are continuous. Such a set can then be viewed as exceptional, although the exceptionality is weaker than the at least $1$ co‑dimensionality in spherical symmetry. Almost equivalently, it is also proved that, arbitrarily fixing an incoming null cone $\underline{C}_{\,\varepsilon}$ to the future of the initial incoming null cone, the set of the initial conformal metrics such that the maximal future development has at least one closed trapped surface before $\underline{C}_{\,\varepsilon}$, contains an open and dense subset of the whole space. Since the initial scalar field can be chosen such that the singularity is naked if the initial shear is set to be zero, we may say that the spherical naked singularities of a self-gravitating scalar field are not stable under gravitational perturbations. This in particular gives new families of non-spherically symmetric gravitational perturbations different from the original spherically symmetric scalar perturbations given by Christodoulou.

Triple Hill’s Vortex Synthetic Eddy Method

The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergence-free anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on both isotropic and anisotropic turbulent velocity fields, in the framework of grid turbulence decay and turbulent channel flow, respectively. The transition from artificial to realistic turbulence in the proximity to the inflow boundary was found to be small in all test cases that were considered.

Dynamical formation and stability of fermion-boson stars

Gravitationally bound structures composed by fermions and scalar particles known as fermion-boson stars are regular and static configurations obtained by solving the coupled Einstein-Klein-Gordon-Euler (EKGE) system. In this work, we discuss one possible scenario through which these fermion-boson stars may form by solving numerically the EKGE system under the simplifying assumption of spherical symmetry. Our initial configurations assume an already existing neutron star surrounded by an accreting cloud of a massive and complex scalar field. The results of our simulations show that once part of the initial scalar field is expelled via gravitational cooling the system gradually oscillates around an equilibrium configuration that is asymptotically consistent with a static solution of the system. The formation of fermion-boson stars for large positive values of the coupling constant in the self-interaction term of the scalar-field potential reveal the presence of a node in the scalar field. This suggests that a fermionic core may help stabilize configurations with nodes in the bosonic sector, as happens for purely boson stars in which the ground state and the first excited state coexist.

Dynamically Generated Inflationary ΛCDM

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

Initial conditions for inflation in an FRW universe

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.

The Born–Oppenheimer method, quantum gravity and matter

We illustrate and examine diverse approaches to the quantum matter–gravity system which refer to the Born–Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It does not involve the classical limit for gravitation and has a highly peaked initial scalar field state. We point out that it does not resemble in any way our traditional BO approach. Instead it does resemble an alternative, canonically quantised, non BO approach which we have also previously discussed.

A Lagrangian fluctuation–dissipation relation for scalar turbulence. Part I. Flows with no bounding walls

An exact relation is derived between scalar dissipation due to molecular diffusivity and the randomness of stochastic Lagrangian trajectories for flows without bounding walls. This ‘Lagrangian fluctuation–dissipation relation’ equates the scalar dissipation for either passive or active scalars to the variance of scalar inputs associated with initial scalar values and internal scalar sources, as these are sampled backward in time by the stochastic Lagrangian trajectories. As an important application, we reconsider the phenomenon of ‘Lagrangian spontaneous stochasticity’ or persistent non-determinism of Lagrangian particle trajectories in the limit of vanishing viscosity and diffusivity. Previous work on the Kraichnan (Phys. Fluids, 1968, vol. 11, pp. 945–953) model of turbulent scalar advection has shown that anomalous scalar dissipation is associated in that model with Lagrangian spontaneous stochasticity. There has been controversy, however, regarding the validity of this mechanism for scalars advected by an actual turbulent flow. We here completely resolve this controversy by exploiting the fluctuation–dissipation relation. For either a passive or an active scalar advected by any divergence-free velocity field, including solutions of the incompressible Navier–Stokes equation, and away from walls, we prove that anomalous scalar dissipation requires Lagrangian spontaneous stochasticity. For passive scalars, we prove furthermore that spontaneous stochasticity yields anomalous dissipation for suitable initial scalar fields, so that the two phenomena are there completely equivalent. These points are illustrated by numerical results from a database of homogeneous isotropic turbulence, which provide both additional support to the results and physical insight into the representation of diffusive effects by stochastic Lagrangian particle trajectories.

Far-from-equilibrium initial conditions probed by a nonlocal observable

Using the gauge/gravity duality, we investigate the evolution of an out-of-equilibrium strongly-coupled plasma from the viewpoint of the two-point function of scalar gauge-invariant operators with large conformal dimension. This system is out of equilibrium due to the presence of anisotropy and/or a massive scalar field. Considering various functions for the initial anisotropy and scalar field, we conclude that the effect of the anisotropy on the evolution of the two-point function is considerably more than the effect of the scalar field. We also show that the ordering of the equilibration time of the one-point function for the non-probe scalar field and the correlation function between two points with a fixed separation can be reversed by changing the initial configuration of the plasma, when the system is out of the equilibrium due to the presence of at least two different sources like our problem. In addition, we find the equilibration time of the two-point function to be linearly increasing with respect to the separation of the two points with a fixed slope, regardless of the initial configuration that we start with. Finally we observe that, for larger separations the geodesic connecting two points on the boundary crosses the event horizon after it has reached its final equilibrium value, meaning that the two-point function can probe behind the event horizon.

Upscaling of absolute permeability for a super element model of petroleum reservoir

This paper presents a new method of local upscaling of absolute permeability for super element simulation of an oil reservoir. Upscaling was performed for each block of a super element unstructured grid. For this purpose, a set of problems of a one-phase steady-state flow was solved on a fine computational grid with the initial scalar field of absolute permeability with various boundary conditions. These conditions reflect the specific variants of filtrational flow through the super element and take into account the presence or absence of boreholes in the coarse block. The resulting components of the effective permeability tensor in each super element were found from the solution of the problem of minimizing the deviations of the normal flows through the super element faces, averaged on a detailed computational grid, from those approximated on a coarse super element grid. The results of using the method are demonstrated for reservoirs with river-type absolute permeability. The method is compared with the traditional methods of local upscaling.

Beginning inflation in an inhomogeneous universe

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

Computational characterization of ignition regimes in a syngas/air mixture with temperature fluctuations

Auto-ignition characteristics of compositionally homogeneous reactant mixtures in the presence of thermal non-uniformities and turbulent velocity fluctuations were computationally investigated. The main objectives were to quantify the observed ignition characteristics and numerically validate the theory of the turbulent ignition regime diagram recently proposed by Im et al. 2015 [29] that provides a framework to predict ignition behavior a priori based on the thermo-chemical properties of the reactant mixture and initial flow and scalar field conditions. Ignition regimes were classified into three categories: weak (where deflagration is the dominant mode of fuel consumption), reaction-dominant strong, and mixing-dominant strong (where volumetric ignition is the dominant mode of fuel consumption). Two-dimensional (2D) direct numerical simulations (DNS) of auto-ignition in a lean syngas/air mixture with uniform mixture composition at high-pressure, low-temperature conditions were performed in a fixed volume. The initial conditions considered two-dimensional isotropic velocity spectrums, temperature fluctuations and localized thermal hot spots. A number of parametric test cases, by varying the characteristic turbulent Damköhler and Reynolds numbers, were investigated. The evolution of the auto-ignition phenomena, pressure rise, and heat release rate were analyzed. In addition, combustion mode analysis based on front propagation speed and computational singular perturbation (CSP) was applied to characterize the auto-ignition phenomena. All results supported that the observed ignition behaviors were consistent with the expected ignition regimes predicted by the theory of the regime diagram. This work provides new high-fidelity data on syngas ignition characteristics over a broad range of conditions and demonstrates that the regime diagram serves as a predictive guidance in the understanding of various physical and chemical mechanisms controlling auto-ignition in thermally inhomogeneous and compositionally homogeneous turbulent reacting flows.

Evolution of material surfaces in the temporal transition in channel flow

We report a Lagrangian study on the evolution of material surfaces in the Klebanoff-type temporal transitional channel flow. Based on the Eulerian velocity field from the direct numerical simulation, a backward-particle-tracking method is applied to solve the transport equation of the Lagrangian scalar field, and then the isosurfaces of the Lagrangian field can be extracted as material surfaces in the evolution. Three critical issues for Lagrangian investigations on the evolution of coherent structures using material surfaces are addressed. First, the initial scalar field is uniquely determined based on the proposed criteria, so that the initial material surfaces can be approximated as vortex surfaces, and remain invariant in the initial laminar state. Second, the evolution of typical material surfaces initially from different wall distances is presented, and then the influential material surface with the maximum deformation is identified. Large vorticity variations with the maximum curvature growth of vortex lines are also observed on this surface. Moreover, crucial events in the transition can be characterized in a Lagrangian approach by conditional statistics on the material surfaces. Finally, the influential material surface, which is initially a vortex surface, is demonstrated as a surrogate of the vortex surface before significant topological changes of vortical structures. Therefore, this material surface can be used to elucidate the continuous temporal evolution of vortical structures in transitional wall-bounded flows in a Lagrangian perspective. The evolution of the influential material surface is divided into three stages: the formation of a triangular bulge from an initially disturbed streamwise–spanwise sheet, rolling up of the vortex sheet near the bulge ridges with the vorticity intensification and the generation and evolution of signature hairpin-like structures with self-induced dynamics of vortex filaments.

A DNS study of the ignition of lean PRF/air mixtures with temperature inhomogeneities under high pressure and intermediate temperature

Two-dimensional direct numerical simulations (DNSs) of ignition of lean primary reference fuel (PRF)/air mixtures at high pressure and intermediate temperature near the negative temperature coefficient (NTC) regime were performed with a 116 species-reduced mechanism to elucidate the effects of fuel composition, thermal stratification, and turbulence on PRF homogeneous charge compression-ignition (HCCI) combustion. In the DNSs, temperature and velocity fluctuations are superimposed on the initial scalar fields with different PRF compositions. In general, it was found that the mean heat release rate increases slowly and the overall combustion occurs rapidly with increasing thermal stratification regardless of the fuel composition. In addition, the effect of the fuel composition on the ignition characteristics of PRF/air mixtures was found to be significantly reduced with increasing thermal stratification. Chemical explosive mode (CEM) and displacement speed analyses verified that nascent ignition kernels induced by hot spots due to a high degree of thermal stratification usually develop into deflagration waves rather than spontaneous auto-ignition at reaction fronts and as such, the mean heat release rate becomes more distributed over time. These analyses also revealed that the fuel composition effect vanishes as the degree of thermal stratification is increased because the deflagration mode of combustion, of which propagation characteristics are nearly identical for different PRF/air mixtures, becomes more prevailing with increasing degree of thermal stratification. Ignition Damköhler number was proposed to quantify the successful development of deflagration waves from nascent ignition kernels; for cases with large ignition Damköhler number, turbulence with high intensity and short timescale can advance the overall combustion by increasing the overall turbulent flame area instead of homogenizing initial mixture inhomogeneities.

Direct numerical simulations of the ignition of a lean biodiesel/air mixture with temperature and composition inhomogeneities at high pressure and intermediate temperature

The effects of the stratifications of temperature, T, and equivalence ratio, ϕ, on the ignition characteristics of a lean homogeneous biodiesel/air mixture at high pressure and intermediate temperature are investigated using direct numerical simulations (DNSs). 2-D DNSs are performed at a constant volume with the variance of temperature and equivalence ratio (T′ and ϕ′) together with a 2-D isotropic velocity spectrum superimposed on the initial scalar fields. In addition, three different T–ϕ correlations are investigated: (1) baseline cases with T′ only or ϕ′ only, (2) uncorrelated T–ϕ distribution, and (3) negatively-correlated T–ϕ distribution. It is found that the overall combustion is more advanced and the mean heat release rate is more distributed over time with increasing T′ and/or ϕ′ for the baseline and uncorrelated T–ϕ cases. However, the temporal advancement and distribution of the overall combustion caused by T′ or ϕ′ only are nearly annihilated by the negatively-correlated T–ϕ fields. The chemical explosive mode and Damköhler number analyses verify that for the baseline and uncorrelated T–ϕ cases, the deflagration mode is predominant at the reaction fronts for large T′ and/or ϕ′. On the contrary, the spontaneous ignition mode prevails for cases with small T′ or ϕ′, especially for cases with negative T–ϕ correlations, and hence, simultaneous auto-ignition occurs throughout the entire domain, resulting in an excessive rate of heat release. It is also found that turbulence with large intensity, u′, and a short time scale can effectively smooth out initial thermal and compositional fluctuations such that the overall combustion is induced primarily by spontaneous ignition. Based on the present DNS results, the generalization of the effects of T′,ϕ′, and u′ on the HCCI combustion is made to clarify each effect. These results suggest that temperature and composition stratifications together with a well-designed T–ϕ correlation can alleviate an excessive rate of pressure rise and control the ignition-timing in homogeneous charge compression-ignition (HCCI) combustion.

Direct numerical simulations of the ignition of lean primary reference fuel/air mixtures with temperature inhomogeneities

The effects of fuel composition, thermal stratification, and turbulence on the ignition of lean homogeneous primary reference fuel (PRF)/air mixtures under the conditions of constant volume and elevated pressure are investigated by direct numerical simulations (DNSs) with a new 116-species reduced kinetic mechanism. Two-dimensional DNSs were performed in a fixed volume with a two-dimensional isotropic velocity spectrum and temperature fluctuations superimposed on the initial scalar fields with different fuel compositions to elucidate the influence of variations in the initial temperature fluctuation and turbulence intensity on the ignition of three different lean PRF/air mixtures. In general, it was found that the mean heat release rate increases slowly and the overall combustion occurs fast with increasing thermal stratification regardless of the fuel composition under elevated pressure and temperature conditions. In addition, the effect of the fuel composition on the ignition characteristics of PRF/air mixtures was found to vanish with increasing thermal stratification. Chemical explosive mode (CEM), displacement speed, and Damköhler number analyses revealed that the high degree of thermal stratification induces deflagration rather than spontaneous ignition at the reaction fronts, rendering the mean heat release rate more distributed over time subsequent to thermal runaway occurring at the highest temperature regions in the domain. These analyses also revealed that the vanishing of the fuel effect under the high degree of thermal stratification is caused by the nearly identical propagation characteristics of deflagrations of different PRF/air mixtures. It was also found that high intensity and short-timescale turbulence can effectively homogenize mixtures such that the overall ignition is apt to occur by spontaneous ignition. These results suggest that large thermal stratification leads to smooth operation of homogeneous charge compression-ignition (HCCI) engines regardless of the PRF composition.