Inhomogeneous Perturbations Research Articles

Anisotropic instability in a higher order gravity theory

We study a metric cubic gravity theory considering odd-parity modes of linear inhomogeneous perturbations on a spatially homogeneous Bianchi type I manifold close to the isotropic de Sitter spacetime. We show that in the regime of small anisotropy, the theory possesses new degrees of freedom compared to General Relativity, whose kinetic energy vanishes in the limit of exact isotropy. From the mass dispersion relation we show that such theory always possesses at least one ghost mode as well as a very short-time-scale (compared to the Hubble time) classical tachyonic (or ghost-tachyonic) instability. In order to confirm our analytic analysis, we also solve the equations of motion numerically and we find that this instability is developed well before a single e-fold of the scale factor. This shows that this gravity theory, as it is, cannot be used to construct viable cosmological models.

Anisotropy screening in Horndeski cosmologies

We consider anisotropic cosmologies in a particular shift-symmetric Horndeski theory containing the $G^{\mu\nu}\partial_\mu\phi \partial_\nu\phi$ coupling, where $G^{\mu\nu}$ is the Einstein tensor. This theory admits stable in the future self-accelerating cosmologies whose tensor perturbations propagate with the velocity very close to the speed of light such that the theory agrees with the gravity wave observations. Surprisingly, we find that the anisotropies within the Bianchi I homogeneous spacetime model are screened at early time by the scalar charge, whereas at late times they are damped in the usual way. Therefore, contrary to what one would normally expect, the early state of the universe in the theory cannot be anisotropic and (locally) homogeneous in the absence of spatial curvature. The early universe cannot be isotropic either, because it should then be unstable with respect to inhomogeneous perturbations. As a result, the early universe should be inhomogeneous. At the same time, we find that in the spatially curved Bianchi IX case the anisotropies can be strong at early times even in the presence of a scalar charge.

Spatio-temporal numerical solutions of the coupled real and complex Ginzburg-Landau amplitude equations for one-dimensional systems near the Turing-Hopf bifurcation

In this paper, the solutions of the coupled Ginzburg-Landau equations are numerically studied with the aim to describe the dynamics of systems close to the Turing-Hopf bifurcation. We found that the spatial modulations of the Turing and Hopf amplitudes increase with the domain size due to inhomogeneous perturbations. By measuring the growth of spatial Fourier modes in systems initialized with random initial conditions, the effective size of the domain where the generalized Eckhaus and Benjamin-Feir-Newell instabilities occur was determined. Besides, we have numerically corroborated that such instabilities can be quantified by recent theoretical results on secondary instabilities of the Mixed mode solution. Furthermore, this study exemplifies diverse spatiotemporal patterns related to intermittency and chaos previously studied for the uncoupled complex Ginzburg-Landau equation as well a new features related to the interaction of Turing and Hopf modes, as the appearance of backbones patterns, foliar figures and wormlike structures in the space-time maps.

Inhomogeneous perturbations and stability analysis of the Einstein static universe in $f(R,T)$ gravity

The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy tensor, respectively). The static and perturbed field equations are constructed for perfect fluid parameterized by linear equation of state parameter. We obtain solutions manifesting the Einstein static state by considering peculiar $f(R,T)$ forms for vanishing and non-vanishing conservation of the stress-energy tensor. It is observed that stable static Einstein regions exist for both closed as well as open FLRW universe models for an appropriate choice of parameters. We conclude that this theory is efficient for presenting such cosmological solutions leading to emergent universe scenario.

Near-Field Wireless Power Transfer to Deep-Tissue Implants for Biomedical Applications

Wireless power transfer (WPT) plays critical roles in powering deep-tissue implants, which also contributes to several emerging advances for biomedical engineering. To enable a high-power density region in implants, this article presents a method, termed the self-phasing technology, to focus electromagnetic fields from various paths at a deep-tissue spot. By performing the phase-conjugated operation on the incident signal and then retransfer back to the source, coherent RF power can be achieved without learning the precise or even dynamic locations of sources and concerning inhomogeneous medium perturbations. An external slot antenna array placed above skin surface 4 mm is considered as a transmitter and an implanted rectenna consisting of a magnetic resonant coil and an RF-to-dc rectifier circuit is treated as a receiver. The conversion efficiency of the rectifier circuit is optimized within the received power range and the measured efficiency of 50% can be achieved at 0 dBm. To visualize the transceiver effects of the integrated system under safety thresholds, a light-emitting diode (LED) is soldered at the terminal of the rectenna and measurements show that smooth drive can be achieved. Certain brightness of LED can demonstrate that the self-phasing technology can support WPT for biomedical applications.

Euclidean Axion Wormholes Have Multiple Negative Modes.

We show that Euclidean axion wormholes in theories of gravity coupled to a single axion have several independent inhomogeneous perturbations that lower the Euclidean action. Our analysis relies on a judiciously chosen gauge-invariant variable which makes the negative mode structure about axion wormholes transparent. Perturbations lowering the action are concentrated in the neck region and exist for wormholes in flat space and in AdS. Their presence means axion wormholes are not relevant saddle points of the functional integral in quantum gravity. This resolves the paradoxes associated with these solutions from the viewpoint of AdS/CFT.

No-boundary proposal in biaxial Bianchi IX minisuperspace

We implement the no-boundary proposal for the wave function of the universe in an exactly solvable Bianchi IX minisuperspace model with two scale factors. We extend our earlier work (Phys. Rev. Lett. 121, 081302, 2018 / arXiv:1804.01102) to include the contribution from the $\mathbb{C}\text{P}^2 \setminus B^4$ topology. The resulting wave function yields normalizable probabilities and thus fits into a predictive framework for semiclassical quantum cosmology. We find that the amplitude is low for large anisotropies. In the isotropic limit the usual Hartle-Hawking wave function for the de Sitter minisuperspace model is recovered. Inhomogeneous perturbations in an extended minisuperspace are shown to be initially in their ground state. We also demonstrate that the precise mathematical implementation of the no-boundary proposal as a functional integral in minisuperspace depends on detailed aspects of the model, including the choice of gauge-fixing. This shows in particular that the choice of contour cannot be fundamental, adding weight to the recent proposal that the semiclassical no-boundary wave function should be defined solely in terms of a collection of saddle points. We adopt this approach in most of this paper. Finally we show that the semiclassical tunneling wave function of the universe is essentially equal to the no-boundary state in this particular minisuperspace model, at least in the subset of the classical domain where the former is known.

Emergent universe scenario, bouncing universes, and cyclic universes in degenerate massive gravity

We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.

Asymptotic diagonalization of the fermionic Hamiltonian in hybrid loop quantum cosmology

We use the freedom available in hybrid loop quantum cosmology to split the degrees of freedom between the geometry and the matter fields so as to build a quantum field theory for the matter content with good quantum properties. We investigate this issue in an inflationary, flat cosmology with inhomogeneous perturbations, and focus the discussion on a Dirac field, minimally coupled to the cosmological background and treated as a perturbation. After truncating the action at the lowest nontrivial order in perturbations, one must define canonical variables for the matter content, for which one generally employs canonical transformations that mix the homogeneous background and the perturbations. Each of these possible definitions comes associated with a different matter contribution to the Hamiltonian of the complete system, that may, in general, contain terms that are quadratic in creationlike variables, and in annihilationlike variables, with the subsequent production and destruction of pairs of fermionic particles and antiparticles. We determine a choice of the fermionic canonical variables for which the interaction part of the Hamiltonian can be made as negligible as desired in the asymptotic regime of large particle/antiparticle wave numbers. Finally, we study the quantum dynamics for this choice, imposing the total Hamiltonian constraint on the quantum states and assuming that their gravitational part is not affected significantly by the presence of fermions. In this way, we obtain a Schr\"odinger equation for the fermionic degrees of freedom in terms of quantum expectation values of the geometry that leads to asymptotically diagonal Heisenberg relations and Bogoliubov evolution transformations, with no divergences in the associated normal-ordered Hamiltonian.

Phenomenology of minimal theory of quasidilaton massive gravity

The minimal theory of quasidilaton massive gravity with or without a Horndeski-type kinetic term for the quasidilaton field propagates only three physical modes: the two massive tensor polarizations and one scalar mode. This reduced number of degrees of freedom is realized by a Lorentz symmetry violation at cosmological scales and the presence of appropriate constraints that remove unwanted modes. Vacuum cosmological solutions have been considered in a previous work, and it has been shown that the late-time de Sitter attractor is stable under inhomogeneous perturbations. In this work, we explore the stability of cosmological solutions in the presence of matter fields. Assuming for simplicity that the quasidilaton scalar is on an attractor at the level of the background, we derive stability conditions in the subhorizon limit, and find the scalar sound speeds, as well as the modification with respect to general relativity to the gravitational potential in the quasistatic approximation. We also find that the speed limit of gravitational waves coincides with the speed of light for any homogeneous and isotropic cosmological background, on or away from the attractor.

Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients

Nonequilibrium fluctuation–dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of inhomogeneous and nonlinear external perturbations. Furthermore, we prove the uniqueness of the conjugate observables and clarify the precise mathematical conditions and ranges of applicability for the two types of FDTs. Examples are also given to illustrate the main results of this paper.

Using statistical functionals for effective control of inhomogeneous complex turbulent dynamical systems

Efficient statistical control strategies are developed for general complex turbulent systems with energy conserving nonlinearity. Instead of direct control on the high-dimensional turbulent equations concerning a large number of instabilities, a statistical functional that characterizes the total statistical structure of the complex system is adopted here as the control object. First the statistical energy equation reduces the control of the complex nonlinear system to a linear statistical control problem; then the explicit form of the forcing control is recovered through nonlocal inversion of the optimal control functional using approximate statistical linear response theory for attribution of the feedback. Through this control strategy with statistical energy conservation, the explicit form of the control forcing is determined offline only requiring the initial configuration of total statistical energy change and the autocorrelation functions in the most sensitive modes of the target statistical equilibrium, with no need of knowing the explicit forcing history and running the complex system. The general framework of the statistical control method can be applied directly on various scenarios with both homogeneous and inhomogeneous perturbations. The effectiveness of the statistical control strategy is demonstrated using the Lorenz ’96 system and a turbulent barotropic system with topography and a large number of instabilities.

On the stability of Einstein static universe in general scalar–tensor theory with non-minimal derivative coupling

The emergent scenario claims that our universe stems from an Einstein static universe, and provides a possible way to avoid the big bang singularity. A successful Einstein static universe requires to be stable past eternally against both homogeneous and inhomogeneous scalar perturbations. In this paper, we study the stability of Einstein static universes in general scalar–tensor theory with non-minimal derivative coupling by analyzing scalar and tensor perturbations. Our results show that the Einstein static solutions are stable against both scalar and tensor perturbations, and the emergent scenario is viable to avoid the initial singularity in this theory.

Backreaction of fermionic perturbations in the Hamiltonian of hybrid loop quantum cosmology

We discuss the freedom available in hybrid loop quantum cosmology to define canonical variables for the matter content and investigate whether this can be used to derive a quantum field theory with good properties for the matter sector. We study a primordial, inflationary, cosmological spacetime with inhomogeneous perturbations at lowest nontrivial order, and focus our attention on the contribution of minimally coupled fermionic perturbations of Dirac type. Within the framework of the hybrid quantization, we analyze the different possible separations of the homogeneous background and the inhomogeneous perturbations, by means of canonical transformations that mix the two separated sectors. These possibilities provide a family of sets of annihilation and creationlike fermionic variables, each of them with a different associated contribution to the total Hamiltonian. In all cases, imposing the quantum constraints and introducing a Born-Oppenheimer approximation, one can derive a Schr\"odinger equation for the fermionic part of the wave functions. The resulting evolution turns out to be generated, for each of the allowed choices of variables, by a version of the fermionic contribution to the Hamiltonian which is obtained by evaluating all the dependence on the homogeneous geometry at quantum expectation values. This equation contains a term that encodes the backreaction of the fermionic perturbations on the quantum dynamics of the homogeneous sector. We analyze this backreaction by solving the associated Heisenberg evolution of the fermionic annihilation and creation operators. Then, we identify the conditions that the choice of those operators must satisfy in order to lead to a finite backreaction. Finally, we discuss further restrictions on this choice so that the fermionic Hamiltonian that dictates the Schr\"odinger dynamics is densely defined in Fock space.

Inhomogeneous perturbations and stability in f ( G , T ) $f(\mathcal{G},T)$ gravity

In this paper, we study stability of the Einstein static universe against inhomogeneous scalar perturbations parameterized by equation of state parameter in \(f(\mathcal{G},T)\) gravity (\(\mathcal{G}\) and \(T\) represent the Gauss-Bonnet invariant and trace of energy-momentum tensor, respectively). We formulate static as well as perturbed field equations in the presence of perfect fluid and analyze the stability regions. This is accomplished for particular \(f(\mathcal{G},T)\) models corresponding to zero as well as non-zero covariant divergence of the energy-momentum tensor. It is found that stable Einstein universe exists both for spatially closed as well as open universe models for suitable choice of parameters.

Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$, for the parameter values $0<\epsilon < \epsilon_0$. These solutions exist globally to the future, converge as $\epsilon \searrow 0$ to solutions of the cosmological Poison-Euler equations of Newtonian gravity, and are inhomogeneous non-linear perturbations of FLRW fluid solutions.

Stability of Einstein universe against inhomogeneous perturbations in $\mathrm{ f(R,T,R_{\mu\nu}T^{\mu\nu})}$ f ( R , T , R μ ν T μ ν ) gravity

This paper is devoted to the study of the existence and stability of the Einstein universe against scalar inhomogeneous perturbations in the background of f (R, T, Q) gravity (R, T represent the scalar curvature, trace of the energy-momentum tensor and $ Q=R_{\sigma\xi}T^{\sigma\xi}$ . We construct static as well as perturbed field equations using the linear equation of state in the presence of perfect fluid and examine the stability regions. Considering conserved and non-conserved cases of the energy-momentum tensor for specific models of this gravity, it is found that the stable Einstein static universe exists for both open as well as closed FRW universe models corresponding to the appropriate choice of parameters.

Large-scale stability and astronomical constraints for coupled dark-energy models

We study large-scale inhomogeneous perturbations and instabilities of interacting dark energy (IDE) models. Past analysis of large-scale perturbative instabilities, has shown that we can only test IDE models with observational data when its parameter ranges are either $w_{x}\geq -1$ and $\xi \geq 0,$ or $w_{x}\leq -1~$ and $~\xi \leq 0$, where $w_{x}$ is the dark energy equation of state (EoS), and $\xi$ is a coupling parameter governing the strength and direction of the energy transfer. We show that by adding a factor $(1+w_{x})$ to the background energy transfer, the whole parameter space can be tested against all the data and thus, the instabilities in such interaction models can be removed. We test three classes of interaction model using the latest astronomical data from different sources. Precise constraints are found. Our analysis shows that a very small but non-zero deviation from pure $\Lambda$-cosmology is suggested by the observational data while the no-interaction scenario can be recovered at the 68.3% confidence-level. In particular, for three IDE models, identified as IDE 1, IDE 2, and IDE 3, the 68.3% CL constraints on the interaction coupling strengths are, $\xi= 0.0360_{-0.0360}^{+0.0091}$ (IDE 1), $\xi= 0.0433_{-0.0433}^{+0.0062}$ (IDE 2), $\xi= 0.1064_{-0.1064}^{+0.0437}$ (IDE 3). In addition, we find that the dark energy EoS tends towards the phantom region taking the 68.3% CL constraints, $w_x= -1.0230_{-0.0257}^{+0.0329}$ (IDE 1), $w_x= -1.0247_{-0.0302}^{+0.0289}$ (IDE 2), and $w_x= -1.0275_{-0.0318}^{+0.0228}$ (IDE 3). However, the possibility of $w_{x}>-1$ is also not rejected by the astronomical data used here. Moreover, we find in all IDE models that, as the value of Hubble constant decreases, the behavior of the dark energy EoS shifts from phantom to quintessence type with its EoS very close to that a simple cosmological constant at the present time.

Inhomogeneous perturbations in the pseudo-Hermitian quantum cosmology

We consider the quantum cosmology of the phantom fields within the Wheeler-DeWitt approach using the classically equivalent model with complex potential. The Born-Oppenheimer approximation is used to study the behaviour of the inhomogeneous perturbations over the minisuperspace background. The evolution Hamiltonian is treated as a pseudo-Hermitian one and the conserved inner product is constructed within WKB approximation of the homogeneous wavefunction.

Fast computation of MT curves for a horizontally layered earth with laterally inhomogeneous conductivity perturbations

A new algorithm is proposed to compute magnetotelluric (MT) curves for a horizontally layered earth with laterally inhomogeneous conductivity. It is fast and ensures correction of induced eddy currents and galvanic distortions of MT curves produced by 3D inhomogeneities. The computation time is short (~1 min) due to the use of the perturbation method for solving Maxwell’s equations. The suggested algorithm has a better performance than the more costly classical Trefftz method but has an applicability limitation.