Dynamics Of Linear Perturbations Research Articles

Electrically charged black hole solutions in semiclassical gravity and dynamics of linear perturbations

Electrically charged black hole solutions in semiclassical gravity and dynamics of linear perturbations

Linear Stability of Semiclassical Theories of Gravity

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution.

Linearized supergravity with a dynamical preferred frame

We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether. Embedding aether into a chiral vector superfield, we construct the most general action which describes dynamics of linear perturbations around the Lorentz-violating vacuum and is invariant under the linearized supergravity transformations. The analysis is performed both in the off-shell non-minimal superfield formulation of supergravity and in the “on-shell” approach invoking only physical component fields. The resulting model contains a single free coupling, in addition to the standard supergravity parameters. The spectrum of physical excitations features an enhanced on-shell gravity multiplet comprising four states with helicities 2, 3/2, 3/2 and 1 propagating with superluminal velocity. The remaining excitations propagate with the speed of light. We outline the observational constraints on the model following from its low-energy phenomenology.

Perturbation dynamics in Keplerian flow under external stochastic forcing

ABSTRACT We investigate the dynamics of linear perturbations in Keplerian flow under external stochastic force. To abstract from the details of flow structure and boundary conditions, we consider the problem in the shearing box approximation. An external force is assumed to have zero mean, even so, induced perturbations form a steady state, which provides angular momentum transfer to the periphery of the flow. The most effective scenario is based on the transient amplification of induced vortices with the following emission of a shearing sound wave, wherein the maximum of the flux linearly depends on Reynolds number. Thus such a mechanism is significant for astrophysical flows, for which enormous Reynolds numbers are typical. At the same time, addressing the problem analytically, we find that for incompressible fluid in the shearing box approximation stochastic forcing does not lead to average angular momentum transfer. Thus the compressibility of the fluid plays an important role here, and one cannot neglect it.

Integrated Sachs-Wolfe-galaxy cross-correlation bounds on the two branches of the minimal theory of massive gravity

The minimal theory of massive gravity (MTMG) has two branches of stable cosmological solutions: a self-accelerating branch, which, except for the mass of tensor modes has exactly the same behavior of linear perturbations as $\Lambda$CDM in general relativity (GR), and a normal branch with nontrivial behavior. We explore the influence of the integrated Sachs-Wolfe-galaxy correlation constraints on the normal branch of MTMG, which, in its simplest implementation, has one free parameter more than $\Lambda$CDM in GR (or the self-accelerating branch of MTMG): $\theta$. This parameter is related to the graviton mass and only affects the behavior of the cosmological linear perturbation dynamics. Using 2d-mass and SDSS data, we check which values of $\theta$ lead to a positive or negative cross-correlation. We find that positive cross-correlation is achieved for a large parameter-space interval. Within this allowed region of parameter space, we perform a $\chi^2$ analysis in terms of the parameter $\theta$, while keeping the other background parameters fixed to the best-fit values of Planck. We then infer that the normal branch of MTMG fits the data well in a nontrivial portion of the parameter space, and future experiments should be able to distinguish such a model from $\Lambda$CDM in GR (or the self-accelerating branch of MTMG).

Transient effects in unstable ablation fronts and mixing layers in HEDP

We report results obtained for two elementary unstable flow configurations relevant to high energy density physics: the ablation front instability and the Rayleigh–Taylor -instability induced mixing layer. These two flows are characterized by a transience of their perturbation dynamics. In the ablative flow case, this perturbation dynamics transience takes the form of finite-durations of successive linear-perturbation evolution phases until reaching regimes of decaying oscillations. This behaviour is observed in various regimes: weakly or strongly accelerated ablation fronts, irradiation asymmetries or initial external-surface defects, and is a result of the mean-flow unsteadiness and stretching. In the case of the Rayleigh–Taylor-instability induced mixing layer, perturbation dynamics transience manifests itself through the extinction of turbulence and mixing as the flow reaches a stable state made of two stably stratified layers of pure fluids separated by an unstratified mixing layer. A second feature, also due to compressibility, takes the form of an intense acoustic wave production, mainly localized in the heavy fluid. Finally, we point out that a systematic short-term linear-perturbation dynamics analysis should be undertaken within the framework of non-normal stability theory.

Testing Hu–Sawickif(R) gravity with the effective field theory approach

We show how to fully map a specific model of modified gravity into the Einstein–Boltzmann solver eftcamb. This approach consists in few steps and allows to obtain the cosmological phenomenology of a model with minimal effort. We discuss all these steps, from the solution of the dynamical equations for the cosmological background of the model to the use of the mapping relations to cast the model into the effective field theory language and use the latter to solve for perturbations. We choose the Hu–Sawicki f(R) model of gravity as our working example. After solving the background and performing the mapping, we interface the algorithm with eftcamb and take advantage of the effective field theory framework to integrate the full dynamics of linear perturbations, returning all quantities needed to accurately compare the model with observations. We discuss some observational signatures of this model, focusing on the linear growth of cosmic structures. In particular we present the behaviour of fσ8 and EG that, unlike the Λ cold dark matter (ΛCDM) scenario, are generally scale dependent in addition to redshift dependent. Finally, we study the observational implications of the model by comparing its cosmological predictions to the Planck 2015 data, including cosmic microwave background lensing, the WiggleZ galaxy survey and the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS), weak-lensing survey measurements. We find that while WiggleZ data favour a non-vanishing value of the Hu–Sawicki model parameter, |$\log _{10}(-f^0_{R})$|⁠, and consequently a large value of σ8, CFHTLenS drags the estimate of |$\log _{10}(-f^0_{R})$| back to the ΛCDM limit.

Spin waves scattering on a Bloch point

We show that, after a transformation, the dynamics of linear perturbations (spin waves) around a singular Bloch point soliton is formally equivalent to a quantum system of an electron in a magnetic monopole field. The analytical solution to this problem is known and allows us to find the spectrum and the scattering of a wave in a Bloch point field.

Effective field theory of cosmic acceleration: An implementation in CAMB

We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several objectives. It can be employed to evolve the full dynamics of linear scalar perturbations in any given single field dark energy or modified gravity model, once the latter is mapped into the EFT formalism. It offers a numerical implementation of EFT as a model-independent framework to test gravity on cosmological scales. EFTCAMB has a built-in check for the fulfillment of general stability conditions such as the absence of ghost and superluminal propagation of perturbations. It handles phantom-divide crossing models and does not contain any quasi-static approximation, but rather evolves the full dynamics of perturbations on linear scales. As we will show, the latter is an important feature in view of the accuracy and scale range of upcoming surveys. We show the reliability and applicability of our code by evolving the dynamics of linear perturbations and extracting predictions for power spectra in several models. In particular we perform a thorough analysis of f(R) theories, comparing our outputs with those of an existing code for LCDM backgrounds, and finding an agreement that can reach 0.1% for models with a Compton wavelength consistent with current cosmological data. We then showcase the flexibility of our code studying two different scenarios. First we produce new results for designer f(R) models with a time-varying dark energy equation of state. Second, we extract predictions for linear observables in some parametrized EFT models with a phantom-divide crossing equation of state for dark energy.

Dynamics of linear perturbations in the hybrid metric-Palatini gravity

In this work we focus on the evolution of the linear perturbations in the novel hybrid metric-Palatini theory achieved by adding a $f(\mathcal{R})$ function to the gravitational action. Working in the Jordan frame, we derive the full set of linearized evolution equations for the perturbed potentials and present them in the Newtonian and synchronous gauges. We also derive the Poisson equation, and perform the evolution of the lensing potential, ${\mathrm{\ensuremath{\Phi}}}_{+}$, for a model with a background evolution indistinguishable from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. In order to do so, we introduce a designer approach that allows one to retrieve a family of functions $f(\mathcal{R})$ for which the effective equation of state is exactly ${w}_{\text{eff}}=\ensuremath{-}1$. We conclude, for this particular model, that the main deviations from standard general relativity and the cosmological constant model arise in the distant past, with an oscillatory signature in the ratio between the Newtonian potentials, $\mathrm{\ensuremath{\Phi}}$ and $\mathrm{\ensuremath{\Psi}}$.

Essential building blocks of dark energy

We propose a minimal description of single field dark energy/modified gravity within the effective field theory formalism for cosmological perturbations, which encompasses most existing models. We start from a generic Lagrangian given as an arbitrary function of the lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusing on linear perturbations, we identify seven Lagrangian operators that lead to equations of motion containing at most two (space or time) derivatives, the background evolution being determined by the time-dependent coefficients of only three of these operators. We then establish a dictionary that translates any existing or future model whose Lagrangian can be written in the above form into our parametrized framework. As an illustration, we study Horndeski's — or generalized Galileon — theories and show that they can be described, up to linear order, by only six of the seven operators mentioned above. This implies, remarkably, that the dynamics of linear perturbations can be more general than that of Horndeski while remaining second order. Finally, in order to make the link with observations, we provide the entire set of linear perturbation equations in Newtonian gauge, the effective Newton constant in the quasi-static approximation and the ratio of the two gravitational potentials, in terms of the time-dependent coefficients of our Lagrangian.

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.

Primordial perturbations and non-Gaussianities in DBI and general multifield inflation

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

The effect of acoustic radiation on the development of instabilities in convergent spherical liquid-gas systems

We extend previous analytical work on instability growth in spherically convergent fluid systems by characterizing linear perturbation dynamics on the collapse of a gas-filled spherical cavity surrounded by an incompressible fluid. We also investigate energy damping mechanisms related to fluid compressibility and provide estimates of the conditions under which dynamic compressibility significantly affects modal behavior. The number of modes affected by compressibility is a function of the maximum radial Mach number achieved during the cavity collapse. At a maximum Mach number (Mm) of about 0.04 only the radial mode (spherical harmonic n=0) is affected. At Mm about 0.4, modes with n≤4 are affected and at Mm greater than about 0.5 all modes are strongly influenced.

Overreflection and Generation of Gravito‐Alfven Waves in Solar‐Type Stars

The dynamics of linear perturbations is studied in magnetized plasma shear flows with a constant shearing rate and with gravity-induced stratification. The general set of linearized equations is derived, and the two-dimensional case is considered in detail. The Boussinesq approximation is used in order to examine relatively small scale perturbations of low-frequency modes: gravito-Alfven waves (GAWs) and entropy-mode (EM) perturbations. It is shown that for flows with arbitrary shearing rate, there exists a finite time interval of nonadiabatic evolution of the perturbations. The nonadiabatic behavior manifests itself in a twofold way, viz., by the overreflection of the GAWs and by the generation of GAWs from EM perturbations. It is shown that these phenomena act as efficient transformers of the equilibrium flow energy into the energy of the perturbations for moderate and high shearing rate solar plasma flows. Efficient generation of GAWs by EM perturbations takes place for shearing rates about an order of magnitude smaller than necessary for development of a shear instability. The latter fact could have important consequences for the problem of angular momentum redistribution within the Sun and solar-type stars.

Radiation-condensation instability in a highly ionized dusty plasma

The dynamics of linear perturbations in a radiatively cooling dusty plasma is considered, with the charge of both dust (Zd) and plasma (Zp) components being allowed to vary with their densities. It is shown that in the long-wavelength limit corresponding to the characteristic cooling length, when the plasma can be treated as quasineutral, the presence of dust particles changes the criteria for radiation instability, regardless of the charging process of the dust particles. In particular, the condensation (isobaric) mode is shown to be stabilized (destabilized) if in the equilibrium, the relation between densities of the dust nd and plasma n under the quasineutrality condition, (d ln nd/d ln n)q<1 (>1) is satisfied, while the isentropic mode is stabilized (destabilized) when the opposite inequalities take place; the isochoric mode is unaltered. Numerical estimates show that these effects can be important in hot phases (T∼106 K) of the interstellar plasma, and in tokamak plasma near the walls.

The nonlinear viscoelastic cosserat model for the wave propagation with generation of subharmonics

A Cosserat model is developed in nonlinear form to describe the appearance of lower frequencies in seismic waves spectra. As in the Ericksen theory of liquid crystals, elastic and viscous rheological elements are combined to get sensible results. The translational degrees of freedom are described by linear elasticity but the rotational kinematically independent motion is governed by the nonlinear elastic potential and linear viscosity. The dynamics of linear perturbations show that the longitudinal translations and rotations both decouple completely from other motions. These rotations represent local oscillations due to the existence of the potential and they do not propagate. However, the linear transverse translations and microrotations are coupled. It is shown that they describe seismic and acoustic waves. In the nonlinear case these motions demonstrate some new interesting phenomena. For instance, if the propagation of the harmonic elastic wave is considered the microrotations behave like nonlinear oscillators excited by the external harmonic force. Thus the system produces the same effects as those obtained recently for the Duffing type equation with the help of the theory of attractors. This means that the initial harmonic wave generates secondary waves with lower frequencies. These secondary frequencies are usually commensurable with the initial ones. Numerical results show that the phenomenon still takes place if the initial wave consists of continuously distributed harmonics. The generation of lower frequencies in granular media has been observed and reported but the theoretical explanation was lacking since it was thought conventionally that weak nonlinearities were able to produce higher frequencies only.

Covariant cosmological perturbation dynamics in the large-scale limit

Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations which encodes the entire linear perturbation dynamics in a closed time integral. On this basis we discuss perturbation modes in different cosmological epochs.