Entropy Perturbations Research Articles

Parametrizing dark sector perturbations via equations of state

The evolution of perturbations is a crucial part of the phenomenology of the dark sector cosmology. We advocate parametrizing these perturbations using equations of state for the entropy perturbation and the anisotropic stress. For small perturbations, these equations of state will be linear in the density, velocity and metric perturbations, and in principle these can be related back to the field content of the underlying model allowing for confrontation with observations. We illustrate our point by constructing gauge-invariant entropy perturbations for theories where the dark sector Lagrangian is a general function of a scalar field, its first and second derivatives, and the metric and its first derivative, $\mathcal{L}=\mathcal{L}(\ensuremath{\phi},{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi},{\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\partial}}_{\ensuremath{\nu}}\ensuremath{\phi},{g}_{\ensuremath{\mu}\ensuremath{\nu}},{\ensuremath{\partial}}_{\ensuremath{\alpha}}{g}_{\ensuremath{\mu}\ensuremath{\nu}})$. As an example, we show how to apply this approach to the case of models of kinetic gravity braiding.

A nonlinear model for indirect combustion noise through a compact nozzle

AbstractThe present paper deals with the generation of sound by the passage of acoustic or entropy perturbations through a nozzle in the nonlinear regime and in the low-frequency limit. The analytical model of Marble and Candel for compact nozzles (J. Sound Vib., vol. 55, 1977, pp. 225–243), initially developed for excitations in the linear regime, is rederived and extended to the nonlinear domain. Full nonlinear and second-order models are written for both subcritical and supercritical nozzles in the absence of shock and a detailed methodology is provided for the resolution of the second-order system. The accuracy of the second-order model is assessed for entropy forcings. It is shown to be accurate for all waves, with the exception of the upstream generated wave for subcritical diverging geometries where higher-order nonlinear contributions cannot be neglected. In the context of indirect combustion noise, the phenomenon of regime change of the nozzle due to an incoming entropy fluctuation is also addressed. Regime change is related to a Mach number modification induced by temperature and velocity fluctuations. In the present study, it translates into a limitation of the maximum amplitude of the incoming entropy forcing. Such limitations are to be considered for subcritical nozzles with significant inlet or outlet Mach numbers, where the flow transition is observed even for very low-amplitude entropy excitations. With the constraint of those limitations, the analytical extended nozzle describing functions representing the full nonlinear response for indirect combustion noise are validated through detailed comparisons with numerical simulations.

The dissipation and shear dispersion of entropy waves in combustor thermoacoustics

AbstractThis paper considers the effect of flow advection on entropy waves. The interest is in whether entropy waves persist in gas turbine combustors, between the flame, where they are generated, and the combustor exit, where their acceleration generates acoustic waves (known as ‘entropy noise’ or ‘indirect combustion noise’). Entropy wave advection within a simplified fully developed turbulent channel-flow simulation is investigated. Entropy wave dissipation is found to be negligible, with loss of entropy wave strength caused predominantly by mean flow shear dispersion. The impulse response of entropy perturbations downstream of where they are generated is shown to be well modelled by a Gaussian profile in time. This yields a (different) Gaussian form for the inlet–outlet transfer function of entropy perturbations. For representative gas turbine flows, the magnitude of this transfer function is such that significant entropy wave strength will remain at the combustor exit, confirming that entropy-generated acoustic waves are likely to be important.

Unified dark fluid with fast transition: Including entropic perturbations

In this paper, we investigate a unified dark fluid model with a fast transition and entropic perturbations. An effective sound speed is designated as an additional free model parameter when the entropic perturbations are included, and, if the entropic perturbations are zero, the effective sound speed will decrease to the adiabatic sound speed. In order to analyze the viability of the unified model, we calculate the squared Jeans wave number with the entropic perturbations. Furthermore, by using the Markov Chain Monte Carlo method, we perform a global fitting for the unified dark fluid model from the type Ia supernova Union 2.1, baryon acoustic oscillation, and the full information of the cosmic microwave background measurement given by the WMAP 7 yr data points. The constrained results favor a small effective sound speed. Compared to the cosmological constant and cold dark matter, it is found that the cosmic observations do not favor the phenomenon of a fast transition for the unified dark fluid model.

Note on the production of scale-invariant entropy perturbation in the Ekpyrotic universe

In the standard entropic mechanism adopted in the simple Ekpyrotic models to generate the nearly scale-invariant and Gaussian primordial perturbation, the entropy direction is tachyonically unstable. In this Letter, we consider the stable production of the scale-invariant entropy perturbation in the Ekpyrotic universe via non-minimal couplings. In this model the non-minimally coupled massless scalar field serves as a spectator and is stabilized by the introduced non-minimal couplings. It always corresponds to the entropy field during the contraction and with appropriate couplings can obtain a scale-invariant spectrum. This scenario requires additional mechanisms such as curvaton or modulated preheating to convert the entropy perturbation to the curvature perturbation after the bounce.

Quantum cosmological perturbations of generic fluids in quantum universes

In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put in a simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In this paper, we generalize this result to general fluids, which includes entropy perturbations, and to arbitrary spacelike hyper-surfaces through a new method together with the Faddeev-Jackiw procedure for the constraint reduction. A simple second order Hamiltonian involving the Mukhanov-Sasaki variable is obtained, again without ever using the background equations of motion.

Unified dark fluid with constant adiabatic sound speed: Including entropic perturbations

In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Because of the relations between the adiabatic sound speed and equations of state ${c}_{s,ad}^{2}(a)=w(a)\ensuremath{-}d\mathrm{ln}(1+w(a))/3d\mathrm{ln}a$, the equation of state can be determined up to an integration constant, in principle, when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its microscale properties are characterized by its equations of state or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscillation, and WMAP 7-yr data of cosmic background radiation, to constrain the possible entropic perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo method. The results show that the cosmic observations favor a small effective sound speed ${c}_{s,\mathrm{eff}}^{2}={0.00155}_{\ensuremath{-}0.00155}^{+0.000319}$ in the $1\ensuremath{\sigma}$ region.

Perturbative analysis of topological entanglement entropy from conditional independence

We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of the quantum double or Levin-Wen model, we obtain a bound on the first-order perturbation of topological entanglement entropy in terms of its energy gap and subsystem size. The bound decreases superpolynomially with the size of the subsystem, provided the energy gap is nonzero. We also study the finite-temperature stability of stabilizer models, for which we prove a stronger statement than the strong subadditivity of entropy. Using this statement and assuming (i) finite correlation length and (ii) small conditional mutual information of certain configurations, first-order perturbation effect for arbitrary local perturbation can be bounded. We discuss the technical obstacles in generalizing these results.

Massive cosmological scalar perturbations

We study the cosmological perturbations of the new bimetric gravity proposed by Hassan and Rosen [J. High Energy Phys. 02 (2012) 126] as a representation of massive gravity. The mass term in the model, in addition to ensuring ghost freedom for both metrics, causes the two scale factors to mix at the cosmological level, and this affects the cosmological perturbation of the model. We find two combinations corresponding to the entropy and adiabatic perturbations of the theory. In this sense we show that the adiabatic perturbations could be a source for the entropy perturbations. So in addition to the adiabatic perturbations, entropy perturbations can also be present in this theory. We also show that the adiabatic perturbations are not constant at the superhorizon scales, implying that the theory could not be used to describe the inflationary epoch, even if it can impose some corrections to the standard inflationary scenarios.

The Transmembrane Helix Tilt May Be Determined by the Balance between Precession Entropy and Lipid Perturbation

Hydrophobic helical peptides interact with lipid bilayers in various modes, determined by the match between the length of the helix’s hydrophobic core and the thickness of the hydrocarbon region of the bilayer. For example, long helices may tilt with respect to the membrane normal to bury their hydrophobic cores in the membrane, and the lipid bilayer may stretch to match the helix length. Recent molecular dynamics simulations and potential of mean force calculations have shown that some TM helices whose lengths are equal to, or even shorter than, the bilayer thickness may also tilt. The tilt is driven by a gain in the helix precession entropy, which compensates for the free energy penalty resulting from membrane deformation. Using this free energy balance, we derived theoretically an equation of state, describing the dependence of the tilt on the helix length and membrane thickness. To this end, we conducted coarse-grained Monte Carlo simulations of the interaction of helices of various lengths with lipid bilayers of various thicknesses, reproducing and expanding the previous molecular dynamics simulations. Insight from the simulations facilitated the derivation of the theoretical model. The tilt angles calculated using the theoretical model agree well with our simulations and with previous calculations and measurements.

IR divergences in inflation and entropy perturbations

We study leading order perturbative corrections to the two pointcorrelation function of the scalar field describing the curvature perturbationin a slow-roll inflationary background, paying particularattention to the contribution of entropy mode loops. We find thatthe infrared divergences are worse than in pure de Sitter space:they are power law rather than logarithmic. The validity of perturbationtheory and thus of the effective field theory of cosmologicalperturbations leads to stringent constraints on the coupling constantsdescribing the interactions, in our model the quarticself-interaction coupling constant of the entropy field. If theself coupling constant is larger than some critical value whichdepends in particular on the duration of the inflationary phase,then perturbation theory breaks down. Our analysis may haveimplications for the stability of de Sitter space: thequantum effects which lead to an instability of de Sitter space willbe larger in magnitude in the presence of entropy fluctuations.

Effective field theory of multi-field inflation a la Weinberg

We generalise Weinberg's effective field theory approach to multiple-field inflation.In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity.Generally we find that the speed of sound differs from, but is close to unity,however large non-Gaussianities are possible in the multi-field case.The non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude with the amount of the non-Gaussianity depending on the curvature of the classical field path in phase-space. We emphasize that in general the time derivative of adiabatic and entropy perturbations do not invariant due to the shift symmetry. However we find two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.

Numerical modeling of the receptivity of a supersonic boundary layer to entropy disturbances

Numerical modeling of the receptivity of a two-dimensional flat-plate boundary layer to entropy disturbances is carried out at the freestream Mach number M∞ = 6. Low-intensity perturbations considered are in the form of temperature spots of various shapes and with different initial positions downstream of the shock. They are shown to be able to generate unstable disturbances in the boundary layer. This receptivity mechanism is relatively weak as compared with the receptivity to acoustic waves. When the entropy perturbations are introduced upstream of the bow shock, they first pass across the shock. Downstream of the shock this interaction generates acoustic waves which, in turn, penetrate into the boundary layer thus exciting unstable disturbances of a considerably greater amplitude than the temperature spots. Thus, the bow shock can change the receptivity mechanism.

Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities

AbstractWe present an analytical model that describes the linear interaction of two successive shocks launched into a non-uniform density field. The re-shock problem is important in different fields, inertial confinement fusion among them, where several shocks are needed to compress the non-uniform target. At first, we present a linear theory model that studies the interaction of two successive shocks with a single-mode density perturbation field ahead of the first shock. The second shock is launched after the sonic waves emitted by the first shock wave have vanished. Therefore, in the case considered in this work, the second shock only interacts with the entropic and vortical perturbations left by the first shock front. The velocity, vorticity and density fields are later obtained in the space behind the second shock. With the results of the single-mode theory, the interaction with a full spectrum of random-isotropic density perturbations is considered by decomposing it into Fourier modes. The model describes in detail how the second shock wave modifies the turbulent field generated by the first shock wave. Averages of the downstream quantities (kinetic energy, vorticity, acoustic flux and density) are easily obtained either for two-dimensional or three-dimensional upstream isotropic spectra. The asymptotic limits of very strong shocks are discussed. The study shown here is an extension of previous works, where the interaction of a planar shock wave with random isotropic vorticity/entropy/acoustic spectra were studied independently. It is also a preliminary step towards the understanding of the re-shock of a fully turbulent flow, where all three of the modes, vortical, entropic and acoustic, might be present.

Problem of proper decomposition and initialization of acoustic and entropy modes in a gas affected by the mass force

The relations connecting perturbations specific for acoustic and entropy modes in an accelerated fluid or in a fluid affected by constant mass force, are derived. They allow to decompose the total vector of perturbations and the overall energy into acoustic and non-acoustic parts uniquely at any instant. In order to do this, three quantities are required, for example total perturbations in entropy, pressure and velocity. The evaluations are made in regard to the content of acoustic and non-acoustic parts of the total energy excluding its kinetic part. In some cases, exact relations may be derived.

Role of entropy perturbations in third-order nonlinear acoustic tomography problems

The effect of the entropy perturbations on the acoustic pressure, which arises due to third-order nonlinear interaction, has been considered. The contribution to entropy perturbation due to the presence of viscosity and thermal conductivity (by means of the general equation of heat transfer) and also due to the nonlinearity of the considered medium has been estimated. It has been shown that when all possible factors responsible for the change in entropy are taken into account, the third-order contribution to the acoustic pressure due to density perturbations in primary waves strongly exceeds that due to entropy perturbations. It has been concluded that an isoentropic mathematical description of third-order nonlinear effects in nonlinear acoustic tomography problems is appropriate.

Adiabatic and nonadiabatic perturbations for loop quantum cosmology

We generalize the perturbations theory of loop quantum cosmology to a hydrodynamical form and define an effective curvature perturbation on an uniform density hypersurfaces $\zeta_e$. As in the classical cosmology, $\zeta_e$ should be gauge-invariant and conservation on the large scales. The evolutions of both the adiabatic and the non-adiabatic perturbations for a multi-fluids model are investigated in the framework of the effective hydrodynamical theory of loop quantum cosmology with the inverse triad correction. We find that, different from the classical cosmology, the evolution of the large-scales non-adiabatic entropy perturbation can be driven by an adiabatic curvature perturbation and this adiabatic source for the non-adiabatic perturbation is a quantum effect. As an application of the related formalism, we study a decay model and give out the numerical results.

Influence of Gauge Artifact on Adiabatic and Entropy Perturbations during Inflation

In recent publications we proposed one way to calculate gauge-invariant variables in a local observable universe which is limited to a portion of the whole universe. To provide a theoretical prediction of the observable fluctuations, we need to preserve the gauge-invariance in the local universe, which is referred to the genuine gauge-invariance. The importance of the genuine gauge invariance is highlighted in the study of primordial fluctuations in the infrared (IR) limit. The stability against IR loop corrections to primordial fluctuations is guaranteed in requesting the genuine gauge invariance. The genuine gauge-invariance also gives impacts on the detectable fluctuations. We showed that at observable scales the bi-spectrum calculated in the conventional perturbation theory vanishes in the squeezed limit, if we request the genuine gauge invariance. This indicates that the conventional bi-spectrum is, in this limit, dominated by a gauge artifact, which cannot be observed. These studies have been elaborated in single-field models of inflation. In this paper we generalize our argument to multi-field models of inflation, where, in addition to the adiabatic field, the entropy field can participate in the generation of primordial fluctuations. We will find that the entropy field can generate the observable fluctuations, which cannot be eliminated by gauge transformations in the local universe.

Assessing non-normal effects in thermoacoustic systems with mean flow

In this paper, non-normal interactions in a thermoacoustic system are studied, using a low-order expansion of the state variables in terms of eigenmodes. The thermoacoustic eigenmodes are determined as solutions of the Helmholtz equation or the linearized Euler equations, respectively, in the presence of a time-lagged heat source. Subsequently, non-normal effects are evaluated in a post-processing analysis based on the computed eigenmodes. In the case where the eigenmode analysis is based on the linearized Euler equations, effects of a non-zero mean flow velocity can be taken into account. The energy associated with the eigenmodes may then contain contributions of convected entropy and vorticity modes as well as the acoustic field. The notion of transient growth of perturbation energy is thus extended from an expression based on the classical acoustic energy density to a form based on a generalized disturbance energy. The expansion in terms of eigenmodes is computationally efficient, making the approach potentially applicable to complex, 3D configurations including non-trivial boundary conditions and spatio-temporal distributions of heat release fluctuations. In the present paper, the method is applied to a 1D configuration that consists of a duct including a 1D heat source, followed by a choked isentropic nozzle. It is shown that for such a case, it is essential to include the contribution of entropy perturbations in the calculation of the optimal initial perturbation and the maximum transient energy growth. Subsequently, the impact of increasing mean flow Mach number and increasing strength of flame/acoustic interaction on non normal effects is assessed in a parameter study.

Unified models of the cosmological dark sector

We model the cosmological substratum by a viscous fluid that is supposed to provide a unified description of the dark sector and pressureless baryonic matter. In the homogeneous and isotropic background the total energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically non-adiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS (DR7) data. A joint statistical analysis, using also Hubble-function and supernovae Ia data, shows that, different from other studies, there exists a maximum in the probability distribution for a negative present value q0 ≈ −0.53 of the deceleration parameter. Moreover, different from other approaches, the unified model presented here favors a matter content that is of the order of the baryonic matter abundance suggested by big-bang nucleosynthesis.