Entropy Perturbations Research Articles

The running curvaton * * LH is funded by Hunan Natural Science Foundation (2020JJ5452) and Hunan Provincial Department of Education (19B464). WL is funded by NSFC (1175012)

In this paper, we propose a homogeneous curvaton mechanism that operates during the preheating process and in which the effective mass is running (i.e., its potential consists of a coupling term and an exponential term whose contribution is subdominant thereto). This mechanism can be classified into either narrow resonance or broad resonance cases, with the spectral index of the curvaton consituting the deciding criteria. The inflationary potential is that of chaotic inflation (i.e., a quadratic potential), which could result in a smooth transition into the preheating process. The entropy perturbations are converted into curvature perturbations, which we validate using the formalism. By neglecting the exponential term's contribution to the curvaton potential, we calculate the power spectrum and the nonlinear non-Gaussian parameter . Our calculations analytically show that these two observables are independent of the inflaton potential. Finally, when the curvaton decays (and the inflaton field vanishes), the exponential potential approaches a constant value similar to that of the cosmological constant, which may play the role of dark energy.

Collapse of spherical overdensities in superfluid models of dark matter

Aims. We intend to understand cosmological structure formation within the framework of superfluid models of dark matter with finite temperatures. Of particular interest is the evolution of small-scale structures where the pressure and superfluid properties of the dark matter fluid are prominent. We compare the growth of structures in these models with the standard cold dark matter paradigm and non-superfluid dark matter. Methods. The equations for superfluid hydrodynamics were computed numerically in an expanding ΛCDM background with spherical symmetry; the effect of various superfluid fractions, temperatures, interactions, and masses on the collapse of structures was taken into consideration. We derived the linear perturbation of the superfluid equations, giving further insights into the dynamics of the superfluid collapse. Results. We found that while a conventional dark matter fluid with self-interactions and finite temperatures experiences a suppression in the growth of structures on smaller scales, as expected due to the presence of pressure terms, a superfluid can collapse much more efficiently than was naively expected due to its ability to suppress the growth of entropy perturbations and thus gradients in the thermal pressure. We also found that the cores of the dark matter halos initially become more superfluid during the collapse, but eventually reach a point where the superfluid fraction falls sharply. The formation of superfluid dark matter halos surrounded by a normal fluid dark matter background is therefore disfavored by the present work.

Normal modes of vibrations around Hubble flow in jellium

A macroscopic Coulomb system of identical charged particles with or without a compensating background charge can evolve maintaining spatial homogeneity and isotropy that mimic the cosmological evolution of a universe with repulsive gravity. Here we study dynamics of small perturbations on the background of the corresponding Hubble flow by analyzing its normal modes of vibrations. Arbitrary disturbance of the flow can be resolved into two electroacoustic, two vortical, and one entropic modes whose dynamics is investigated. Specifically, in the zero pressure or long-wavelength limits perturbations of density and velocity evolve in a manner that is independent of the form of the initial disturbance. The same conclusion applies to vortical perturbations of the velocity for arbitrary pressure while entropic perturbations are advected by the Hubble flow. Without the background charge the underlying Hubble flow describes a Coulomb explosion whose stability with respect to small disturbances is also demonstrated.

Interaction of metastable shock waves with perturbations

The shock wave metastable behavior in equilibrium media is detected in numerical experiments. This phenomenon is directly related to the ambiguous representation of a shock wave discontinuity when the shock belongs to the S-shaped fragment of the pressure-velocity Hugoniot. After interaction with weak perturbations the metastable shock wave recovers its original form and parameters (like stable shock). If the amplitude of the perturbations exceeds some critical value, the shock wave instability is developed. The instability is accompanied by formation of the transverse secondary waves switching local post-shock parameters between two Hugoniot segments separated from each other by the absolute instability region. The problem of the metastable shock wave interaction with local entropy perturbation passing through the shock front is studied in the framework of three-dimensional problem formulation. The shock wave transition to the limiting self-oscillating mode is described. Some features of this mode are completely determined by the shape of the Hugoniot and isentropes and does not depend on the shock wave structure. Namely, the shape of the shock front corrugations and flow structure evolution are analyzed. These features may be served as marker of the corresponding thermodynamic anomalies.

Stronger Hydration of Eu(III) Impedes Its Competition against Am(III) in Binding with N-donor Extractants.

The significance of understanding the interaction between actinide(III)/lanthanide(III) (An(III)/Ln(III)) and N-donor extractants lies in the importance of efficient An3+/Ln3+ separation in advanced nuclear fuel cycles and the high expectation of the application of N-donor extractants. This work reports a density functional theory study aiming at a plausible explanation of the origin of the selectivity of the ligands in An3+/Ln3+ separation and an evaluation of the influence of the bridging groups of typical N-donor extractants. Five bis(triazine) N-donor ligands were considered, differing in their denticity dictated by their bridging groups and in the flexibility of these bridging groups. The results showed much stronger hydration of Eu(III) in comparison to Am(III) in the ligand exchange of aqua ligands by N-donor ligands, while there was a moderate difference in their interaction strengths with the N-donor ligands. This implicated that the distinct difficulty in desolvating Eu(III) and Am(III) may govern their selectivity in liquid-liquid extraction. The analysis of the role of the bridging groups of the ligands confirmed the importance of a ligand to be equipped with preorganized binding sites to minimize the perturbation of entropy. We tentatively propose that this conclusion may hold in the explanation of the low selectivity of oxygenated extractants and the high selectivity of extractants with soft donors in An3+/Ln3+ separation.

Entropy production in affine inflation

Multiple scalar fields nonminimally interacting through pure affine gravity are considered to generate primordial perturbations during an inflationary phase. The couplings considered give rise to two distinct sources of entropy perturbations that may not be suppressed in the long wavelength limit. The first is merely induced by the presence of more than one scalar and arises even in the minimal coupling limit. The second source however is restricted to nonminimal interaction. Unlike the case of metric gravity, and due to the absence of anisotropic stresses, the second source disappears for single scalar, showing that nonminimal couplings become relevant to non-adiabatic perturbations only when more than one scalar field are considered. Hence the notion of adiabaticity is not affected by the transition to minimal coupling contrary to the metric gravity case where it is confused by changing the frames. Precise data that might be able to neatly track different sources of isocurvature modes, if any, must not only distinguish between different models of inflation but also determine the most viable approach to gravity which underlies the inflationary dynamics itself.

Acoustic wave generation in collapsing massive stars with convective shells

ABSTRACT The convection that takes place in the innermost shells of massive stars plays an important role in the formation of core-collapse supernova explosions. Upon encountering the supernova shock, additional turbulence is generated, amplifying the explosion. In this work, we study how the convective perturbations evolve during the stellar collapse. Our main aim is to establish their physical properties right before they reach the supernova shock. To this end, we solve the linearized hydrodynamics equations perturbed on a stationary background flow. The latter is approximated by the spherical transonic Bondi accretion, while the convective perturbations are modelled as a combination of entropy and vorticity waves. We follow their evolution from large radii, where convective shells are initially located, down to small radii, where they are expected to encounter the accretion shock above the proto-neutron star. Considering typical vorticity perturbations with a Mach number ∼0.1 and entropy perturbations with magnitude ∼0.05kb/baryon, we find that the advection of these perturbations down to the shock generates acoustic waves with a relative amplitude $\delta {\rm p}/\gamma {\rm p} \lesssim 10{{\ \rm per\ cent}}$, in agreement with published numerical simulations. The velocity perturbations consist of contributions from acoustic and vorticity waves with values reaching ${\sim}10{{\ \rm per\ cent}}$ of the sound speed ahead of the shock. The perturbation amplitudes decrease with increasing ℓ and initial radii of the convective shells.

Numerical investigation on the generation, mixing and convection of entropic and compositional waves in a flow duct

Recent models and experiments have demonstrated that indirect noise can be generated via acceleration of either entropic or compositional perturbations through a nozzle. These studies found that the acoustic signature depends on the extent of the dispersion effects on the perturbation waves during the convection process. In this work, numerical simulations are undertaken using the URANS formulation to model the mixing of unsteady entropic and compositional waves in an open-ended flow duct in the transitional regime (2500 < Re < 8100). The flow is perturbed by either heat addition or radial injection of an inert gas that is heavier (argon) or lighter (helium) than air. The computed temperature and mass fraction fields are compared to experimental results obtained using both intrusive and non-intrusive techniques. Agreement with the experimental data is good. The signatures of both perturbations are well captured using two-equation turbulence models. However, they lag behind the experimental results at downstream probe locations, suggesting that the centreline velocity is underpredicted. Dispersion effects on the compositional waves are shown to be insignificant for the system studied here. In the heat addition case, heat loss is found to be a key factor in capturing the correct entropic perturbation for long convection lengths.

Adiabatic media inflation

We study the dynamics of inflation driven by an adiabatic self-gravitating medium, extending the previous works on fluid and solid inflation. Such a class of media comprises perfect fluids, zero and finite temperature solids. By using an effective field theory description, we compute the power spectrum for the scalar curvature perturbation of constant energy density hypersurface ζ and the comoving scalar curvature perturbation ℛ in the case of slow-roll, super slow-roll and w-media inflation, an inflationary phase with w constant in the range −1 <w <−1/3. A similar computation is done for the tensor modes. Adiabatic media are characterized by intrinsic entropy perturbations that can give a significant contribution to the power spectrum and can be used to generate the required seed for primordial black holes. For such a media, the Weinberg theorem is typically violated and on super horizon scale neither ζ nor ℛ are conserved and moreover ζ ≠ ℛ. Reheating becomes crucial to predict the spectrum of the imprinted primordial perturbations. We study how the difference between ζ and ℛ during inflation gives rise to relative entropic perturbations in ΛCDM.

The effect of anisotropic stress and non-adiabatic pressure perturbations on the evolution of the comoving curvature perturbation

We derive the equation for the evolution of the curvature perturbation on the comoving time slice, , in the presence of anisotropic and non-adiabatic terms in the energy–momentum tensor of matter fields. The equation is obtained by manipulating the perturbed Einstein’s equations in the comoving time slice. It could be used to study the evolution of the comoving curvature perturbations for systems with an anisotropic energy–momentum tensor, such as in the presence of vector fields, in the presence of entropy, such as in a multi-field system, or in modified gravity theories. As a simple application, after checking that the comoving time slice for a multi-field system does not coincide with the uniform field time slice in general, we use the equation in the case of two minimally coupled scalar fields and derive a closed set of equations for the curvature and entropy perturbations on the comoving time slice.

Reheating and entropy perturbations in fibre inflation * * B.-M. G. was supported by a scholarship granted by the China Scholarship Council (CSC, 201706180072). The research at McGill is supported in part by funds from NSERC and from the Canada Research Chairs program.

We study reheating in some one and two field realizations of fibre inflation. We find that reheating begins with a phase of preheating in which long wavelength fluctuation modes are excited. In two field models there is a danger that the parametric amplification of infrared fluctuations in the second scalar field - associated with an entropy mode - might induce an instability of the curvature fluctuations. We show that, at least in the models we consider, the entropy mode has a sufficiently large mass to prevent this instability. Hence, from the point of view of reheating the models we consider are well-behaved.

Are primordial black holes produced by entropy perturbations in single field inflationary models?

We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices ℛ, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations. We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution. Contrary to previous results derived in the uniform density gauge assuming the gradient term can be neglected on super-horizon scales, the relation is valid on any scale for any minimally coupled single scalar field model, also on sub-horizon scales where gradient terms are large. We apply it to the case of quasi-inflection inflation, showing that while entropy perturbations are decreasing, ℛ can grow on super-horizon scales, due to a large increase of the conversion factor. This happens in the time interval during which a sufficiently fast decrease of the equation of state w transforms into a growing mode what in slow-roll models would be a decaying mode. The same mechanism also explains the super-horizon evolution of ℛ in globally adiabatic systems, for which entropy perturbations vanish on any scale, such as ultra slow roll inflation and its generalizations.

Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Abstract Large-scale convective flows called giant cells were once thought to transport the Sun’s luminosity in the solar convection zone, but recent observations have called their existence into question. In place of large-scale flows, some authors have suggested the solar luminosity may instead be transported by small droplets of rapidly falling, low-entropy fluid. This “entropy rain” could propagate as dense vortex rings, analogous to rising buoyant thermals in the Earth’s atmosphere. In this work, we develop an analytical theory describing the evolution of dense, negatively buoyant thermals. We verify the theory with 2D cylindrical and 3D Cartesian simulations of laminar, axisymmetric thermals in highly stratified atmospheres. Our results show that dense thermals fall in two categories: a stalling regime in which the droplets slow down and expand, and a falling regime in which the droplets accelerate and shrink as they propagate downwards. We estimate that solar downflows are in the falling regime and maintain their entropy perturbation against diffusion until they reach the base of the convection zone. This suggests that entropy rain may be an effective nonlocal mechanism for transporting the solar luminosity.

Dark sector evolution in Horndeski models

We use the Equation of State (EoS) approach to study the evolution of the dark sector in Horndeski models, the most general scalar-tensor theories with second order equations of motion. By including the effects of the dark sector into our code EoS_class, we demonstrate the numerical stability of the formalism and excellent agreement with results from other publicly available codes for a range of parameters describing the evolution of the function characterising the perturbations for Horndeski models, αx, with x = K, B, M, T. After demonstrating that on sub-horizon scales (k≳ 10−3 Mpc−1 at z=0) velocity perturbations in both the matter and the dark sector are typically subdominant with respect to density perturbations in the equation of state for perturbations, we find an attractor solution for the dark sector gauge-invariant density perturbation Δds by neglecting its time derivatives in the equation describing its time evolution, as commonly done in the well-known quasi-static approximation. Using this result, we provide simplified expressions for the equation-of-state functions: the dark sector entropy perturbations wdsΓds and anisotropic stress wdsΠds. From this we derive a growth factor-like equation for both matter and dark sector and are able to capture the relevant physics for several observables with great accuracy. We finally present new analytical expressions for the well-known modified gravity phenomenological functions μ, η and Σ for a generic Horndeski model as functions of αx. We show that on small scales they reproduce expressions presented in previous works, but on large scales, we find differences with respect to other works.

Entropy and Vorticity Wave Generation in Realistic Gas Turbine Combustors

Understanding the nature of the unsteady flow at the combustor exit is required to accurately simulate time-dependent phenomena in the turbine entry, such as indirect noise generation. Using large-eddy simulations of the combustion process in a realistic geometry, the flow at its exit is analyzes. Two realistic near-ground certification operating conditions are considered. Different mechanisms for large-scale flow and thermal structure generation are described, which are ejected into the turbine. Modal decomposition methods are used to extract the spatial and temporal scales at the turbine entry. It is found that, depending on the operating condition, the entropy waves convect as elongated streaks in the core of the combustor annulus or the proximity of the walls. The dominant unsteady character of the fluctuations exhibits different spectral properties: that is, low frequency in the core and high frequency toward walls. At the combustor exit, the vortical field is dominated by the swirl in the air inlet, which is found to have little influence on the entropy perturbations. Furthermore, the importance of considering the interaction of multiple fuel injectors and combustion zones in an annular combustor is investigated. It is shown that pulsating circumferential vorticity modes can occur in multisector annular combustors, but these do not affect the entropy wave distribution.

Modelling of Intrinsic Thermoacoustic Instability of Premixed Flame in Combustors with Changes in Cross Section

ABSTRACTThis work investigates the effects of a moving flame front on the thermoacoustic oscillations in nonuniform combustors considering both the cavity and intrinsic resonant feedbacks. This theoretical study shows that the entropic perturbations can be generated by a perfectly premixed moving flame front in combustors with changes in cross section. Comparing with Direct Numerical Simulation (DNS) results shows the influence of the perturbation of a moving flame front on the intrinsic thermoacoustic stability. Applied to the verification of experimental results of a combustor consisting of multiple components, the present work predicts correctly the frequency and growth of both chamber resonant and intrinsic thermoacoustic (ITA) modes. Numerical research shows that alteration of reflection coefficients may both stabilize the chamber resonant and ITA modes of an experimental test rig. However, stabilizing the thermoacoustic oscillation by adjusting the boundary conditions seems less efficient in complicated combustion networks.

Spectra and entropy of multifield warm inflation

We study the power spectra and entropy of two-field warm inflationary scenario with canonical condition which is described by many-dimensional stochastic differential equations. The field perturbations are analytically calculated via a Volterra integral equation of the second kind, based on which we obtain a spectra with leading order and first order of slow-roll parameters. We also find the evolutions of background are not independent but relying on dissipative coefficients, which is distinguished from that in cold inflation. Then, we calculate the entropy on the basis of statistical physics theory by introducing an entropy matrix. On super-horizon scale, the entropy matrix follows the fluctuation-dissipation relation consistent with the scale-invariance of spectra or the stationarity of field perturbations. The entropy perturbation vanishes at both super-horizon and sub-horizon scale, while narrow peaks generate at a specific scale which could be considered as horizon. In addition, the second law of thermodynamics is followed as well.

Curvature and topology dependency of the cosmological spectra

In this article we investigate dependency of the adiabatic and entropy spectral indices of the cosmological perturbations on the geometry and topology of the background universe. Our discussion includes the post-inflationary universe i.e. radiation-dust mixture era. For this purpose, we first extract an explicit equation describing evolution of the comoving curvature perturbation in the FLRW universe with arbitrary spatial sectional curvature. We may percept when $K\neq 0$, curvature scale would be as significant as the perturbations scales to recognize the behavior of the spectral indices. We also focus on the entropy perturbation in order to extract behavior of the isocurvature spectral index in terms of the curvature index and time. Our analysis shows that spectra of curvature and entropy perturbations in sub-horizon scales could be function of topology. Moreover, an accurate analysis makes clear that time-average of isocurvature index in case $K=0$ is about zero,so that imprint of entropy perturbation in time duration may be negligible. We also consider evolution of the cosmological indices for super-curvature modes in the case $K=-1$. In the most results dependency to curvature, initial conditions and scale modes are thoroughly vivid.

Cosmologically viable generalized Einstein-aether theories

We investigate generalized Einstein-Aether theories that are compatible with the Planck Cosmic Microwave Background (CMB) temperature anisotropy, polarisation, and lensing data. For a given dark energy equation of state, $w_{\rm de}$, we formulate a designer approach and we investigate their impact on the CMB temperature anisotropy and matter power spectra. We use the Equation of State approach to parametrize the perturbations and find that this approach is particularly useful in identifying the most suitable and numerically efficient parameters to explore in a Markov chain Monte Carlo (MCMC) analysis. We find the data constrains models with $w_{\rm de} = -1$ to be compatible with $\Lambda$CDM. For $w_{\rm de} \not= -1$ models, which avoid the gravitational waves constraint through the entropy perturbation, we constrain $w_{\rm de}$ to be $w_{\rm de } = -1.06^{+0.08}_{-0.03}$ (CMB) and $w_{\rm de } =-1.04^{+0.05}_{-0.02}$ (CMB+Lensing) at $68\%$C.L., and find that these models can be different from $\Lambda$CDM and still be compatible with the data. We also find that these models can ameliorate some anomalies in $\Lambda$CDM when confronted with data, such as the low-$\ell$ and high-$k$ power in the CMB temperature anisotropy and matter power spectra respectively, but not simultaneously. We also investigate the anomalous lensing amplitude, quantified by $A_{\rm lens}$, and find that that for $w_{\rm de} = -1$ models, $A_{\rm lens} = 1.15^{+0.07}_{-0.08}$ (CMB) and $A_{\rm lens} = 1.12\pm0.05$ (CMB+Lensing) at $68\%$C.L. $\sim$ 2$\sigma$ larger than expected, similar to previous analyses of $\Lambda$CDM.

Propagation of acoustic perturbations in non-uniform ducts with non-uniform mean flow using eigen analysis in general curvilinear coordinate systems

A new framework, Eigen Analysis in General Curvilinear Coordinates (EAGCC), is presented for internal propagation of linear acoustic flow disturbances through irregular but smoothly varying duct geometries and non-uniform but smoothly varying mean flows. The framework is based on an eigen analysis of the linearised Euler equations for a perfect gas formulated in a general curvilinear coordinate system. A series of test cases are studied, from a simple uniform cylindrical annular duct with uniform mean flow to an axially and circumferentially non-uniform duct with non-uniform mean flow, which together validate the method for acoustic propagation through non-uniform annular ducts and non-uniform but irrotational and homentropic mean flow: although the framework provides for rotational and non-homentropic mean flow, and for modelling vortical and entropic flow perturbations, these features are not validated in this paper. Two propagation methods are presented. The first is a one-way “single sweep” calculation, in which only information travelling in the direction of propagation is retained. The second is an iterative “two-way sweep” method that accurately captures reflected waves and returns transmitted and reflected perturbations. Previous eigenvector analyses were subject to limitations on geometry and mean flow (for instance slowly-varying ducts) that are not required in the current method, for which the only limitations are that the duct and mean flow vary smoothly with position. This work extends the scope of the eigenvector approach to include acoustic problems previously limited to volumetric or surface-based methods.