# Posts Tagged perturbation

## Recent Postings from perturbation

### Multi-field inflation and cosmological perturbations [Cross-Listing]

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.

### Multi-field inflation and cosmological perturbations [Cross-Listing]

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.

### Multi-field inflation and cosmological perturbations

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.

### Multi-field inflation and cosmological perturbations [Cross-Listing]

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.

### One-Loop Transition Amplitudes in the D1D5 CFT

We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.

### Global adiabaticity and non-Gaussianity consistency condition [Cross-Listing]

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\delta P_{nad}\equiv\delta P-c_w^2\delta\rho$ where $c_w^2=\dot P/\dot\rho$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $R_c$ on super-horizon scales. In this paper, we consider models that satisfies $\delta P_{nad}=0$ on all scales, which we call global adiabaticity (GA), which is guaranteed if $c_s^2=c_w^2$ where $c_s$ is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll inflation in which $c_s^2=c_w^2=1$. We first establish the general model independent condition for super-horizon growth of $R_c$ in terms of the behavior as functions of the scale factor of the slow roll parameter $\epsilon(a)$, the energy density $\rho(a)$ and $c_s$. We then develop a general inversion method which allows to find the Lagrangian of a GA K-inflation scalar field from the evolution of these background quantities. Applying this inversion method we show that there indeed exists a wide class of GA K-inflation models with $c_s^2=c_w^2$, which allows $R_c$ to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition

### Global adiabaticity and non-Gaussianity consistency condition

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\delta P_{nad}\equiv\delta P-c_w^2\delta\rho$ where $c_w^2=\dot P/\dot\rho$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $R_c$ on super-horizon scales. In this paper, we consider models that satisfies $\delta P_{nad}=0$ on all scales, which we call global adiabaticity (GA), which is guaranteed if $c_s^2=c_w^2$ where $c_s$ is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll inflation in which $c_s^2=c_w^2=1$. We first establish the general model independent condition for super-horizon growth of $R_c$ in terms of the behavior as functions of the scale factor of the slow roll parameter $\epsilon(a)$, the energy density $\rho(a)$ and $c_s$. We then develop a general inversion method which allows to find the Lagrangian of a GA K-inflation scalar field from the evolution of these background quantities. Applying this inversion method we show that there indeed exists a wide class of GA K-inflation models with $c_s^2=c_w^2$, which allows $R_c$ to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition

### Global adiabaticity and non-Gaussianity consistency condition [Replacement]

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $\R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $\R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $\R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\delta P_{nad}\equiv\delta P-c_w^2\delta\rho$ where $c_w^2=\dot P/\dot\rho$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $\R_c$ on super-horizon scales. In this paper, we consider models that satisfy $\delta P_{nad}=0$ on all scales, which we call global adiabaticity (GA), which is guaranteed if $c_w^2=c_s^2$, where $c_s$ is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll(USR) inflation in which $c_w^2=c_s^2=1$. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with $c_w^2=c_s^2$, which allows $\R_c$ to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.

### Global adiabaticity and non-Gaussianity consistency condition [Replacement]

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $\R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $\R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $\R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\delta P_{nad}\equiv\delta P-c_w^2\delta\rho$ where $c_w^2=\dot P/\dot\rho$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $\R_c$ on super-horizon scales. In this paper, we consider models that satisfy $\delta P_{nad}=0$ on all scales, which we call global adiabaticity (GA), which is guaranteed if $c_w^2=c_s^2$, where $c_s$ is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll(USR) inflation in which $c_w^2=c_s^2=1$. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with $c_w^2=c_s^2$, which allows $\R_c$ to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.

### Quasi Normal Modes and P-V Criticallity for scalar perturbations in a class of dRGT massive gravity around Black Holes

We investigate black holes in a class of dRGT massive gravity for their quasi normal modes (QNMs) for neutral and charged ones using Improved Asymptotic Iteration Method (Improved AIM) and their thermodynamic behavior. The QNMs are studied for different values of the massive parameter m_g for both neutral and charged dRGT black holes under a massless scalar perturbation. As m_g increases, the magnitude of the quasi normal frequencies are found to be increasing. The results are also compared with the Schwarzchild de Sitter (SdS) case. P-V criticallity of the aforesaid black hoels under massles scalar perturbation in the de Sitter space are also studied in this paper. It is found that the thermodynamic behavior of a neutral black hole shows no physically feasible phase transition while a charged black hole shows a definite phase transition.

### On the Time Dependence of Adiabatic Particle Number

We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naively, this is not a well-defined notion for such a non-equilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and anti-particles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with non-trivial temporal sub-structure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, Spectral Function and Schrodinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.

### Stability of Charged Global AdS$_4$ Spacetimes [Cross-Listing]

We study linear and nonlinear stability of asymptotically AdS$_4$ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of this stability band scales down with the charge Q, and does not survive the blow up limit to a planar geometry.

### Stability of Charged Global AdS$_4$ Spacetimes

We study linear and nonlinear stability of asymptotically AdS$_4$ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of this stability band scales down with the charge Q, and does not survive the blow up limit to a planar geometry.

### Isgur-Wise function and a new approach to Potential Model

Considering the Cornell potential $V(r)=-\frac{4\alpha_s}{3r}+br+c$, we have revisited the Dalgarno's method of perturbation by incorporating two scales $r^{short}$ and $r^{long}$ as an integration limit so that the perturbative procedure can be improved in a potential model. With the improved version of the wave function the ground state masses of the heavy light mesons $D, D_s, B, B_s$ and $B_c$ are computed. The slopes and curvatures of the form factors of semi-leptonic decays of heavy-light mesons in both HQET limit and finite mass limit are calculated and compared with the available data and our previous work.

### Quasinormal modes of gravitational field perturbation of regular phantom black holes

We study the gravitational quasi-normal modes (QNMs) for a kind of regular black hole named as phantom black hole (BH), which is a solution of a self-gravitating minimally coupled scalar field with an arbitrary potential.The parameter conditions of such BH are investigated in asymptotically flat, de sitter (dS), and anti de sitter (AdS) spacetimes separately. Considering the standard odd parity and even parity of gravitational perturbation, the corresponding master equations are derived and quasi-normal perturbation are discussed in asymptotically flat and dS spacetimes. The dynamic evolution of the perturbation field indicates the stability of gravitational perturbation directly. On the whole in asymptotically flat and dS spacetimes, the gravitational perturbations have the similar characteristics for odd and even parities. The decay speed of perturbation is strongly dependent on the scale $b$. Furthermore through the analysis of Hawking radiation, the thermodynamics of such regular phantom black hole is also influenced by $b$ significantly. This might be hopeful to support a bridge for quantum interpretation of QNMs perturbation.

### Butterflies with rotation and charge

We explore the butterfly effect for black holes with rotation or charge. We perturb rotating BTZ and charged black holes in 2+1 dimensions by adding a small perturbation on one asymptotic region, described by a shock wave in the spacetime, and explore the effect of this shock wave on the length of geodesics through the wormhole and hence on correlation functions. We find the effect of the perturbation grows exponentially at a rate controlled by the temperature; dependence on the angular momentum or charge does not appear explicitly. We comment on issues affecting the extension to higher-dimensional charged black holes.

### Relating metric and covariant perturbation theories in $f(R)$ gravity

Modified theories of gravity have been invoked recently as an alternative to dark energy, in an attempt to explain the apparent accelerated expansion of the universe at the present time. In order to describe inhomogeneities in cosmological models, cosmological perturbation theory is used, of which two formalisms exist: the metric approach and the covariant approach. In this paper I present the relationship between the metric and covariant approaches for modeling $f(R)$ theories of gravity. This provides a useful resource that researchers primarily working with one formalism can use to compare or translate their results to the other formalism.

### Relating metric and covariant perturbation theories in $f(R)$ gravity [Cross-Listing]

Modified theories of gravity have been invoked recently as an alternative to dark energy, in an attempt to explain the apparent accelerated expansion of the universe at the present time. In order to describe inhomogeneities in cosmological models, cosmological perturbation theory is used, of which two formalisms exist: the metric approach and the covariant approach. In this paper I present the relationship between the metric and covariant approaches for modeling $f(R)$ theories of gravity. This provides a useful resource that researchers primarily working with one formalism can use to compare or translate their results to the other formalism.

### On the mass-coupling relation of multi-scale quantum integrable models

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the $\Theta$ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.

### Cosmic walls and filaments formation in modified Chaplygin gas cosmology

We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of structure formation in the Modified Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, it is shown that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a final highly non-spherical structure which can be considered as a candidate for justifying already known cosmological structures as cosmic walls and filaments.

### Cosmic walls and filaments formation in modified Chaplygin gas cosmology [Cross-Listing]

We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of structure formation in the Modified Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, it is shown that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a final highly non-spherical structure which can be considered as a candidate for justifying already known cosmological structures as cosmic walls and filaments.

### Adler function and Bjorken polarized sum rule: perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit [Replacement]

We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\{\beta\}$-expanded perturbation coefficients at $O(\alpha_s^4)$ level in $\bar{\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\{\beta\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the perturbative $\{\beta\}$-expansion for the nonsinglet Adler function and the Bjorken polarized sum rule, which follow from the conformal symmetry limit and its violation, are presnted. The relevance to the possible new analysis of the experimental data for the Bjorken polarized sum rule is briefly discussed.

### Adler function and Bjorken polarized sum rule: perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit

We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\{\beta\}$-expanded perturbation coefficients at $O(\alpha_s^4)$ level in $\overline{\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\{\beta\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are presented between terms of the $\{\beta\}$-expansion of perturbation coefficients, for the nonsinglet Adler function and the Bjorken polarized sum rule, relations which follow from the conformal symmetry limit and its violation.

### Dynamics of the Area Law of Entanglement Entropy

We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.

### The peculiar velocities in the Galactic outer disk--hints of the elliptical disk and the perturbation of the spiral structures

We present the peculiar in-plane velocities derived from the LAMOST red clump stars. From the variations of the in-plane velocity with the Galactocentric radius for the young and old red clump stars, we are able to identify two types of peculiar velocities: 1) both the two red clump populations show that the radial velocity is negative within $R=9.0$\,kpc and becomes positive beyond (denoted as the \emph{long-wave} mode); and 2) the young red clump stars show larger mean radial velocity than the old population by about 3\,km$\rm s^{-1}$ between $R=9$ and 12\,kpc (denoted as the \emph{short-wave} mode). We find that the elliptical disk induced by the rotating bar can well explain the \emph{long-wave} mode peculiar velocity. The axis ratio of the elliptical disk is around 0.8-0.95 and the disk keeps circular at $R=9.24\pm0.2$\,kpc, which should be the location of the outer Lindblad resonance radius (OLR). Adopting the circular speed of 238\,km$\rm s^{-1}$, the pattern speed of the bar is then derived as $48\pm3$\,km$\rm s^{-1}$kpc$^{-1}$ from the location of OLR. On the other hand, the \emph{short-wave} mode is likely the perturbation of the spiral arms as density waves.

### Instability of Non-uniform Toroidal Magnetic Fields in Accretion Disks

A new type of instability that is expected to drive magnetohydrodynamic (MHD) turbulence from a purely toroidal magnetic field in an accretion disk is presented. It is already known that in a differentially rotating system, the uniform toroidal magnetic field is unstable due to a magnetorotational instability (MRI) under a non-axisymmetric and vertical perturbation, while it is stable under a purely vertical perturbation. Contrary to the previous study, this paper proposes an unstable mode completely confined to the equatorial plane, driven by the expansive nature of the magnetic pressure gradient force under a non-uniform toroidal field. The basic nature of this growing eigenmode, to which we give a name "magneto-gradient driven instability", is studied using linear analysis, and the corresponding nonlinear evolution is then investigated using two-dimensional ideal MHD simulations. Although a single localized magnetic field channel alone cannot provide sufficient Maxwell stress to contribute significantly to the angular momentum transport, we find that the mode coupling between neighboring toroidal fields under multiple localized magnetic field channels drastically generates a highly turbulent state and leads to the enhanced transport of angular momentum, comparable to the efficiency seen in previous studies on MRIs. This horizontally confined mode may play an important role in the saturation of an MRI through complementray growth with the toroidal MHDs and coupling with magnetic reconnection.

### Instability of black strings in third-order Lovelock theory [Replacement]

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension $D=9$, which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet and third-order Lovelock theory. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

### Instability of black strings in third-order Lovelock theory [Replacement]

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension $D=9$, which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet and third-order Lovelock theory. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

### Perturbation growth in accreting filaments

We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long, initially sub-critical but accreting filaments. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length scale which is roughly 4 times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength and growth rate. These are due to gravo-acoustic oscillations along the longitudinal axis during the sub-critical phase of growth. The positions of the peaks in growth rate have a strong dependence on both the mass accretion rate onto the filament and the temperature of the gas. When seeded with a multi-wavelength density power spectrum there exists a clear preferred core separation equal to the largest peak in the dispersion relation. Our results allow one to estimate a minimum age for a filament which is breaking up into regularly spaced fragments, as well as a maximum accretion rate. We apply the model to observations of filaments in Taurus by Tafalla & Hacar (2015) and find accretion rates consistent with those estimated by Palmeirim et al. (2013).

### Perturbation growth in accreting filaments [Replacement]

We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long, initially sub-critical but accreting filaments. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length scale which is roughly 4 times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength and growth rate. These are due to gravo-acoustic oscillations along the longitudinal axis during the sub-critical phase of growth. The positions of the peaks in growth rate have a strong dependence on both the mass accretion rate onto the filament and the temperature of the gas. When seeded with a multi-wavelength density power spectrum there exists a clear preferred core separation equal to the largest peak in the dispersion relation. Our results allow one to estimate a minimum age for a filament which is breaking up into regularly spaced fragments, as well as a maximum accretion rate. We apply the model to observations of filaments in Taurus by Tafalla & Hacar (2015) and find accretion rates consistent with those estimated by Palmeirim et al. (2013).

### Cosmological dynamics of extended chameleons [Cross-Listing]

We investigate the cosmological dynamics of the recently proposed extended chameleon models at both background and linear perturbation levels. Dynamical systems techniques are employed to fully characterize the evolution of the universe at the largest distances, while structure formation is analysed at sub-horizon scales within the quasi-static approximation. The late time dynamical transition from dark matter to dark energy domination can be well described by almost all extended chameleon models considered, with no deviations from $\Lambda$CDM results at both background and perturbation levels. The results obtained in this work confirm the cosmological viability of extended chameleons as alternative dark energy models.

### Cosmological dynamics of extended chameleons

We investigate the cosmological dynamics of the recently proposed extended chameleon models at both background and linear perturbation levels. Dynamical systems techniques are employed to fully characterize the evolution of the universe at the largest distances, while structure formation is analysed at sub-horizon scales within the quasi-static approximation. The late time dynamical transition from dark matter to dark energy domination can be well described by almost all extended chameleon models considered, with no deviations from $\Lambda$CDM results at both background and perturbation levels. The results obtained in this work confirm the cosmological viability of extended chameleons as alternative dark energy models.

### Absorption Cross-section and Decay Rate of Rotating Linear Dilaton Black Holes

We analytically study the scalar perturbation of non-asymptotically flat (NAF) rotating linear dilaton black holes (RLDBHs) in 4-dimensions. We show that both radial and angular wave equations can be solved in terms of the hypergeometric functions. The exact greybody factor (GF), the absorption cross-section (ACS), and the decay rate (DR) for the massless scalar waves are computed for these black holes (BHs). The results obtained for ACS and DR are discussed through graphs.

### The B-mode polarization of CMB and Cosmic Neutrino Background [Cross-Listing]

It is known that in contrast with the E-mode polarization, the B-mode polarization of the Cosmic Microwave Background cannot be generated by the Compton scattering in the case of scalar mode of metric perturbation. However it is possible to generate the B-mode by the Compton scattering in the case of tensor mode of metric perturbation. For this reason, the ratio of tensor to scalar modes of metric perturbation ($r\sim C_{Bl}/C_{El}$) is estimated by comparing the B-mode power spectrum with the E-mode at least for small $l$. We study the CMB polarization specially B-mode due to the weak interaction of Cosmic Neutrino Background (CNB) and CMB, in addition to the Compton scattering in both cases of scalar and tensor metric perturbations. It is shown that the power spectrum $C_{Bl}$ of the B-mode polarization receives some contributions from scalar and tensor modes, which have effects on the value of $r$-parameter. We also show that the B-mode polarization power spectrum can be used as an indirect probe into the CNB.

### The B-mode polarization of CMB and Cosmic Neutrino Background [Cross-Listing]

It is known that in contrast with the E-mode polarization, the B-mode polarization of the Cosmic Microwave Background cannot be generated by the Compton scattering in the case of scalar mode of metric perturbation. However it is possible to generate the B-mode by the Compton scattering in the case of tensor mode of metric perturbation. For this reason, the ratio of tensor to scalar modes of metric perturbation ($r\sim C_{Bl}/C_{El}$) is estimated by comparing the B-mode power spectrum with the E-mode at least for small $l$. We study the CMB polarization specially B-mode due to the weak interaction of Cosmic Neutrino Background (CNB) and CMB, in addition to the Compton scattering in both cases of scalar and tensor metric perturbations. It is shown that the power spectrum $C_{Bl}$ of the B-mode polarization receives some contributions from scalar and tensor modes, which have effects on the value of $r$-parameter. We also show that the B-mode polarization power spectrum can be used as an indirect probe into the CNB.

### The B-mode polarization of CMB and Cosmic Neutrino Background

It is known that in contrast with the E-mode polarization, the B-mode polarization of the Cosmic Microwave Background cannot be generated by the Compton scattering in the case of scalar mode of metric perturbation. However it is possible to generate the B-mode by the Compton scattering in the case of tensor mode of metric perturbation. For this reason, the ratio of tensor to scalar modes of metric perturbation ($r\sim C_{Bl}/C_{El}$) is estimated by comparing the B-mode power spectrum with the E-mode at least for small $l$. We study the CMB polarization specially B-mode due to the weak interaction of Cosmic Neutrino Background (CNB) and CMB, in addition to the Compton scattering in both cases of scalar and tensor metric perturbations. It is shown that the power spectrum $C_{Bl}$ of the B-mode polarization receives some contributions from scalar and tensor modes, which have effects on the value of $r$-parameter. We also show that the B-mode polarization power spectrum can be used as an indirect probe into the CNB.

### On the Origin of Flux Ratio Anomaly in Quadruple Lens Systems [Cross-Listing]

We explore the origin of flux ratio anomaly in quadruple lens systems. Using a semi-analytic method based on $N$-body simulations, we estimate the effect of possible magnification perturbation caused by subhaloes with a mass scale of <~ $10^9\,h^{-1} \textrm{M}_\odot$ in lensing galaxy haloes. Taking into account astrometric shifts by perturbers, we find that the expected change to the flux ratios per a multiply lensed image is just a few percent and the mean of the expected convergence perturbation at the effective Einstein radius of the lensing galaxy halo is $\langle \delta \kappa_{\textrm{sub}} \rangle = 0.003$, corresponding to the mean of the ratio of a projected dark matter mass fraction in subhaloes $\langle f_{\textrm{sub}} \rangle = 0.006$ for observed 11 quadruple lens systems. In contrast, the expected change to the flux ratio caused by line-of-sight structures in intergalactic spaces is typically ~10 percent and the mean of the convergence perturbation is $\langle |\delta \kappa_{\textrm{los}}| \rangle = 0.008$, corresponding to $\langle f_{\textrm{los}} \rangle = 0.017$. The contribution of magnification perturbation caused by subhaloes is $\sim 40$ percent of the total at a source redshift $z_\textrm{S}= 0.7$ and decreases monotonically in $z_\textrm{S}$ to $\sim 20$ percent at $z_\textrm{S}= 3.6$. Assuming statistical isotropy, the convergence perturbation estimated from the 11 systems has a positive correlation with the source redshift $z_\textrm{S}$, which is much stronger than that with the lens redshift $z_{\textrm{L}}$. This feature also supports the idea that the flux ratio anomaly is caused mainly by line-of-sight structures rather than subhaloes. We also discuss about a possible imprint of line-of-sight structures in demagnification of minimum images due to locally underdense structures in the line of sight.

### On the Origin of Flux Ratio Anomaly in Quadruple Lens Systems

We explore the origin of flux ratio anomaly in quadruple lens systems. Using a semi-analytic method based on $N$-body simulations, we estimate the effect of possible magnification perturbation caused by subhaloes with a mass scale of <~ $10^9\,h^{-1} \textrm{M}_\odot$ in lensing galaxy haloes. Taking into account astrometric shifts by perturbers, we find that the expected change to the flux ratios per a multiply lensed image is just a few percent and the mean of the expected convergence perturbation at the effective Einstein radius of the lensing galaxy halo is $\langle \delta \kappa_{\textrm{sub}} \rangle = 0.003$, corresponding to the mean of the ratio of a projected dark matter mass fraction in subhaloes $\langle f_{\textrm{sub}} \rangle = 0.006$ for observed 11 quadruple lens systems. In contrast, the expected change to the flux ratio caused by line-of-sight structures in intergalactic spaces is typically ~10 percent and the mean of the convergence perturbation is $\langle |\delta \kappa_{\textrm{los}}| \rangle = 0.008$, corresponding to $\langle f_{\textrm{los}} \rangle = 0.017$. The contribution of magnification perturbation caused by subhaloes is $\sim 40$ percent of the total at a source redshift $z_\textrm{S}= 0.7$ and decreases monotonically in $z_\textrm{S}$ to $\sim 20$ percent at $z_\textrm{S}= 3.6$. Assuming statistical isotropy, the convergence perturbation estimated from the 11 systems has a positive correlation with the source redshift $z_\textrm{S}$, which is much stronger than that with the lens redshift $z_{\textrm{L}}$. This feature also supports the idea that the flux ratio anomaly is caused mainly by line-of-sight structures rather than subhaloes. We also discuss about a possible imprint of line-of-sight structures in demagnification of minimum images due to locally underdense structures in the line of sight.

### Attractor non-equilibrium stationary states in perturbed long-range interacting systems [Cross-Listing]

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.

### Non-linear dense core formation in the dark cloud L1517

We present a solution for the observed core fragmentation of filaments in the Taurus L1517 dark cloud which previously could not be explained \citep{hacar2011}. Core fragmentation is a vital step for the formation of stars. Observations suggest a connection to the filamentary structure of the cloud gas but it remains unclear which process is responsible. We show that the gravitational instability process of an isothermal cylinder can account for the exhibited fragmentation under the assumption that the perturbation grows on the dominant wavelength. We use numerical simulations with the code RAMSES, estimate observed column densities and line-of-sight velocities and compare them to the observations. A critical factor for the observed fragmentation is that cores grow by redistributing mass within the filament and thus the density between the cores decreases over the fragmentation process. This often leads to wrong dominant wavelength estimates as it is strongly dependent on the initial central density. We argue that non-linear effects also play an important role on the evolution of the fragmentation. Once the density perturbation grows above the critical line-mass, non-linearity leads to an enhancement of the central core density in comparison to the analytical prediction. Choosing the correct initial conditions with perturbation strengths of around 20\%, leads to inclination corrected line-of-sight velocities and central core densities within the observational measurement error in a realistic evolution time.

### Cosmological perturbations in mimetic Horndeski gravity [Cross-Listing]

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

### Cosmological perturbations in mimetic Horndeski gravity [Replacement]

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

### Cosmological perturbations in mimetic Horndeski gravity

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

### Cosmological perturbations in mimetic Horndeski gravity [Replacement]

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

### Cosmological perturbations in mimetic Horndeski gravity [Replacement]

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

### Transient dynamics of perturbations in astrophysical disks

This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational instability? In this case a rotational homogeneous inviscid flow with a Keplerian angular velocity profile is spectrally stable, making the transient growth of perturbations a candidate mechanism for energy transfer from the regular motion to perturbations. Transient perturbations differ qualitatively from perturbation modes and can grow substantially in shear flows due to the nonnormality of their dynamical evolution operator. Since the eigenvectors of this operator, alias perturbation modes, are mutually nonorthogonal, they can mutually interfere, resulting in the transient growth of their linear combinations. Physically, a growing transient perturbation is a leading spiral whose branches are shrunk as a result of the differential rotation of the flow. This paper discusses in detail the transient growth of vortex shear harmonics in the spatially local limit as well as methods for identifying the optimal (fastest growth) perturbations. Special attention is given to obtaining such solutions variationally, by integrating the direct and adjoint equations forward and backward in time, respectively. The material is presented in a newcomer-friendly style.

### Asteroid flux towards circumprimary habitable zones in binary star systems: II. Dynamics

Secular and mean motion resonances (hearafter MMR) are effective perturbations to shape planetary systems. In binary star systems, they play a key role during the early and late phases of planetary formation as well as the dynamical stability of a planetary system. In this study, we aim to correlate the presence of orbital resonances with the rate of icy asteroids crossing the habitable zone (hearafter HZ), from a circumprimary disk of planetesimals in various binary star systems. We modelled a belt of small bodies in the inner and outer regions, respectively below and beyond the orbit of a gas giant planet. The planetesimals are equally placed around a primary G-type star and move under the gravitational influence of the two stars and the gas giant. We numerically integrated the system for 50 Myr considering various parameters for the secondary star. Its stellar type varies from a M- to F-type; its semimajor axis is either 50 au or 100 au and its eccentricity is either 0.1 or 0.3. Our simulations highlight that a disk of planetesimals will suffer from perturbations due to a perturbed gas giant, mean motion and secular perturbations. We show that a secular perturbation -- which location and width vary according to the secondary star's characteristics -- can exist in the region of the icy asteroid belt region and overlap with MMRs which will have an impact on the dynamical lifetime of the disk. In addition, we point out that in any case, the 2:1 MMR, the 5:3 MMR and the secular perturbed area are powerful perturbations for the transport of icy material into the HZ.

### Thermal Fluctuations of Dark Matter in Bouncing Cosmology

We investigate the statistical nature of the dark matter particles produced in bouncing cosmology, including its total energy and the evolution of its sub-horizon and super-horizon thermal fluctuations. We find that the super-horizon modes of the dark matter thermal perturbations are developing during the generic bouncing universe scenario--in contrast to the case that no significant super-horizon thermal perturbations of dark matter appear in the inflation scenario such as WIMP(-less) miracles. By explicitly deriving and solving the equation of motion of super-horizon mode, we fully determine the evolution of thermal perturbation of dark matter in a generic bouncing background. And we also prove that the evolution of super-horizon modes is stable and will not ruin out the background evolution till the Planck scale.

### Thermal Fluctuations of Dark Matter in Bouncing Cosmology [Replacement]

We investigate the statistical nature of the dark matter particles produced in bouncing cosmology, especially, the evolution of its thermal fluctuations. By explicitly deriving and solving the equation of motion of super-horizon mode, we fully determine the evolution of thermal perturbation of dark matter in a generic bouncing background. And we also show that the evolution of super-horizon modes is stable and will not ruin the background evolution of a generic bouncing universe till the Planck scale. Given no super-horizon thermal perturbation of dark matter appears in standard inflation scenario such as WIMP(-less) miracles, such super-horizon thermal perturbation of dark matter generated during the generic bouncing universe scenario may be significant for testing and distinguishing these two scenario in near future.

### Adiabaticity and gravity theory independent conservation laws for cosmological perturbations [Cross-Listing]

We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\delta P_{nad}$, another is for a general matter field $\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\dot P/\dot\rho$. Assuming the adiabaticity in the general sense, $\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\neq c_w$, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if $\delta P_{nad}=0$ approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation $R_c$ and the uniform density curvature perturbation $\zeta$ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which $c_w=c_s$, where $\delta P_{nad}=\delta P_{c,nad}=0$ exactly, but the equivalence between $R_c$ and $\zeta$ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both $R_c$ and $\zeta$ are not conserved. In particular, as for $\zeta$, we find that it is crucial to take into account the next-to-leading order term in $\zeta$'s spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity is not always enough to ensure the conservation of $R_c$ or $\zeta$.

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