# Posts Tagged perturbation

## Recent Postings from perturbation

### Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs

The equation describing the secular diffusion of a self-gravitating collisionless system induced by an exterior perturbation is derived while assuming that the timescale corresponding to secular evolution is much larger than that corresponding to the natural frequencies of the system. Its two dimensional formulation for a tepid galactic disc is also derived using the epicyclic approximation. Its WKB limit is found while assuming that only tightly wound transient spirals are sustained by the disc. It yields a simple quadrature for the diffusion coefficients which provides a straightforward understanding of the loci of maximal diffusion within the disc.

### Non-Zero $\theta_{13}$ and $\delta_{CP}$ in a Neutrino Mass Model with $A_4$ Symmetry

In this paper, we consider a neutrino mass model based on $A_4$ symmetry. The spontaneous symmetry breaking in this model is chosen to obtain tribimaximal mixing in the neutrino sector. We introduce $Z_2 \times Z_2$ invariant perturbations in this model which can give rise to acceptable values of $\theta_{13}$ and $\delta_{CP}$. Perturbation in the charged lepton sector alone can lead to viable values of $\theta_{13}$, but cannot generate $\delta_{CP}$. Perturbation in the neutrino sector alone can lead to acceptable $\theta_{13}$ and maximal CP violation. By adjusting the magnitudes of perturbations in both sectors, it is possible to obtain any value of $\delta_{CP}$.

### Correlation of isocurvature perturbation and non-Gaussianity

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting bispectrum is large, we find that the form of the correlation depends mostly upon the inflation model and weakly on the axion parameters.

### Correlation of isocurvature perturbation and non-Gaussianity [Cross-Listing]

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting bispectrum is large, we find that the form of the correlation depends mostly upon the inflation model and weakly on the axion parameters.

### Correlation of isocurvature perturbation and non-Gaussianity [Cross-Listing]

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting bispectrum is large, we find that the form of the correlation depends mostly upon the inflation model and weakly on the axion parameters.

### Correlation of isocurvature perturbation and non-Gaussianity [Replacement]

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting bispectrum is large, we find that the form of the correlation depends mostly upon the inflation model but only weakly on the axion parameters.

### Correlation of isocurvature perturbation and non-Gaussianity [Replacement]

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting bispectrum is large, we find that the form of the correlation depends mostly upon the inflation model but only weakly on the axion parameters.

### Disformal invariance of curvature perturbation [Cross-Listing]

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski’s theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that this is also the case for any theory that is disformally related to Horndeski’s scalar-tensor theory. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Combining this with the fact that such an attractor regime is known to be realised on superhorizon scales in Horndeski’s theory, and that the comoving curvature perturbation is known to be conserved in this regime, we conclude that on superhorizon scales the nonlinear comoving curvature perturbation is both disformally invariant and conserved in any theory that is related to Horndeski’s by a disformal transformation. Finally, we confirm that theories disformally related to Horndeski’s theory give rise to second order equations of motion, meaning that they do not suffer from so-called Ostrogradsky instabilities.

### Disformal invariance of curvature perturbation

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski’s theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that this is also the case for any theory that is disformally related to Horndeski’s scalar-tensor theory. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Combining this with the fact that such an attractor regime is known to be realised on superhorizon scales in Horndeski’s theory, and that the comoving curvature perturbation is known to be conserved in this regime, we conclude that on superhorizon scales the nonlinear comoving curvature perturbation is both disformally invariant and conserved in any theory that is related to Horndeski’s by a disformal transformation. Finally, we confirm that theories disformally related to Horndeski’s theory give rise to second order equations of motion, meaning that they do not suffer from so-called Ostrogradsky instabilities.

### Disformal invariance of curvature perturbation [Cross-Listing]

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski’s theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that this is also the case for any theory that is disformally related to Horndeski’s scalar-tensor theory. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Combining this with the fact that such an attractor regime is known to be realised on superhorizon scales in Horndeski’s theory, and that the comoving curvature perturbation is known to be conserved in this regime, we conclude that on superhorizon scales the nonlinear comoving curvature perturbation is both disformally invariant and conserved in any theory that is related to Horndeski’s by a disformal transformation. Finally, we confirm that theories disformally related to Horndeski’s theory give rise to second order equations of motion, meaning that they do not suffer from so-called Ostrogradsky instabilities.

### Scrambling time from local perturbations of the eternal BTZ black hole

We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time $t_\omega$ in the large $c$ limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time $t_\omega$. In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.

### Thermalization in a Holographic Confining Gauge Theory [Cross-Listing]

Time dependent perturbations of states in a 3+1 dimensional confining gauge theory are considered in the context of holography. The perturbations are induced by varying the gauge theory’s coupling to a dimension three scalar operator in time. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of motion subject to these boundary conditions. We compute the characteristic time scale of many thermalization processes, noting that in every case we examine, this time scale is determined by the imaginary part of the lowest lying quasi-normal mode of the final state black brane. We quantify the dependence of this final state on parameters of the quench, and construct a dynamical phase diagram. Further support for a universal scaling regime in the abrupt quench limit is provided.

### Thermalization in a Holographic Confining Gauge Theory [Cross-Listing]

Time dependent perturbations of states in a 3+1 dimensional confining gauge theory are considered in the context of holography. The perturbations are induced by varying the gauge theory’s coupling to a dimension three scalar operator in time. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of motion subject to these boundary conditions. We compute the characteristic time scale of many thermalization processes, noting that in every case we examine, this time scale is determined by the imaginary part of the lowest lying quasi-normal mode of the final state black brane. We quantify the dependence of this final state on parameters of the quench, and construct a dynamical phase diagram. Further support for a universal scaling regime in the abrupt quench limit is provided.

### Thermalization in a Holographic Confining Gauge Theory

Time dependent perturbations of states in a 3+1 dimensional confining gauge theory are considered in the context of holography. The perturbations are induced by varying the gauge theory’s coupling to a dimension three scalar operator in time. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of motion subject to these boundary conditions. We compute the characteristic time scale of many thermalization processes, noting that in every case we examine, this time scale is determined by the imaginary part of the lowest lying quasi-normal mode of the final state black brane. We quantify the dependence of this final state on parameters of the quench, and construct a dynamical phase diagram. Further support for a universal scaling regime in the abrupt quench limit is provided.

### Tidal deformation of a slowly rotating material body. I. External metric

We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric-tracefree tidal moments E_{ab} and B_{ab}, and the body is characterized by its mass M, its radius R, and a dimensionless angular-momentum vector \chi^a << 1. The perturbation accounts for all couplings between \chi^a and the tidal moments. The body’s gravitational response to the applied tidal field is measured in part by the familiar gravitational Love numbers K^{el}_2 and K^{mag}_2, but we find that the coupling between the body’s rotation and the tidal environment requires the introduction of four new quantities, which we designate as rotational-tidal Love numbers. All these Love numbers are gauge invariant in the usual sense of perturbation theory, and all vanish when the body is a black hole.

### Black Strings in Gauss-Bonnet Theory are Unstable [Cross-Listing]

We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<\alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $\alpha$ is the Gauss-Bonnet coupling.

### Black Strings in Gauss-Bonnet Theory are Unstable

We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<\alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $\alpha$ is the Gauss-Bonnet coupling.

### Black Strings in Gauss-Bonnet Theory are Unstable [Replacement]

We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<\alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $\alpha$ is the Gauss-Bonnet coupling.

### Black Strings in Gauss-Bonnet Theory are Unstable [Replacement]

We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<\alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $\alpha$ is the Gauss-Bonnet coupling.

### Parity violating effects in an exotic perturbation of the rigid rotator [Cross-Listing]

The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.

### Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order [Cross-Listing]

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We here furnish construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.

### Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We here furnish construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.

### Long-lived Light Mediator to Dark Matter and Primordial Small Scale Spectrum [Cross-Listing]

We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. As a result, the population of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.

### Long-lived Light Mediator to Dark Matter and Primordial Small Scale Spectrum

We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. As a result, the population of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.

### Extended theory of the Taylor problem in the plasmoid-unstable regime [Replacement]

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.

### Extended theory of the Taylor problem in the plasmoid-unstable regime [Cross-Listing]

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.

### On the breakdown of the curvature perturbation $\zeta$ during reheating [Cross-Listing]

It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. In the linearized theory, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

### On the breakdown of the curvature perturbation $\zeta$ during reheating [Cross-Listing]

It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. In the linearized theory, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

### On the breakdown of the curvature perturbation \zeta\ during reheating [Replacement]

It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

### On the breakdown of the curvature perturbation \zeta\ during reheating [Replacement]

It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

### On the breakdown of the curvature perturbation ζ during reheating [Replacement]

It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

### Propagation and dispersion of sausage wave trains in magnetic flux tubes

A localized perturbation of a magnetic flux tube produces a pair of wave trains that propagate in opposite directions along the tube. These wave packets disperse as they propagate, where the extent of dispersion depends on the physical properties of the magnetic structure, on the length of the initial excitation, and on its nature (e.g., transverse or axisymmetric). In Oliver et al. (2014) we considered a transverse initial perturbation, whereas the temporal evolution of an axisymmetric one is examined here. In both papers we use a method based on Fourier integrals to solve the initial value problem. Previous studies on wave propagation in magnetic wave guides have emphasized that the wave train dispersion is influenced by the particular dependence of the group velocity on the longitudinal wavenumber. Here we also find that long initial perturbations result in low amplitude wave packets and that large values of the magnetic tube to environment density ratio yield longer wave trains. To test the detectability of propagating transverse or axisymmetric wave packets in magnetic tubes of the solar atmosphere (e.g., coronal loops, spicules, or prominence threads) a forward modelling of the perturbations must be carried out. This is left for a future work.

### Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the $<\sigma (\mathbf {r})\sigma(0)>$, $<\sigma (\mathbf {r})\epsilon(0)>$ and $<\epsilon (\mathbf {r})\epsilon(0)>$ correlators from which we extract the values of $C^{\sigma}_{\sigma\epsilon}=1.07(3)$ and $C^{\epsilon}_{\epsilon\epsilon}=1.45(30)$. Our estimate for $C^{\sigma}_{\sigma\epsilon}$ agrees with those recently obtained using conformal bootstrap methods, while $C^{\epsilon}_{\epsilon\epsilon}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

### Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators [Replacement]

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the $<\sigma (\mathbf {r})\sigma(0)>$, $<\sigma (\mathbf {r})\epsilon(0)>$ and $<\epsilon (\mathbf {r})\epsilon(0)>$ correlators from which we extract the values of $C^{\sigma}_{\sigma\epsilon}=1.07(3)$ and $C^{\epsilon}_{\epsilon\epsilon}=1.45(30)$. Our estimate for $C^{\sigma}_{\sigma\epsilon}$ agrees with those recently obtained using conformal bootstrap methods, while $C^{\epsilon}_{\epsilon\epsilon}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

### Black Hole Instabilities and Exponential Growth

Recently, a general analysis has been given of the stability with respect to axisymmetric perturbations of stationary-axisymmetric black holes and black branes in vacuum general relativity in arbitrary dimensions. It was shown that positivity of canonical energy on an appropriate space of perturbations is necessary and sufficient for stability. However, the notions of both "stability" and "instability" in this result are significantly weaker than one would like to obtain. In this paper, we prove that if a perturbation of the form $\pounds_t \delta g$—with $\delta g$ a solution to the linearized Einstein equation—has negative canonical energy, then that perturbation must, in fact, grow exponentially in time. The key idea is to make use of the $t$- or ($t$-$\phi$)-reflection isometry, $i$, of the background spacetime and decompose the initial data for perturbations into their odd and even parts under $i$. We then write the canonical energy as $\mathscr E\ = \mathscr K + \mathscr U$, where $\mathscr K$ and $\mathscr U$, respectively, denote the canonical energy of the odd part (kinetic energy) and even part (potential energy). One of the main results of this paper is the proof that $\mathscr K$ is positive definite for any black hole background. We use $\mathscr K$ to construct a Hilbert space $\mathscr H$ on which time evolution is given in terms of a self-adjoint operator $\tilde {\mathcal A}$, whose spectrum includes negative values if and only if $\mathscr U$ fails to be positive. Negative spectrum of $\tilde{\mathcal A}$ implies exponential growth of the perturbations in $\mathscr H$ that have nontrivial projection into the negative spectral subspace. This includes all perturbations of the form $\pounds_t \delta g$ with negative canonical energy. A "Rayleigh-Ritz" type of variational principle is derived, which can be used to obtain lower bounds on the rate of exponential growth.

### Black Hole Instabilities and Exponential Growth [Cross-Listing]

Recently, a general analysis has been given of the stability with respect to axisymmetric perturbations of stationary-axisymmetric black holes and black branes in vacuum general relativity in arbitrary dimensions. It was shown that positivity of canonical energy on an appropriate space of perturbations is necessary and sufficient for stability. However, the notions of both "stability" and "instability" in this result are significantly weaker than one would like to obtain. In this paper, we prove that if a perturbation of the form $\pounds_t \delta g$—with $\delta g$ a solution to the linearized Einstein equation—has negative canonical energy, then that perturbation must, in fact, grow exponentially in time. The key idea is to make use of the $t$- or ($t$-$\phi$)-reflection isometry, $i$, of the background spacetime and decompose the initial data for perturbations into their odd and even parts under $i$. We then write the canonical energy as $\mathscr E\ = \mathscr K + \mathscr U$, where $\mathscr K$ and $\mathscr U$, respectively, denote the canonical energy of the odd part (kinetic energy) and even part (potential energy). One of the main results of this paper is the proof that $\mathscr K$ is positive definite for any black hole background. We use $\mathscr K$ to construct a Hilbert space $\mathscr H$ on which time evolution is given in terms of a self-adjoint operator $\tilde {\mathcal A}$, whose spectrum includes negative values if and only if $\mathscr U$ fails to be positive. Negative spectrum of $\tilde{\mathcal A}$ implies exponential growth of the perturbations in $\mathscr H$ that have nontrivial projection into the negative spectral subspace. This includes all perturbations of the form $\pounds_t \delta g$ with negative canonical energy. A "Rayleigh-Ritz" type of variational principle is derived, which can be used to obtain lower bounds on the rate of exponential growth.

### Effective Field Theory of non-Attractor Inflation [Cross-Listing]

We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter \eta. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.

### Effective Field Theory of non-Attractor Inflation

We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter \eta. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.

### NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD [Replacement]

We determine the next-to-leading order dispersion laws for slow-moving quarks in hard-thermal-loop perturbation of high-temperature QCD where weak coupling is assumed. Real-time formalism is used. The next-to-leading order quark self-energy is written in terms of three and four HTL-dressed vertex functions. The hard thermal loops contributing to these vertex functions are calculated ab initio and expressed using the Feynman parametrization which allows the calculation of the solid-angle integrals involved. We use a prototype of the resulting integrals to indicate how finite results are obtained in the limit of vanishing regularizer.

### NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD

We determine the next-to-leading order dispersion laws for slow-moving quarks in hard-thermal-loop perturbation of high-temperature QCD where weak coupling is assumed. Real-time formalism is used. The next-to-leading order quark self-energy is written in terms of three and four HTL-dressed vertex functions. The hard thermal loops contributing to these vertex functions are calculated ab initio and expressed using the Feynman parametrization which allows the calculation of the solid-angle integrals involved. We use a prototype of the resulting integrals to indicate how finite results are obtained in the limit of vanishing regularizer.

### Gravitational perturbation induced by a rotating ring around a Kerr black hole [Cross-Listing]

The linear perturbation of a Kerr black hole induced by a rotating massive circular ring is discussed by using the formalism by Teukolsky, Chrzanowski, Cohen and Kegeles. In these formalism, the perturbed Weyl scalars, $\psi_0$ and $\psi_4$, are first obtained from the Teukolsky equation. The perturbed metric is obtained in a radiation gauge via the Hertz potential. The computation can be done in the same way as in our previous paper, in which we considered the perturbation of a Schwarzschild black hole induced by a rotating ring. By adding lower multipole modes such as mass and angular momentum perturbation which are not computed by the Teukolsky equation, and by appropriately setting the parameters which are related to the gauge freedom, we obtain the perturbed gravitational field which is smooth except on the equatorial plane outside the ring.

### Gravitational perturbation induced by a rotating ring around a Kerr black hole

The linear perturbation of a Kerr black hole induced by a rotating massive circular ring is discussed by using the formalism by Teukolsky, Chrzanowski, Cohen and Kegeles. In these formalism, the perturbed Weyl scalars, $\psi_0$ and $\psi_4$, are first obtained from the Teukolsky equation. The perturbed metric is obtained in a radiation gauge via the Hertz potential. The computation can be done in the same way as in our previous paper, in which we considered the perturbation of a Schwarzschild black hole induced by a rotating ring. By adding lower multipole modes such as mass and angular momentum perturbation which are not computed by the Teukolsky equation, and by appropriately setting the parameters which are related to the gauge freedom, we obtain the perturbed gravitational field which is smooth except on the equatorial plane outside the ring.

### Deriving super-horizon curvature perturbations from the dynamics of preheating

We present a framework for calculating super-horizon curvature perturbation from the dynamics of preheating, which gives a reasonable match to the lattice results. Hubble patches with different initial background field values evolve differently. From the bifurcation of their evolution trajectories we find curvature perturbation using Lyapunov theorem and $\delta N$ formulation. In this way we have established a connection between the finer dynamics of preheating and the curvature perturbation produced in this era. From the calculated analytical form of the curvature perturbation we have derived the effective super-horizon curvature perturbation smoothed out on large scales of CMB. The order of the amount of local form non-gaussianity generated in this process has been calculated and problems regarding the precise determination of it have been pointed out.

### Confinement and stability in presence of scalar fields and perturbation in the bulk [Cross-Listing]

In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behaviour of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed condition.

### Confinement and stability in presence of scalar fields and perturbation in the bulk

In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behaviour of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed condition.

### Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

Hartle’s model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in General Relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function $m_0$ (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.

### Hartle's model within the general theory of perturbative matchings: the change in mass

Hartle’s model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged.

### Scalar Perturbation Produced at the Pre-inflationary Stage in Eddington-inspired Born-Infeld Gravity

We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born-Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low $k$-modes. The tensor-to-scalar ratio can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of the gravitational wave radiation between PLANCK and BICEP2.

### Scalar Perturbation Produced at the Pre-inflationary Stage in Eddington-inspired Born-Infeld Gravity [Cross-Listing]

We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born-Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low $k$-modes. The tensor-to-scalar ratio can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of the gravitational wave radiation between PLANCK and BICEP2.

### Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings [Cross-Listing]

In this paper we develop a completely gauge and tetrad invariant perturbation approach to deal with the gravitoelectromagnetic fluctuations of rotating charged black strings. The associated background metric tensor and gauge field represent an exact four-dimensional solution of Einstein-Maxwell equations with a negative cosmological constant and a non-trivial spacetime topology. As usual, for any charged black hole, a perturbation in the background electromagnetic field induces a metric perturbation and vice versa. In spite of this coupling and the non-vanishing angular momentum, we show that, in the Newman-Penrose formalism, and in the presence of sources, the linearization of the field equations leads to a pair of second-order complex equations for suitable combinations of the spin coefficients, the Weyl and the Maxwell scalars. Then, we generalize the Chandrasekhar transformation theory by the inclusion of source terms and apply it to reduce the perturbation problem to four decoupled inhomogeneous wave equations — a pair for each sector of perturbations. The radial part of such wave equations can be put into Schrodinger-like forms after Fourier transforming them with respect to time. We find that the resulting effective potentials form two pairs of supersymmetric partner potentials and, as a consequence, the fundamental variables of one perturbation sector are related to the variables of the other sector.