# Posts Tagged perturbation

## Recent Postings from perturbation

### Inclusion of isospin breaking effects in lattice simulations [Cross-Listing]

Isospin symmetry is explicitly broken in the Standard Model by the mass and electric charge of the up and down quarks. These effects represent a perturbation of hadronic amplitudes at the percent level. Although these contributions are small, they play a crucial role in hadronic and nuclear physics. Moreover, as lattice computations are becoming increasingly precise, it is becoming more and more important to include these effects in numerical simulations. We summarize here how to properly define QCD and QED on a finite and discrete space-time so that isospin corrections to hadronic observables can be computed ab-initio and we review the main results on the isospin corrections to the hadron spectrum. We mainly focus on the recent work going beyond the electro-quenched approximation.

### Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

### Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

### Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

### Dark energy and non-linear power spectrum

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

### Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with modified Chaplygin gas model. Different parameters of this scenario for positive and negative values of A are computed. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts for different values of alpha are computed; the results are in relatively good agreement with current observational data.

### Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Cross-Listing]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with modified Chaplygin gas model. Different parameters of this scenario for positive and negative values of A are computed. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts for different values of alpha are computed; the results are in relatively good agreement with current observational data.

### Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Replacement]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.

### Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Replacement]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.

### Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo [Replacement]

We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of "active longitudes" with cyclic 180 degree "flip-flop" changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.

### Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo

We explore a response of the non-linear non-axisymmetric mean-field solar dynamo model to the shallow non-axisymmetric perturbations with the strength of 1G. The amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, the depth of perturbation. It is found that perturbation which is anchored at the 0.9R have a profound effect and it produce the transient magnetic cycle of the axisymmetric magnetic field if it is initiated at the growing phase of the cycle. The non-symmetric about equator perturbation results the hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on how well the magnetic helicity is conserved. In the range of Rm=10^{4-6} the evolution returns to the normal course in the next cycle and the non-axisymmetric field is generated due to non-linear alpha-effect and the magnetic buoyancy. In the stationary state of evolution the large-scale magnetic field demonstrate, the phenomena of the "active longitude" and the cyclic 180 degree flip-flop of the orientation of the large-scale magnetic field. We do not use any assumptions about the non-axisymmetric distribution of the turbulent parameters. The flip-flop effect is demonstrated for the first time in the solar type dynamo model. This effect disappears in the model which includes meridional circulation. The rotation periods of the equatorial dipole evolves from the period of 25.2 days during the relaxation epoch to the period of 27 days at the stationary state of evolution.

### On the coupling of vector fields to the Gauss-Bonnet invariant

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

### On the coupling of vector fields to the Gauss-Bonnet invariant [Cross-Listing]

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

### On the coupling of vector fields to the Gauss-Bonnet invariant [Cross-Listing]

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

### On the coupling of vector fields to the Gauss-Bonnet invariant [Cross-Listing]

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature 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 [Replacement]

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 $\delta_{CP}$.

### 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 [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

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.

### 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

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.

### 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.

### 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.

### 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 [Replacement]

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.

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

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.