Posts Tagged perturbation

Recent Postings from perturbation

Disformal transformation of cosmological perturbations

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

Disformal transformation of cosmological perturbations [Cross-Listing]

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

Gravitational Collapse of Inhomogenous Perfect Fluid

We study the complete gravitational collapse of a class of inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models can lead to the formation of a naked singularity as the final state.

Temperature fluctuations in an inhomogeneous diffusive fluid

We discuss metric perturbations of the relativistic diffusion equation around the homogeneous Juttner equilibrium of massless particles in a homogeneous expanding universe. The metric perturbation describes matter distribution and the gravitational wave background in an inhomogeneous universe. We show that the lowest order perturbation can be treated as a variation of temperature. We derive a formula expressing temperature fluctuations in terms of the diffusion and tensor power spectrum. We discuss the multipole expansion of the fluctuations in the presence of diffusion.

Scalar perturbation in warm tachyon inflation in LQC in light of Plank and BICEP2 [Cross-Listing]

We study warm-tachyon inflationary universe model in the context of the effective field theory of loop quantum cosmology. In slow-roll approximation the primordial perturbation spectrums for this model are calculated. We also obtain the general expressions of the tensor-to-scalar ratio, scalar spectral index. We develop this model by using exponential potential, the characteristics of this model is calculated in great details. The parameters of the model are restricted by recent observational data from Planck, WMAP9 and BICEP2.

Dynamical evolution of the electromagnetic perturbation coupling to Einstein tensor

We have investigated the wave dynamics of an electromagnetic perturbation coupling to Einstein tensor in the four-dimensional Reissner-Nordstr\"{o}m black hole spacetime. Our results show that besides the dependence on the coupling between electromagnetic field and Einstein tensor, the wave dynamic equation of the perturbation strongly depends on the parity of the electromagnetic field itself, which is quite different from that of the usual electromagnetic perturbation without the coupling in the four-dimensional spacetime. Moreover, we also find that the electromagnetic perturbation with odd parity grows with exponential rate and the instability happens if the coupling strength is stronger than certain a critical value. However, the electromagnetic perturbation with even parity always decays in the Reissner-Nordstr\"{o}m black hole spacetime.

Perturbations to $\mu-\tau$ Symmetry, Leptogenesis and Lepton Flavour Violation with Type II Seesaw

We study the possibility of generating non-zero reactor mixing angle $\theta_{13}$ by perturbing the $\mu-\tau$ symmetric neutrino mass matrix. The leading order $\mu-\tau$ symmetric neutrino mass matrix originates from type I seesaw mechanism whereas the perturbations to $\mu-\tau$ symmetry originate from type II seesaw term. We consider four different realizations of $\mu-\tau$ symmetry: Bimaximal Mixing(BM), Tri-bimaximal Mixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) all giving rise to $\theta_{13} = 0, \theta_{23} = \frac{\pi}{4}$ but different non-zero values of solar mixing angle $\theta_{12}$. We assume a minimal $\mu-\tau$ symmetry breaking type II seesaw mass matrix as a perturbation and calculate the neutrino oscillation parameters as a function of type II seesaw strength. We then consider the origin of non-trivial leptonic CP phase in the charged lepton sector and calculate the lepton asymmetry arising from the lightest right handed neutrino decay by incorporating the presence of both type I and type II seesaw. We constrain the type II seesaw strength as well as leptonic CP phase (and hence the charged lepton sector) by comparing our results with experimental neutrino oscillation parameters as well as Planck bound on baryon to photon ratio. Finally, we extend our analysis on lepton flavour violating decays like $\mu \to e \gamma$ and $\mu \to eee$ due to exchange of TeV scale Higgs triplet scalar within the low scale type II seesaw framework. The branching ratios for these lepton flavour processes are examined with the small type II perturbation term $\omega$ and the estimated values are very close to the experimental bound coming from current search experiments.

Tensor-to-Scalar Ratio in Eddington-inspired Born-Infeld Inflation

We investigate the scalar perturbation of the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. We focus on the perturbation at the attractor stage in which the first and the second slow-roll conditions are satisfied. The scalar perturbation exhibits the corrections to the chaotic inflation model in general relativity. We find that the tensor-to-scalar ratio becomes smaller than that of the usual chaotic inflation.

Tensor-to-Scalar Ratio in Eddington-inspired Born-Infeld Inflation [Cross-Listing]

We investigate the scalar perturbation of the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. We focus on the perturbation at the attractor stage in which the first and the second slow-roll conditions are satisfied. The scalar perturbation exhibits the corrections to the chaotic inflation model in general relativity. We find that the tensor-to-scalar ratio becomes smaller than that of the usual chaotic inflation.

Axial gravitational perturbations of an infinite static line source

In this paper we study axial gravitational perturbations of an infinite static line source, represented by a form of the Levi-Civita metric. The perturbations are restricted to axial symmetry but break the cylindrical symmetry of the background metric. We analyze the gauge issues that arise in setting up the appropriate form of the perturbed metric and show that it is possible to restrict to diagonal terms, but that this does not fix the gauge completely. We derive the perturbation equations and show that they can be solved by solving a third order ordinary differential equation for an appropriately chosen function of the perturbed metric coefficients. The set of solutions of this equation contains gauge trivial parts, and we show how to extract the gauge non trivial components. We introduce appropriate boundary conditions on the solutions and show that these lead to a boundary value problem that determines the allowed functional forms of the perturbation modes. The associated eigenvalues determine a sort of "dispersion relation" for the frequencies and corresponding "wave vector" components. The central result of this analysis is that the spectrum of allowed frequencies contains one unstable (imaginary frequency) mode for every possible choice of the background metric. The completeness of the mode expansion in relation to the initial value problem and to the gauge problem is discussed in detail, and we show that the perturbations contain an unstable component for generic initial data, and, therefore, that the Levi-Civita space times are gravitationally unstable. We also include, for completeness, a set of approximate eigenvalues, and examples of the functional form of the solutions.

Higher derivatives and power spectrum in effective single field inflation [Cross-Listing]

We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from applying higher order derivative operators of the effective theory expansion with respect to the mass scale of the heavy modes. We find that the correction terms are suppressed by the ratio of the Hubble parameter to the heavy mass scale. The corresponding corrections to the power spectrum of the curvature perturbation are presented for a simple illustrative example.

Higher derivatives and power spectrum in effective single field inflation [Cross-Listing]

We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from applying higher order derivative operators of the effective theory expansion with respect to the mass scale of the heavy modes. We find that the correction terms are suppressed by the ratio of the Hubble parameter to the heavy mass scale. The corresponding corrections to the power spectrum of the curvature perturbation are presented for a simple illustrative example.

Higher derivatives and power spectrum in effective single field inflation

We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from applying higher order derivative operators of the effective theory expansion with respect to the mass scale of the heavy modes. We find that the correction terms are suppressed by the ratio of the Hubble parameter to the heavy mass scale. The corresponding corrections to the power spectrum of the curvature perturbation are presented for a simple illustrative example.

On the thermal sensitivity of binary formation in collapsing molecular clouds

We report the results of a numerical study on the initial formation stages of low-mass protostellar binary systems. We determine the separation of protostellar binaries formed as a function of the initial thermal state by varying the initial temperature in a slightly modified version of the Burkert and Bodenheimer collapse test. We find that the outcome is highly sensitive to both the initial temperature of the cloud and the initial amplitude of azimuthal density perturbation A. For A=10 %, variations of only 1 unit Kelvin below 10 K lead to changes of up to 100 AU ( i.e. of order 30 %) in the instantaneous separation, whereas for this small A the initial temperatures above 10 K yield, instead of a binary, a single low-mass fragment that never reaches protostellar densities. Protostellar binaries, however, do emerge when the perturbation amplitude is increased from 10 % to 25 %. We also investigate the impact of the critical density which governs the transition from isothermal to adiabatic thermodynamic behaviour of the collapsing gas. We find that the critical density not only affects the overall structural evolution of the gas envelope, but also the size of the rotating disk structures formed during collapse as well as the number of protostellar fragments resulting from the final fragmentation of the disks. This mechanism can give rise to young protostellar objects constituting bound multiple stellar systems.

Entropy of conformal perturbation defects

We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.

Testable constraint on near-tribimaximal neutrino mixing

General lowest order perturbations to hermitian squared mass matrices of leptons are considered away from the tribimaximal (TBM) limit in which a weak flavor basis with mass diagonal charged leptons is chosen. The three measurable TBM-deviants are expressed linearly in terms of perturbation induced dimensionless coefficients appearing in the charged lepton and neutrino flavor eigenstates. With unnatural cancellations assumed to be absent and the charged lepton perturbation contributions to their flavor eigenstates argued to be small, we analytically derive that a deviation from maximal atmospheric neutrino mixing and CP violation in neutrino oscillations cannot both be observably large, posing the challenge of verification to forthcoming experiments at the intensity frontier.

Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the total entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.

Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario [Cross-Listing]

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the total entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.

Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario [Cross-Listing]

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the total entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.

Comparison of two approximation schemes for solving perturbations in a LTB cosmological model

Recently, the present authors studied perturbations in the Lemaitre-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaitre-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaitre-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we investigate differences between these two approaches. It is shown that, in general, these two approaches are not compatible with each other. That is, in our perturbative procedure, the Clarkson-Clifton-February assumption is not valid at the order of our interest.

A Nonminimal Coupling Model and its Short-Range Solar System Impact

The objective of this work is to present the effects of a nonminimally coupled model of gravity on a Solar System short range regime. For this reason, this study is only valid when the cosmological contribution is considered irrelevant. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$, where the last one multiplies the matter Lagrangian. Using a Taylor expansion around $R=0$ for both functions $f^1(R)$ and $f^2(R)$, it was found that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric. The $tt$ component of the metric, a Newtonian plus a Yukawa perturbation term, is constrained using the available observational results. First it is shown that this effect is null when the characteristic mass scales of each function $f^1(R)$ and $f^2(R)$ are identical. Besides, the conclusion is that the nonminimal coupling only affects the Yukawa contribution strength and not its range and that the Starobinsky model for inflation is not experimentally constrained. Moreover, the geodetic precession effect, obtained also from the radial perturbation of the metric, reveals to be of no relevance for the constraints.

Acoustic geometry through perturbation of mass accretion rate - axisymmetric flow in static spacetimes [Replacement]

This is the second of our series of papers devoted to the study of the stability analysis of the stationary transonic integral solutions for accretion flow onto a static compact object, using the acoustic geometry. Precisely, we consider accretion of an axisymmetric, inviscid and irrotational fluid in a general static axisymmetric spacetime and study the perturbation of the mass accretion rate, and demonstrate the natural emergence of the general relativistic acoustic geometry. In other words, the astrophysical accretion process has a natural interpretation as an example of the acoustic analogue gravity phenomenon. We also discuss two explicit examples of the Schwarzschild and the Rindler spacetimes. For the later, in particular, we demonstrate that for smooth flow fileds there can be no sonic point.

Acoustic geometry through perturbation of accretion rate : II - radial flow in stationary axisymmetric spacetime

We introduce a novel perturbation scheme to study the stability properties of the stationary transonic integral solutions for low angular momentum axisymmetric accretion flow in a general stationary axisymmetric space time around non rotating black holes for generalized geometric configuration of infalling matter. We discuss the emergence of the relativistic acoustic geometry as a consequence of such stability analysis and establish the fact that the space time structure of such acoustic geometry is independent of the matter geometry as well as the perturbation scheme. The acoustic metric elements obtained by perturbing the velocity potential of the background fluid flow remains the same as of that obtained by perturbing the mass accretion rate.

Acoustic geometry through perturbation of mass accretion rate - axisymmetric flow in static spacetimes [Replacement]

This is the second of our series of papers devoted to the study of the stability analysis of the stationary transonic integral solutions for accretion flow onto a static compact object, using the acoustic geometry. Precisely, we consider accretion of an axisymmetric, inviscid and irrotational fluid in a general static axisymmetric spacetime and study the perturbation of the mass accretion rate, and demonstrate the natural emergence of the general relativistic acoustic geometry. In other words, the astrophysical accretion process has a natural interpretation as an example of the acoustic analogue gravity phenomenon. We also discuss two explicit examples of the Schwarzschild and the Rindler spacetimes. For the later, in particular, we demonstrate that for smooth flow fileds there can be no sonic point.

Near Horizon Extremal Geometry Perturbations: Dynamical Field Perturbations vs. Parametric Variations

In arXiv:1310.2737 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed by the linearized equations of motion and symmetry conditions which we carefully specify, satisfy the EPL. We also show that these perturbations are limited to those coming from difference of two NHEG solutions (i.e. variations on the NHEG solution parameter space). Our analysis and discussions shed light on the "no-dynamics" statements of arXiv:0906.2380 and arXiv:0906.2376.

Acoustic geometry through perturbation of accretion rate : I - radial flow in static spacetime

We propose a novel perturbation scheme to perform the linear stability analysis of stationary transonic integral accretion solutions corresponding to the hydrodynamic non self-gravitating spherically symmetric flow of matter in a generalized static black hole spacetime. We demonstrate that a metric independent perturbation scheme, which also does not depend on the mode of perturbation, can be developed, which, not only ensures the stability of the aforementioned stationary solutions, it rather leads to the emergence of a relativistic acoustic geometry represented by a pseudo-Riemannian curved manifold as well. The acoustic metric and the corresponding line elements remains the same irrespective of whether they are obtained by perturbing the velocity potential or the mass accretion rate. This conclusion holds, as we will show in our forthcoming papers, for axisymmetric flow in any arbitrary black hole metric as well.

Acoustic geometry through perturbation of mass accretion rate : I - radial flow in general static spacetime [Replacement]

We propose a novel perturbation scheme to perform the linear stability analysis of stationary transonic integral accretion solutions corresponding to the hydrodynamic non self-gravitating radial flow of matter in a general static black hole spacetime. We demonstrate that a metric independent perturbation scheme can be developed, which leads to the emergence of the relativistic acoustic geometry and ensures the stability of the background stationary solutions. The acoustic metric obtained by perturbing the mass accretion rate rate is found to be identical with that obtained through the perturbation of the velocity potential. Our work thus makes a crucial connection between two apparently disjoint fields of study – accretion astrophysics and analogue gravity phenomena. We also formally prove that acoustic horizons never form in the Rindler spacetime.

Acoustic geometry through perturbation of mass accretion rate : I - radial flow in general static spacetime [Replacement]

We propose a novel perturbation scheme to perform the linear stability analysis of stationary transonic integral accretion solutions corresponding to the hydrodynamic non self-gravitating radial flow of matter in a general static black hole spacetime. We demonstrate that a metric independent perturbation scheme can be developed, which leads to the emergence of the relativistic acoustic geometry and ensures the stability of the background stationary solutions. The acoustic metric obtained by perturbing the mass accretion rate rate is found to be identical with that obtained through the perturbation of the velocity potential. Our work thus makes a crucial connection between two apparently disjoint fields of study – accretion astrophysics and analogue gravity phenomena. We also formally prove that acoustic horizons never form in the Rindler spacetime.

On the realizability of relativistic acoustic geometry under a generalized perturbation scheme for axisymmetric matter flow onto black holes [Replacement]

We propose a novel linear perturbation scheme to study the stability properties of the stationary transonic integral solutions for axisymmetric matter flow around astrophysical black holes for the Schwarzschild as well as for rotating Rindler space time. We discuss the emergence of the relativistic acoustic geometry as a consequence of such stability analysis. Our work thus makes a crucial connection between two apparently non-overlapping fields of research – the accretion astrophysics and the analogue gravity phenomena.

On the realizability of relativistic acoustic geometry under a generalized perturbation scheme for axisymmetric matter flow onto black holes [Replacement]

We propose a novel linear perturbation scheme to study the stability properties of the stationary transonic integral solutions for axisymmetric matter flow around astrophysical black holes for the Schwarzschild as well as for rotating Rindler space time. We discuss the emergence of the relativistic acoustic geometry as a consequence of such stability analysis. Our work thus makes a crucial connection between two apparently non-overlapping fields of research – the accretion astrophysics and the analogue gravity phenomena.

On the realizability of relativistic acoustic geometry under a generalized perturbation scheme for axi-symmetric matter flow onto black holes

We propose a novel linear perturbation scheme to study the stability properties of the stationary transonic integral solutions for axisymmetric matter flow around astrophysical black holes for the Schwarzschild as well as for rotating Rindler space time. We discuss the emergence of the relativistic acoustic geometry as a consequence of such stability analysis. Our work thus makes a crucial connection between two apparently non-overlapping fields of research – the accretion astrophysics and the analogue gravity phenomena.

Calculating the mass spectrum of primordial black holes [Cross-Listing]

We reinspect the calculation for the mass fraction of primordial black holes (PBHs) which are formed from primordial perturbations, finding that performing the calculation using the comoving curvature perturbation $\mathcal{R}_{c}$ in the standard way vastly overestimates the number of PBHs, by many orders of magnitude. This is because PBHs form shortly after horizon entry, meaning modes significantly larger than the PBH are unobservable and should not affect whether a PBH forms or not – this important effect is not taken into account by smoothing the distribution in the standard fashion. We discuss alternative methods and argue that the density contrast, $\Delta$, should be used instead as super-horizon modes are damped by a factor $k^{2}$. We make a comparison between using a Press-Schechter approach and peaks theory, finding that the two are in close agreement in the region of interest. We also investigate the effect of varying the spectral index, and the running of the spectral index, on the abundance of primordial black holes.

Calculating the mass spectrum of primordial black holes [Replacement]

We reinspect the calculation for the mass fraction of primordial black holes (PBHs) which are formed from primordial perturbations, finding that performing the calculation using the comoving curvature perturbation $\mathcal{R}_{c}$ in the standard way vastly overestimates the number of PBHs, by many orders of magnitude. This is because PBHs form shortly after horizon entry, meaning modes significantly larger than the PBH are unobservable and should not affect whether a PBH forms or not – this important effect is not taken into account by smoothing the distribution in the standard fashion. We discuss alternative methods and argue that the density contrast, $\Delta$, should be used instead as super-horizon modes are damped by a factor $k^{2}$. We make a comparison between using a Press-Schechter approach and peaks theory, finding that the two are in close agreement in the region of interest. We also investigate the effect of varying the spectral index, and the running of the spectral index, on the abundance of primordial black holes.

Calculating the mass spectrum of primordial black holes [Replacement]

We reinspect the calculation for the mass fraction of primordial black holes (PBHs) which are formed from primordial perturbations, finding that performing the calculation using the comoving curvature perturbation $\mathcal{R}_{c}$ in the standard way vastly overestimates the number of PBHs, by many orders of magnitude. This is because PBHs form shortly after horizon entry, meaning modes significantly larger than the PBH are unobservable and should not affect whether a PBH forms or not – this important effect is not taken into account by smoothing the distribution in the standard fashion. We discuss alternative methods and argue that the density contrast, $\Delta$, should be used instead as super-horizon modes are damped by a factor $k^{2}$. We make a comparison between using a Press-Schechter approach and peaks theory, finding that the two are in close agreement in the region of interest. We also investigate the effect of varying the spectral index, and the running of the spectral index, on the abundance of primordial black holes.

Stability analysis of (a class of) anisotropic spacetimes [Replacement]

We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We apply our results to three diverse examples. Two examples arise as endpoints of collapse of a ball of fluid — one describes a well-behaved stellar interior and the other has a naked singularity. We prove the stability of the stellar interior both with respect to Dirichlet and quasinormal mode boundary conditions on the perturbation. Surprisingly, the naked singularity is also stable under axial perturbations. Lastly, we take the example of anisotropic cosmology to show that in this case, the relevant perturbations are those in which the direction of anisotropy is also perturbed.

Stability analysis of (a class of) anisotropic spacetimes [Cross-Listing]

We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We apply our results to three diverse examples. Two examples arise as endpoints of collapse of a ball of fluid — one describes a well-behaved stellar interior and the other has a naked singularity. We prove the stability of the stellar interior both with respect to Dirichlet and quasinormal mode boundary conditions on the perturbation. Surprisingly, the naked singularity is also stable under axial perturbations. Lastly, we take the example of anisotropic cosmology to show that in this case, the relevant perturbations are those in which the direction of anisotropy is also perturbed.

Stability analysis of (a class of) anisotropic spacetimes [Replacement]

We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We apply our results to three diverse examples. Two examples arise as endpoints of collapse of a ball of fluid — one describes a well-behaved stellar interior and the other has a naked singularity. We prove the stability of the stellar interior both with respect to Dirichlet and quasinormal mode boundary conditions on the perturbation. Surprisingly, the naked singularity is also stable under axial perturbations. Lastly, we take the example of anisotropic cosmology to show that in this case, the relevant perturbations are those in which the direction of anisotropy is also perturbed.

Reanalyzing the upper limit on the tensor-to-scalar perturbation ratio r_T in a quartic potential inflationary model

We study the polynomial chaotic inflation model with a single scalar field in a double well quartic potential which has recently been shown to be consistent with Planck data. In particular, we study the effects of lifting the degeneracy the between two vacua on the inflationary observables, i.e. spectral index and tensor-to-scalar perturbation ratio r_T. We find that removing the degeneracy allows the model to satisfy the upper limit constraints on r_T from Planck data. We also calculate the scalar power spectrum and non-Gaussianity parameter f_{NL} for the primordial scalar perturbations in this model.

Reanalyzing the upper limit on the tensor-to-scalar perturbation ratio r_T in a quartic potential inflationary model [Replacement]

We study the polynomial chaotic inflation model with a single scalar field in a double well quartic potential which has recently been shown to be consistent with Planck data. In particular, we study the effects of lifting the degeneracy the between two vacua on the inflationary observables, i.e. spectral index and tensor-to-scalar perturbation ratio r_T. We find that removing the degeneracy allows the model to satisfy the upper limit constraints on r_T from Planck data. We also calculate the scalar power spectrum and non-Gaussianity parameter f_NL for the primordial scalar perturbations in this model.

Reanalyzing the upper limit on the tensor-to-scalar perturbation ratio r_T in a quartic potential inflationary model [Replacement]

We study the polynomial chaotic inflation model with a single scalar field in a double well quartic potential which has recently been shown to be consistent with Planck data. In particular, we study the effects of lifting the degeneracy between the two vacua on the inflationary observables, i.e. spectral index n_s and tensor-to-scalar perturbation ratio r_T. We find that removing the degeneracy allows the model to satisfy the upper limit constraints on r_T from Planck data, provided the field starts near the local maximum. We also calculate the scalar power spectrum and non-Gaussianity parameter f_NL for the primordial scalar perturbations in this model.

Relevant Perturbation of Entanglement Entropy and Stationarity [Replacement]

A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is well-defined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in three-dimensions, and find a qualitative agreement between them. We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare symmetry.

Relevant Perturbation of Entanglement Entropy and Stationarity

A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is well-defined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in three-dimensions, and find a qualitative agreement between them. We argue that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare symmetry.

Relevant Perturbation of Entanglement Entropy and Stationarity [Replacement]

A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is well-defined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in three-dimensions, and find a qualitative agreement between them. We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare symmetry.

3D MHD simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field

Previous studies [Malara et al ApJ, 533, 523 (2000)] considered small-amplitude Alfven wave (AW) packets in Arnold-Beltrami-Childress (ABC) magnetic field using WKB approximation. In this work linearly polarised Alfven wave dynamics in ABC magnetic field via direct 3D MHD numerical simulation is studied for the first time. Gaussian AW pulse with length-scale much shorter than ABC domain length and harmonic AW with wavelength equal to ABC domain length are studied for four different resistivities. While it is found that AWs dissipate quickly in the ABC field, surprisingly, AW perturbation energy increases in time. In the case of the harmonic AW perturbation energy growth is transient in time, attaining peaks in both velocity and magnetic perturbation energies within timescales much smaller than resistive time. In the case of the Gaussian AW pulse velocity perturbation energy growth is still transient in time, attaining a peak within few resistive times, while magnetic perturbation energy continues to grow. It is also shown that the total magnetic energy decreases in time and this is governed by the resistive evolution of the background ABC magnetic field rather than AW damping. On contrary, when background magnetic field is uniform, the total magnetic energy decrease is prescribed by AW damping, because there is no resistive evolution of the background. By considering runs with different amplitudes and by analysing perturbation spectra, possible dynamo action by AW perturbation-induced peristaltic flow and inverse cascade of magnetic energy have been excluded. Therefore, the perturbation energy growth is attributed to a new instability. The growth rate appears to be dependent on the value of the resistivity and spatial scale of the AW disturbance. Thus, when going beyond WKB approximation, AW damping, described by full MHD equations, does not guarantee decrease of perturbation energy.

Inflationary Tensor Perturbation in Eddington-inspired Born-Infeld gravity [Cross-Listing]

We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. For long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation.

Inflationary Tensor Perturbation in Eddington-inspired Born-Infeld gravity

We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. For long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation.

Inducing chaos by breaking axial symmetry in a black hole magnetosphere

While the motion of particles near a rotating, electrically neutral (Kerr) and a charged (Kerr-Newman) black hole is always strictly regular, a perturbation to the gravitational or the electromagnetic field generally leads to chaos. Transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consider the presence of a weak, ordered large-scale magnetic field. An axially symmetric model consisting of a rotating black hole embedded in an aligned magnetic field is generalized by allowing an oblique direction of the field having a general inclination with respect to the rotation axis of the system. Inclination of the field acts as an additional perturbation to the motion of charged particles as it breaks the axial symmetry of the system and cancels the related integral of motion. The axial component of angular momentum is no longer conserved and the resulting system thus has three degrees of freedom. Our primary concern within this contribution is to find out how sensitive the system of bound particles is to the inclination of the field. We employ the method of the maximal Lyapunov exponent to distinguish between regular and chaotic orbits and to quantify their chaoticity. We find that even a small misalignment induces chaotic motion.

Inducing chaos by breaking axial symmetry in a black hole magnetosphere [Replacement]

While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr–Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consider the presence of a weak, ordered, large-scale magnetic field. An axially-symmetric model consisting of a rotating black hole embedded in an aligned magnetic field is generalized by allowing an oblique direction of the field having a general inclination, with respect to the rotation axis of the system. The inclination of the field acts as an additional perturbation to the motion of charged particles as it breaks the axial symmetry of the system and cancels the related integral of motion. The axial component of angular momentum is no longer conserved and the resulting system thus has three degrees of freedom. Our primary concern within this contribution is to find out how sensitive the system of bound particles is to the inclination of the field. We employ the method of the maximal Lyapunov exponent to distinguish between regular and chaotic orbits and to quantify their chaoticity. We find that even a small misalignment induces chaotic motion.

New framework for calculating cosmological perturbations in a scenario of dark energy interacting with cold dark matter [Cross-Listing]

Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a new framework to correctly calculate the cosmological perturbations in the interacting dark energy models. Inspired by the well-known parameterized post-Friedmann approach, the condition of the dark energy pressure perturbation is replaced with the relationship between the momentum density of dark energy and that of the other components on large scales. By reconciling the perturbation evolutions on both the large and small scales with the help of the energy-momentum conservation laws, we can complete the perturbation equations system. The large-scale instability can be successful avoided and the well-behaved density and metric perturbations are obtained within this framework. Our test results show that this new framework works very well and is applicable to all the interacting dark energy models.

Parameterized Post-Friedmann Framework for Interacting Dark Energy [Replacement]

Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a new framework to correctly calculate the cosmological perturbations in the interacting dark energy models. Inspired by the well-known parameterized post-Friedmann approach, the condition of the dark energy pressure perturbation is replaced with the relationship between the momentum density of dark energy and that of other components on large scales. By reconciling the perturbation evolutions on the large and small scales, one can complete the perturbation equations system. The large-scale instability can be successfully avoided and the well-behaved density and metric perturbations are obtained within this framework. Our test results show that this new framework works very well and is applicable to all the interacting dark energy models.

 

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