# Posts Tagged perturbation

## Recent Postings from perturbation

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

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

### Black Hole Instabilities and Exponential Growth

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

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

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

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

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

### Effective Field Theory of non-Attractor Inflation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

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

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

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

### Unimodular Theory of Gravity and Inflation

We study inflation and its scalar perturbations in the unimodular theory of gravity. When the unimodular parameter is $\xi=6$, the classical picture of inflation such as the slow-roll parameters, the number of $e$-foldings and the scale of the scalar field, can be reproduced in the unimodular theory because it recovers the background equations of the standard theory of general relativity. Considering the scalar perturbation, the unimodular gravity constrains the gauge degree of freedom, but the perturbation equations are similar to those in general relativity. For $\xi \neq 6$, we derived the power spectrum and the spectral index, and obtain the unimodular correction to the tensor-to-scalar ratio. Depending on the value of $\xi$, the correction can either raise or lower the value of the tensor-to-scalar ratio.

### Degeneracy between CCDM and $\Lambda$CDM cosmologies [Cross-Listing]

The creation of cold dark matter cosmology model is studied beyond the linear perturbation level. The skewness is explicitly computed and the results are compared to those from the $\Lambda$CDM model. It is explicitly shown that both models have the same signature for the skewness and cannot be distinguished by using this observable.

### Degeneracy between CCDM and $\Lambda$CDM cosmologies [Cross-Listing]

The creation of cold dark matter cosmology model is studied beyond the linear perturbation level. The skewness is explicitly computed and the results are compared to those from the $\Lambda$CDM model. It is explicitly shown that both models have the same signature for the skewness and cannot be distinguished by using this observable.

### Degeneracy between CCDM and $\Lambda$CDM cosmologies

The creation of cold dark matter cosmology model is studied beyond the linear perturbation level. The skewness is explicitly computed and the results are compared to those from the $\Lambda$CDM model. It is explicitly shown that both models have the same signature for the skewness and cannot be distinguished by using this observable.

### RSOS Quantum Chains Associated with Off-Critical Minimal Models and $\mathbb{Z}_n$ Parafermions

We consider the $\varphi_{1,3}$ off-critical perturbation ${\cal M}(m,m’;t)$ of the general non-unitary minimal models where $2\le m\le m’$ and $m, m’$ are coprime and $t$ measures the departure from criticality corresponding to the $\varphi_{1,3}$ integrable perturbation. We view these models as the continuum scaling limit in the ferromagnetic Regime III of the Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice. We also consider the RSOS models in the antiferromagnetic Regime II related in the continuum scaling limit to $\mathbb{Z}_n$ parfermions with $n=m’-2$. Using an elliptic Yang-Baxter algebra of planar tiles encoding the allowed face configurations, we obtain the Hamiltonians of the associated quantum chains defined as the logarithmic derivative of the transfer matrices with periodic boundary conditions. The transfer matrices and Hamiltonians act on a vector space of paths on the $A_{m’-1}$ Dynkin diagram whose dimension is counted by generalized Fibonacci numbers.

### Constraining the growth of perturbations with lensing of supernovae

A recently proposed technique allows one to constrain both the background and perturbation cosmological parameters through the distribution function of supernova Ia apparent magnitudes. Here we extend this technique to alternative cosmological scenarios, in which the growth of structure does not follow the $\Lambda$CDM prescription. We apply the method first to the supernova data provided by the JLA catalog combined with redshift distortion data and with low-redshift cluster data and show that although the supernovae alone are not very constraining, they help in reducing the confidence regions. Then we apply our method to future data from LSST and from a survey that approximates the Euclid satellite mission. In this case we show that the combined data are nicely complementary and can constrain the normalization $\sigma_8$ and the growth rate index $\gamma$ to within $0.6\%$ and $7\%$, respectively. In particular, the LSST supernova catalog is forecast to give the constraint $\gamma (\sigma_8/0.83)^{6.7} = 0.55 \pm 0.1$. We also report on constraints relative to a step-wise parametrization of the growth rate of structures. These results show that supernova lensing serves as a good cross-check on the measurement of perturbation parameters from more standard techniques.

### Constraining the growth of perturbations with lensing of supernovae [Cross-Listing]

A recently proposed technique allows one to constrain both the background and perturbation cosmological parameters through the distribution function of supernova Ia apparent magnitudes. Here we extend this technique to alternative cosmological scenarios, in which the growth of structure does not follow the $\Lambda$CDM prescription. We apply the method first to the supernova data provided by the JLA catalog combined with redshift distortion data and with low-redshift cluster data and show that although the supernovae alone are not very constraining, they help in reducing the confidence regions. Then we apply our method to future data from LSST and from a survey that approximates the Euclid satellite mission. In this case we show that the combined data are nicely complementary and can constrain the normalization $\sigma_8$ and the growth rate index $\gamma$ to within $0.6\%$ and $7\%$, respectively. In particular, the LSST supernova catalog is forecast to give the constraint $\gamma (\sigma_8/0.83)^{6.7} = 0.55 \pm 0.1$. We also report on constraints relative to a step-wise parametrization of the growth rate of structures. These results show that supernova lensing serves as a good cross-check on the measurement of perturbation parameters from more standard techniques.

### Magnetohydrodynamic stability of stochastically driven accretion flows

We investigate the evolution of magnetohydrodynamic perturbations in presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable, but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations/experiments. The mismatch seems to have been resolved, at least in certain regimes, in presence of weak magnetic field revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and hence large energy dissipations of perturbation, which generate instability.

### A Transition from Flat Space to Curved One

We investigate the way the fundamental strings are related to supergravity background. That means once the endpoints of the D-strings are electrified we found that the flat space becomes curved one. To prove that, we study the electrified relative and overall transverse perturbations of fuzzy funnel solutions of intersecting $(N,N_f)$-strings and D5 branes in flat and then supergravity backgrounds. We deal with the linearized equations of these perturbations. As result the perturbations have a discontinuity which corresponds to a zero phase shift realizing Polchinskis open string Neumann boundary condition. Also we get an interesting result; in flat space once the electric field $E$ is turned on these perturbations decrease and when $E$ is close to the critical value the perturbations disappear forever and the string coupling becomes strong. At this stage the space is considered curved. Also the potential associated to the perturbations on the funnel solutions goes to $+\infty$ for all $E$ in curved space but it goes to $-\infty$ for $E\approx \frac{1}{\lambda}$ in flat space. In supergravity background, the $+\infty$ potential could be a sign to the absence of the perturbation effects and in flat background the $-\infty$ potential could mean a kink to increase the $\Phi$ velocity to disappear.

### A Transition from Flat Space to Curved One [Replacement]

We investigate the way the fundamental strings are related to supergravity background. That means once the endpoints of the D-strings are electrified we found that the flat space becomes curved one. To prove that, we study the electrified relative and overall transverse perturbations of fuzzy funnel solutions of intersecting $(N,N_f)$-strings and D5 branes in flat and then supergravity backgrounds. We deal with the linearized equations of these perturbations. As result the perturbations have a discontinuity which corresponds to a zero phase shift realizing Polchinskis open string Neumann boundary condition. Also we get an interesting result; in flat space once the electric field $E$ is turned on these perturbations decrease and when $E$ is close to the critical value the perturbations disappear forever and the string coupling becomes strong. At this stage the space is considered curved. Also the potential associated to the perturbations on the funnel solutions goes to $+\infty$ for all $E$ in curved space but it goes to $-\infty$ for $E\approx \frac{1}{\lambda}$ in flat space. In supergravity background, the $+\infty$ potential could be a sign to the absence of the perturbation effects and in flat background the $-\infty$ potential could mean a kink to increase the $\Phi$ velocity to disappear.

### On the perturbation of the luminosity distance by peculiar motions

We consider some aspects of the perturbation to the luminosity distance $d(z)$ that are of relevance for SN1a cosmology and for future peculiar velocity surveys at non-negligible redshifts. 1) Previous work has shown that the correction to the lowest order perturbation $\delta d / d = -\delta v / c z$ has the peculiar characteristic that it appears to depend on the absolute state of motion of sources, rather than on their motion relative to that of the observer. The resolution of this apparent violation of the equivalence principle is that it is necessary to allow for evolution of the velocities with time, and also, when considering perturbations on the scale of the observer-source separation, to include the gravitational redshift effect. We provide an expression for $\delta d / d$ that provides a physically consistent way to compute the impact of peculiar motions for SN1a cosmology and peculiar velocity surveys. 2) We then calculate the perturbation to the redshift as a function of source flux density, which has been proposed as an alternative probe of large-scale motions. We show how the inclusion of surface brightness modulation modifies the relation between $\delta z(m)$ and the peculiar velocity, and that, while the noise properties of this method might appear promising, the velocity signal is swamped by the effect of galaxy clustering for most scales of interest. 3) We show how, in linear theory, peculiar velocity measurements are biased downwards by the effect of smaller scale motions or by measurement errors (such as in photometric redshifts). Our results nicely explain the effects seen in simulations by Koda et al.\ 2013. We critically examine the prospects for extending peculiar velocity studies to larger scales with near-term future surveys.

### Coupling the non-gravitational forces and Modified Newton Dynamics for cometary orbits [Replacement]

In recent works (Milgrom 2009, Blanchet & Novak 2011), the authors showed that the MOdified Newton Dynamics (MOND) have a non-negligible secular perturbation effect on planets with large semi-major axis (gaseous planets) in the Solar System. There exist comets which have a very eccentric orbit with a large semi-major axis (Halley family comets). This kind of comet have the particularity to go far away from the Sun (more than 15 AU) in a low acceleration regime where they would be subject to MOND perturbation. On the other side, they approach the Sun very closely (less than 3 AU) and are affected by the sublimation of ices from their nucleus. This sublimation triggers a so-called non-gravitational forces. The main goal of this paper is to investigate the effect of MOND perturbation on three comets with various orbital elements (2P/Encke, 1P/Halley and 153P/Ikeya-Zhang) in order to compare it to the non-gravitational perturbations. It is motivated by the fact that when fitting an outgassing model for a comet, we have to take into account all the small perturbing effects in order to not absorb these effects in the non-gravitational parameters. Indeed, it would have the consequence to give a completely wrong estimation of the outgassing. For this work, we use six different forms of MOND functions and compute the secular variations of the orbital elements due to MOND and non-gravitational perturbations. We show that the MONDian effects are not negligible for comets with large semi-major axis compared to the non-gravitational perturbations.

### Michel Henon's first research article: An improved calculation of the perturbation of stellar velocities

Fifteen years after the discovery of dynamical friction by Chandrasekhar, Michel Henon attempts to solve the longstanding problem of the divergence of the friction suffered by the perturber and caused by the most distant cluster stars. His solution laid the foundation to the current understanding of dynamical friction as a non-local transitory force.

### The long-short wavelength mode coupling tightens primordial black hole constraints

The effects of non-gaussianity on the constraints on the primordial curvature perturbation power spectrum from primordial black holes (PBHs) are considered. We extend previous analyses to include the effects of coupling between the modes of the horizon scale at the time the PBH forms and super-horizon modes. We consider terms of up to third order in the Gaussian perturbation. For the weakest constraints on the abundance of PBHs in the early universe (corresponding to a fractional energy density of PBHs of $10^{-5}$ at the time of formation), in the case of gaussian perturbations, constraints on the power spectrum are $\mathcal{P}_{\zeta}<0.05$ but can significantly tighter when even a small amount of non-gaussianity is considered, to $\mathcal{P}_{\zeta}<0.01$, and become approximately $\mathcal{P}_{\zeta}<0.003$ in more special cases. Surprisingly, even when there is negative skew (which naively would suggest fewer areas of high density, leading to weaker constraints), we find that the constraints on the power spectrum become tighter than the purely gaussian case – in strong contrast with previous results. We find that the constraints are highly sensitive to both the non-gaussianity parameters as well as the amplitude of super-horizon perturbations.

### Shell instability of a collapsing dense core

Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of fragmentation and the number of fragments seem to be determined to a large degree by the initial conditions. In this work we study the fate of the linear perturbations of a homogeneous gas sphere both analytically and numerically. In particular, we investigate the stability of the well-known homologous solution that describes the collapse of a uniform spherical cloud. The difficulty of the mathematical singularity in the perturbation equations is surpassed here by explicitly introducing a weak shock next to the sonic point. In parallel, we perform adaptive mesh refinement (AMR) numerical simulations of the linear stages of the collapse and compared the growth rates obtained by each method. With this combination of analytical and numerical tools, we explore the behavior of both spherically symmetric and non-axisymmetric perturbations. The numerical experiments provide the linear growth rates as a function of the core’s initial virial parameter and as a function of the azimuthal wave number of the perturbation. The overlapping regime of the numerical experiments and the analytical predictions is the situation of a cold and large cloud, and in this regime the analytically calculated growth rates agree very well with the ones obtained from the simulations. The use of a weak shock as part of the perturbation allows us to find a physically acceptable solution to the equations for a continuous range of growth rates. The numerical simulations agree very well with the analytical prediction for the most unstable cores, while they impose a limit of a virial parameter of 0.1 for core fragmentation in the absence of rotation.

### Stability and Anti-evaporation of the Schwarzschild-de Sitter Balck Holes in Bigravity

We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity.

### Stability and Anti-evaporation of the Schwarzschild-de Sitter Black Holes in Bigravity [Replacement]

We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity.

### Stability and Anti-evaporation of the Schwarzschild-de Sitter Black Holes in Bigravity [Replacement]

We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity.

### Stability and Anti-evaporation of the Schwarzschild-de Sitter Balck Holes in Bigravity [Cross-Listing]

We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity.

### Perturbing a quantum gravity condensate

In a recent proposal using the group field theory (GFT) approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of ‘atoms of space’, which allows the derivation of an effective cosmological Friedmann equation from the microscopic quantum gravity dynamics. Here we take a first step towards the study of cosmological perturbations over the homogeneous background. We consider a state in which a single ‘atom’ is added to an otherwise homogeneous condensate. Backreaction of the perturbation on the background is negligible and the background dynamics can be solved separately. The dynamics for the perturbation takes the form of a quantum cosmology Hamiltonian for a ‘wavefunction’, depending on background and perturbations, of the product form usually assumed in a Born-Oppenheimer approximation. The perturbation we consider can then be interpreted as a spatially homogeneous metric perturbation. For this case, our results show how perturbations can be added to condensate states in quantum gravity, deriving the usual procedures in quantum cosmology from fundamental quantum gravity.

### Perturbing a quantum gravity condensate [Cross-Listing]

In a recent proposal using the group field theory (GFT) approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of ‘atoms of space’, which allows the derivation of an effective cosmological Friedmann equation from the microscopic quantum gravity dynamics. Here we take a first step towards the study of cosmological perturbations over the homogeneous background. We consider a state in which a single ‘atom’ is added to an otherwise homogeneous condensate. Backreaction of the perturbation on the background is negligible and the background dynamics can be solved separately. The dynamics for the perturbation takes the form of a quantum cosmology Hamiltonian for a ‘wavefunction’, depending on background and perturbations, of the product form usually assumed in a Born-Oppenheimer approximation. The perturbation we consider can then be interpreted as a spatially homogeneous metric perturbation. For this case, our results show how perturbations can be added to condensate states in quantum gravity, deriving the usual procedures in quantum cosmology from fundamental quantum gravity.

### Perturbing a quantum gravity condensate [Replacement]

In a recent proposal using the group field theory (GFT) approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of ‘atoms of space’, which allows the derivation of an effective cosmological Friedmann equation from the microscopic quantum gravity dynamics. Here we take a first step towards the study of cosmological perturbations over the homogeneous background. We consider a state in which a single ‘atom’ is added to an otherwise homogeneous condensate. Backreaction of the perturbation on the background is negligible and the background dynamics can be solved separately. The dynamics for the perturbation takes the form of a quantum cosmology Hamiltonian for a ‘wavefunction’, depending on background and perturbations, of the product form usually assumed in a Born-Oppenheimer approximation. We show that the perturbation we consider corresponds to a spatially homogeneous metric perturbation, and for this case derive the usual procedures in quantum cosmology from fundamental quantum gravity.

### Perturbing a quantum gravity condensate [Replacement]

In a recent proposal using the group field theory (GFT) approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of ‘atoms of space’, which allows the derivation of an effective cosmological Friedmann equation from the microscopic quantum gravity dynamics. Here we take a first step towards the study of cosmological perturbations over the homogeneous background. We consider a state in which a single ‘atom’ is added to an otherwise homogeneous condensate. Backreaction of the perturbation on the background is negligible and the background dynamics can be solved separately. The dynamics for the perturbation takes the form of a quantum cosmology Hamiltonian for a ‘wavefunction’, depending on background and perturbations, of the product form usually assumed in a Born-Oppenheimer approximation. We show that the perturbation we consider corresponds to a spatially homogeneous metric perturbation, and for this case derive the usual procedures in quantum cosmology from fundamental quantum gravity.

### Estimation of Inflation parameters for Perturbed Power Law model using recent CMB measurements

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass $m_{\rm eff}$ for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation $\nu_t$ and change in spectral index for scalar perturbation $\nu_{st}$ to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard $\Lambda$CDM model. With this model, we estimate a non-zero value of tensor spectral index at significance of $5.36$ and a non-zero value of effective mass $\frac{m^2_{\rm eff}}{H^2} = -0.0237 \pm 0.0045$, of the inflaton field.

### Estimation of Inflation parameters for Perturbed Power Law model using recent CMB measurements [Cross-Listing]

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass $m_{\rm eff}$ for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation $\nu_t$ and change in spectral index for scalar perturbation $\nu_{st}$ to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard $\Lambda$CDM model. With this model, we estimate a non-zero value of tensor spectral index at significance of $5.36$ and a non-zero value of effective mass $\frac{m^2_{\rm eff}}{H^2} = -0.0237 \pm 0.0045$, of the inflaton field.

### Super-inflation and generation of first order vector perturbations in ELKO [Cross-Listing]

In this work we construct a model where first order vector perturbations can be generated during inflationary expansion. For the non-standard spinors, known as ELKO, we show that the ($\eta-i$) component of the first order perturbed energy-momentum tensor of the ELKO is non-zero for pure vector part of the metric perturbation ($B_{i}$). We show that vector perturbations do not decay in the super-horizon scale and for a specific super-inflation background model we show that the vector perturbations are nearly scale invariant, while its amplitude is smaller than the primordial scalar perturbations. We also comment on the generation of vorticity.

### Super-inflation and generation of first order vector perturbations in ELKO

In this work we construct a model where first order vector perturbations can be generated during inflationary expansion. For the non-standard spinors, known as ELKO, we show that the ($\eta-i$) component of the first order perturbed energy-momentum tensor of the ELKO is non-zero for pure vector part of the metric perturbation ($B_{i}$). We show that vector perturbations do not decay in the super-horizon scale and for a specific super-inflation background model we show that the vector perturbations are nearly scale invariant, while its amplitude is smaller than the primordial scalar perturbations. We also comment on the generation of vorticity.

### Super-inflation and generation of first order vector perturbations in ELKO [Cross-Listing]

In this work we construct a model where first order vector perturbations can be generated during inflationary expansion. For the non-standard spinors, known as ELKO, we show that the ($\eta-i$) component of the first order perturbed energy-momentum tensor of the ELKO is non-zero for pure vector part of the metric perturbation ($B_{i}$). We show that vector perturbations do not decay in the super-horizon scale and for a specific super-inflation background model we show that the vector perturbations are nearly scale invariant, while its amplitude is smaller than the primordial scalar perturbations. We also comment on the generation of vorticity.

### Multi-field inflation from holography [Cross-Listing]

We initiate the study of multi-field inflation using holography. Bulk light scalar fields correspond to nearly marginal operators in the boundary theory and the dual quantum field theory is a deformation of a CFT by such operators. We compute the power spectra of adiabatic and entropy perturbations in a simple model and find that the adiabatic curvature perturbation is not conserved in the presence of entropy perturbations but becomes conserved when the entropy perturbations are set to zero or the model is effectively a single scalar model, in agreement with expectations from cosmological perturbation theory.

### Multi-field inflation from holography [Cross-Listing]

We initiate the study of multi-field inflation using holography. Bulk light scalar fields correspond to nearly marginal operators in the boundary theory and the dual quantum field theory is a deformation of a CFT by such operators. We compute the power spectra of adiabatic and entropy perturbations in a simple model and find that the adiabatic curvature perturbation is not conserved in the presence of entropy perturbations but becomes conserved when the entropy perturbations are set to zero or the model is effectively a single scalar model, in agreement with expectations from cosmological perturbation theory.

### Multi-field inflation from holography

We initiate the study of multi-field inflation using holography. Bulk light scalar fields correspond to nearly marginal operators in the boundary theory and the dual quantum field theory is a deformation of a CFT by such operators. We compute the power spectra of adiabatic and entropy perturbations in a simple model and find that the adiabatic curvature perturbation is not conserved in the presence of entropy perturbations but becomes conserved when the entropy perturbations are set to zero or the model is effectively a single scalar model, in agreement with expectations from cosmological perturbation theory.

### A short note on the curvature perturbation at second order

Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our starting point, we give our results in terms of field fluctuations in the flat gauge, incorporating both large and small scale behaviour. For ease of future numerical implementation we give our result in terms of the scalar field fluctuations and their time derivatives.

### A short note on the curvature perturbation at second order [Cross-Listing]

Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our starting point, we give our results in terms of field fluctuations in the flat gauge, incorporating both large and small scale behaviour. For ease of future numerical implementation we give our result in terms of the scalar field fluctuations and their time derivatives.