# Posts Tagged perturbation

## Today's Postings

### Large-Scale Structure and Gravitational Waves III: Tidal Effects

The leading locally observable effect of a long-wavelength metric perturbation corresponds to a tidal field. We derive the tidal field induced by scalar, vector, and tensor perturbations, and use second order perturbation theory to calculate the effect on the locally measured small-scale density fluctuations. For sub-horizon scalar perturbations, we recover the standard perturbation theory result ($F_2$ kernel). For tensor modes of wavenumber $k_L$, we find that effects persist for $k_L\tau \gg 1$, i.e. even long after the gravitational wave has entered the horizon and redshifted away, i.e. it is a "fossil" effect. We then use these results, combined with the "ruler perturbations" of arXiv:1204.3625, to predict the observed distortion of the small-scale matter correlation function induced by a long-wavelength tensor mode. We also estimate the observed signal in the B mode of the cosmic shear from a gravitational wave background, including both tidal (intrinsic alignment) and projection (lensing) effects. The non-vanishing tidal effect in the $k_L\tau \gg 1$ limit significantly increases the intrinsic alignment contribution to shear B modes, especially at low redshifts $z \lesssim 2$.

### Large-Scale Structure and Gravitational Waves III: Tidal Effects [Cross-Listing]

The leading locally observable effect of a long-wavelength metric perturbation corresponds to a tidal field. We derive the tidal field induced by scalar, vector, and tensor perturbations, and use second order perturbation theory to calculate the effect on the locally measured small-scale density fluctuations. For sub-horizon scalar perturbations, we recover the standard perturbation theory result ($F_2$ kernel). For tensor modes of wavenumber $k_L$, we find that effects persist for $k_L\tau \gg 1$, i.e. even long after the gravitational wave has entered the horizon and redshifted away, i.e. it is a "fossil" effect. We then use these results, combined with the "ruler perturbations" of arXiv:1204.3625, to predict the observed distortion of the small-scale matter correlation function induced by a long-wavelength tensor mode. We also estimate the observed signal in the B mode of the cosmic shear from a gravitational wave background, including both tidal (intrinsic alignment) and projection (lensing) effects. The non-vanishing tidal effect in the $k_L\tau \gg 1$ limit significantly increases the intrinsic alignment contribution to shear B modes, especially at low redshifts $z \lesssim 2$.

### Sharp parameter bounds for certain maximal point lenses

Starting from an $n$-point circular gravitational lens having $3n+1$ images, Rhie (2003) used a perturbation argument to construct an $(n+1)$-point lens producing $5n$ images. In this note we give a concise proof of Rhie’s result, and we extend the range of parameters in Rhie’s model for which maximal lensing occurs. We also study a slightly different construction given by Bayer and Dyer (2007) arising from the $(3n+1)$-point lens. In particular, we extend their results and give sharp parameter bounds for their lens model. By a substitution of variables and parameters we show that both models are equivalent in a certain sense.

### Maser Radiation in an Astrophysical Context (Overview)

In this paper we will look at the phenomenon of Microwave Amplification by Stimulated Emission of Radiation (a maser system). We begin by deriving amplification by stimulated emission using time-dependent perturbation theory, in which the perturbation provided by external radiation. When this perturbation is applied to an ensemble of particles exhibiting a population inversion, the result is stimulated microwave radiation. We will explore both unsaturated and saturated masers and compare their properties. By understanding their gain, as well as the effect of line broadening, astronomers are to identify astrophysical masers. By studying such masers, we gain new insight into poorly understood physical environments, particularly those around young and old stars, and compact stellar bodies.

### Cosmology of the Spinor Emergent Universe and Scale-invariant Perturbations [Cross-Listing]

A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-invariant power spectrum. We study the stability of the backreaction and constrain the forms of the coupling terms. These almost scale-independent fluctuations are able to be transferred into curvature perturbation after the epoch of emergent universe through a generalized curvaton mechanism and thus can explain cosmological observations.

### Cosmology of the Spinor Emergent Universe and Scale-invariant Perturbations [Cross-Listing]

A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-invariant power spectrum. We study the stability of the backreaction and constrain the forms of the coupling terms. These almost scale-independent fluctuations are able to be transferred into curvature perturbation after the epoch of emergent universe through a generalized curvaton mechanism and thus can explain cosmological observations.

### Second-order cosmological perturbations in two-field inflation and predictions for non-Gaussianity

Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function.

### Application of beyond $\delta N$ formalism -- Varying sound speed

We focus on the evolution of curvature perturbation on superhorizon scales by adopting the spatial gradient expansion and show that the nonlinear theory, called the beyond $\delta N$-formalism as the next-leading order in the expansion. As one application of our formalism for a single scalar field, we investigate the case of varying sound speed. In our formalism, we can deal with the time evolution in contrast to $\delta N$-formalism, where curvature perturbations remain just constant, and nonlinear curvature perturbation follows the simple master equation whose form is similar as one in linear theory. So the calculation of bispectrum can be done in the next-leading order in the expansion as similar as the case of deriving the power spectrum. We discuss localized features of both primordial power and bispectrum generated by the effect of varying sound speed with a finite duration time. We can see a local feature like a bump in the equilateral bispectrum.

### Application of beyond $\delta N$ formalism -- Varying sound speed [Cross-Listing]

We focus on the evolution of curvature perturbation on superhorizon scales by adopting the spatial gradient expansion and show that the nonlinear theory, called the beyond $\delta N$-formalism as the next-leading order in the expansion. As one application of our formalism for a single scalar field, we investigate the case of varying sound speed. In our formalism, we can deal with the time evolution in contrast to $\delta N$-formalism, where curvature perturbations remain just constant, and nonlinear curvature perturbation follows the simple master equation whose form is similar as one in linear theory. So the calculation of bispectrum can be done in the next-leading order in the expansion as similar as the case of deriving the power spectrum. We discuss localized features of both primordial power and bispectrum generated by the effect of varying sound speed with a finite duration time. We can see a local feature like a bump in the equilateral bispectrum.

### Equivalence between the Covariant and Bardeen Perturbation Formalisms

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe the cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors that yields an adequate language to treat both perturbative approaches in a common framework. Additionally, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$. We also stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem, and the same tensor combinations above at first order are also hyper-surface invariant making the gauge invariant variables $\Phi$, $\Psi$ and $\Xi$ both gauge and hyper-surface invariant.

### Equivalence between the Covariant and Bardeen Perturbation Formalisms [Cross-Listing]

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe the cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors that yields an adequate language to treat both perturbative approaches in a common framework. Additionally, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$. We also stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem, and the same tensor combinations above at first order are also hyper-surface invariant making the gauge invariant variables $\Phi$, $\Psi$ and $\Xi$ both gauge and hyper-surface invariant.

### Equivalence between the Covariant and Bardeen Perturbation Formalisms [Replacement]

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe the cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors that yields an adequate language to treat both perturbative approaches in a common framework. Additionally, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$. We also stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem, and the same tensor combinations above at first order are also hyper-surface invariant making the gauge invariant variables $\Phi$, $\Psi$ and $\Xi$ both gauge and hyper-surface invariant.

### Equivalence between the Covariant and Bardeen Perturbation Formalisms [Replacement]

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe the cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors that yields an adequate language to treat both perturbative approaches in a common framework. Additionally, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$. We also stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem, and the same tensor combinations above at first order are also hyper-surface invariant making the gauge invariant variables $\Phi$, $\Psi$ and $\Xi$ both gauge and hyper-surface invariant.

### Angular Momentum Generation by Parity Violation [Cross-Listing]

We generalize our holographic derivation of spontaneous angular momentum generation in 2 + 1 dimensions in several directions. We consider cases when a parity violating perturbation responsible for the angular momentum generation can be non-marginal (while in our previous paper we restricted to a marginal perturbation), including all possible two-derivative interactions, with parity violations triggered both by gauge and gravitational Chern-Simons terms in the bulk. We make only a minimal assumption about the bulk geometry that it is asymptotically AdS, respects the Poincar\’e symmetry in 2 + 1 dimensions, and has a horizon. In this generic setup, we find a remarkably concise and universal formula for the expectation value of the angular momentum density, to all orders in the parity violating perturbation.

### $\Lambda$CDM model with a scalar perturbation vs. preferred direction of the universe

We present a scalar perturbation for the $\Lambda$CDM model, which breaks the isotropic symmetry of the universe. Based on the Union2 data, the least-$\chi^2$ fit of the scalar perturbed $\Lambda$CDM model shows that the universe has a preferred direction $(l,b)=(287^\circ\pm25^\circ,11^\circ\pm22^\circ)$. The magnitude of scalar perturbation is about $-2.3\times10^{-5}$. The scalar perturbation for the $\Lambda$CDM model implies a peculiar velocity, which is perpendicular to the radial direction. We show that the maximum peculiar velocities at redshift $z=0.15$ and $z=0.015$ equal to $73\pm28 \rm km\cdot s^{-1}$ and $1099\pm427 \rm km\cdot s^{-1}$, respectively. They are compatible with the constraints on peculiar velocity given by Planck Collaboration.

### $\Lambda$CDM model with a scalar perturbation vs. preferred direction of the universe [Cross-Listing]

We present a scalar perturbation for the $\Lambda$CDM model, which breaks the isotropic symmetry of the universe. Based on the Union2 data, the least-$\chi^2$ fit of the scalar perturbed $\Lambda$CDM model shows that the universe has a preferred direction $(l,b)=(287^\circ\pm25^\circ,11^\circ\pm22^\circ)$. The magnitude of scalar perturbation is about $-2.3\times10^{-5}$. The scalar perturbation for the $\Lambda$CDM model implies a peculiar velocity, which is perpendicular to the radial direction. We show that the maximum peculiar velocities at redshift $z=0.15$ and $z=0.015$ equal to $73\pm28 \rm km\cdot s^{-1}$ and $1099\pm427 \rm km\cdot s^{-1}$, respectively. They are compatible with the constraints on peculiar velocity given by Planck Collaboration.

### Spatial averaging and a non-Gaussianity [Cross-Listing]

The spatial averaging used for the splitting of the local scale factor on the homogeneous background and small inhomogeneous perturbation leads to a non-local relationship between locally and globally defined comoving curvature perturbations. We study this relationship within a quasi-homogeneous, nearly spatially flat domain of the Universe. It is shown that, on scales larger than the size of the observed patch, the Fourier components of the locally defined comoving curvature perturbation are suppressed. We have also shown that the statistical properties of local and global comoving curvature perturbations are coincide on a small scale. Several examples are discussed in detail.

### Spatial averaging and a non-Gaussianity

The spatial averaging used for the splitting of the local scale factor on the homogeneous background and small inhomogeneous perturbation leads to a non-local relationship between locally and globally defined comoving curvature perturbations. We study this relationship within a quasi-homogeneous, nearly spatially flat domain of the Universe. It is shown that, on scales larger than the size of the observed patch, the Fourier components of the locally defined comoving curvature perturbation are suppressed. We have also shown that the statistical properties of local and global comoving curvature perturbations are coincide on a small scale. Several examples are discussed in detail.

### Time variability of viscosity parameter in differentially rotating discs [Replacement]

We propose a mechanism to produce fluctuation in the viscosity parameter ($\alpha$) in differetially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background $\alpha$ was treated as a passive/slave variable in the sense of dynamical system theory. We demonstrate a complete physical picture of growth, saturation and final degradation of the perturbation as a result due to the nonlinear nature of coupled system of equations. The strong dependence of this fluctuation on the radial location in the accretion disc and the base angular momentum distribution is demonstrated. The growth of fluctuation is shown to have a time scale comparable to the radial drift time and hence the physical significance is discussed. The fluctuation is found to be a power law in time in the growing phase and we briefly discuss its statistical significance.

### A Super-Jupiter orbiting a late-type star: A refined analysis of microlensing event OGLE-2012-BLG-0406 [Replacement]

We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG-0406 based on data obtained from 10 different observatories. Intensive coverage of the lightcurve, especially the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects, we estimate the physical parameters of the lens system. We find that the event was caused by a $2.73\pm 0.43\ M_{\rm J}$ planet orbiting a $0.44\pm 0.07\ M_{\odot}$ early M-type star. The distance to the lens is $4.97\pm 0.29$\ kpc and the projected separation between the host star and its planet at the time of the event is $3.45\pm 0.26$ AU. We find that the additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to a more accurate determination of the physical parameters of the lens.

### A Super-Jupiter orbiting a late-type star: A refined analysis of microlensing event OGLE-2012-BLG-0406

We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG-0406 based on data obtained from 10 different observatories. Intensive coverage of the lightcurve, especially the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects, we estimate the physical parameters of the lens system. We find that the event was caused by a $2.73\pm 0.43\ M_{\rm J}$ planet orbiting a $0.44\pm 0.07\ M_{\odot}$ early M-type star. The distance to the lens is $4.97\pm 0.29$\ kpc and the projected separation between the host star and its planet at the time of the event is $3.45\pm 0.26$ AU. We find that the additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to a more accurate determination of the physical parameters of the lens.

### Covariant perturbations through a simple non-singular bounce

In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examined the validity of linear perturbation theory. The bounce is modeled by a two component perfect fluid. The scalar and vector perturbations become singular at the turning surface, which is the boundary of the spacetime region where the null energy condition is violated. The gravitational waves oscillate around the bounce and the turning surface. By computing the growth of linearity parameters, it has been shown that the perturbations do not remain linear at the turning point. We have also shown that the non-adiabatic modes of comoving curvature perturbation diverge at the turning surface.

### Gravitational self-force from radiation-gauge metric perturbations

Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the perturbation is formulated in a class of radiation gauges, in which the particle singularity is non-isotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We identify 3 types of radiation gauges: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the "regular half" of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, analogous to the standard Lorenz-gauge formula but with modified regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem, and discuss the correspondence between our method and a related approach by Friedman et al.

### Gravitational self-force from radiation-gauge metric perturbations [Replacement]

Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the perturbation is formulated in a class of radiation gauges, in which the particle singularity is non-isotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We identify 3 types of radiation gauges: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the "regular half" of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, analogous to the standard Lorenz-gauge formula but with modified regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem, and discuss the correspondence between our method and a related approach by Friedman et al.

### Gravitational self-force from radiation-gauge metric perturbations [Cross-Listing]

Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the perturbation is formulated in a class of radiation gauges, in which the particle singularity is non-isotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We identify 3 types of radiation gauges: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the "regular half" of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, analogous to the standard Lorenz-gauge formula but with modified regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem, and discuss the correspondence between our method and a related approach by Friedman et al.

### Gravitational self-force from radiation-gauge metric perturbations [Replacement]

Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the perturbation is formulated in a class of radiation gauges, in which the particle singularity is non-isotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We identify 3 types of radiation gauges: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the "regular half" of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, analogous to the standard Lorenz-gauge formula but with modified regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem, and discuss the correspondence between our method and a related approach by Friedman et al.

### Generating Intrinsic Dipole Anisotropy in the Large Scale Structures

There have been recent reports of unexpectedly large velocity dipole in the NRAO VLA Sky Survey data. We investigate whether the excess in the NVSS dipole reported can be of cosmological origin. We assume a long wavelength inhomogeneous scalar perturbation of the form \alpha sin (\kappa z) and study its effects on the matter density contrasts. Assuming an ideal fluid model we calculate, in the linear regime, the contribution of the inhomogeneous mode to the density contrast. We calculate the expected dipole in the LSS for two cases, first assuming that the mode is still superhorizon everywhere, and second assuming the mode is subhorizon, but has crossed the horizon deep in matter domination and is subhorizon everywhere in the region of the survey (NVSS). In both cases we find that such an inhomogeneous scalar perturbation is sufficient to generate the reported values of dipole anisotropy in LSS. For the superhorizon modes we find values which are consistent with both CMB and NVSS results.

### Axion as a Cold Dark Matter Candidate: Proof to Second order

We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale. The proof is made in the axion-comoving gauge. For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size. Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order. We also show that the axion fluid does not generate the rotational (vector-type) perturbation even to the second order. Thus, in the case of axion fluid, we have the relativistic/Newtonian correspondence to the second order, even considering the rotational perturbation. Our analysis is made in the presence of the cosmological constant, and can be easily extended to the realistic situation including other components of fluids and fields.

### Axion as a Cold Dark Matter Candidate: Proof to Second order [Cross-Listing]

We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale. The proof is made in the axion-comoving gauge. For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size. Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order. We also show that the axion fluid does not generate the rotational (vector-type) perturbation even to the second order. Thus, in the case of axion fluid, we have the relativistic/Newtonian correspondence to the second order, even considering the rotational perturbation. Our analysis is made in the presence of the cosmological constant, and can be easily extended to the realistic situation including other components of fluids and fields.

### Aspects of inflation and the very early universe

Until recently our knowledge of the primordial curvature perturbation was relatively modest. Ever since COBE delivered its map of data we know the scalar spectrum of primordial perturbations is approximately flat, with the power being only slightly stronger at larger scales. Most inflationary models predict an approximately scale-invariant spectrum, which therefore cannot be used as a distinctive signature. To distinguish between different inflationary microphysics we need to study higher point statistics of the primordial perturbation, which can encode non-gaussian data. In the first part of this thesis we study the bispectrum in all single-field models with a well-defined quantum field theory during a quasi-de Sitter inflationary phase. Any single-field models without ghost-like instabilities fall into this description: from canonical, to Dirac-Born-Infeld inflation and galileon inflation theories. We investigate the scale and shape- dependences of the bispectrum to next-order in the slow-roll approximation. We illustrate our results by applying them to different models and argue these corrections must be taken into account to keep the theoretical error below the observational precision set by the Planck satellite. We then explore the ability of using bispectrum shapes to distinguish between inflationary models more efficiently. We further extend the study of the bispectrum of single-field models beyond the slow-roll approximation, demanding the spectral index to be close to, but not exactly, unity. In the second part of this thesis we explore the process by which the universe is repopulated with matter particles at the end of a Dirac-Born-Infeld inflation phase. We place some mild bounds on the reheating temperature of these models. We argue that the constraints arising from the preheating analysis are complementary to those derived from the primordial perturbation.

### The parameters of relaxation during the dark matter halo formation: how to fit observational data?

We show that moderate energy relaxation in the formation of dark matter haloes invariably leads to density profiles that match those observed in the central regions of galaxies. The density profile of the central region turns out to be universal and insensitive neither to the seed perturbation shape nor to the details of the relaxation process. The profile has a central core; multiplication of the central density on the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with small index ($n\sim 0.5$); at larger distances it has an extensive region with $\rho\propto r^{-2}$. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons why it could be so.

### The parameters of relaxation during the dark matter halo formation: how to fit observational data? [Replacement]

We show that moderate energy relaxation in the formation of dark matter haloes invariably leads to density profiles that match those observed in the central regions of galaxies. The density profile of the central region turns out to be universal and insensitive neither to the seed perturbation shape nor to the details of the relaxation process. The profile has a central core; multiplication of the central density on the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with small index ($n\sim 0.5$); at larger distances it has an extensive region with $\rho\propto r^{-2}$. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons why it could be so.

### Threshold of primordial black hole formation [Replacement]

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

### Threshold of primordial black hole formation [Replacement]

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

### Threshold of primordial black hole formation

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

### Threshold of primordial black hole formation [Replacement]

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

### Threshold of primordial black hole formation [Replacement]

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\rho c^{2}$ for $w\ge 0$. The formula gives $\delta^{\rm UH}_{H c}=\sin^{2}[\pi \sqrt{w}/(1+3w)]$ and $\tilde{\delta}_{c}=[3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$, where $\delta^{\rm UH}_{H c}$ and $\tilde{\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives $\delta^{\rm UH}_{H c}=w$ and $\tilde{\delta}_{c}=3w(1+w)/(5+3w)$. Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives $\delta^{\rm UH}_{H c}=\sin^{2}(\sqrt{3}\pi/6)\simeq 0.6203$ and $\tilde{\delta}_{c}=(2/3)\sin^{2}(\sqrt{3}\pi/6)\simeq 0.4135$. We also discuss the maximum amplitude and the cosmological implications of the present result.

### Conformal Symmetries of FRW Accelerating Cosmologies [Cross-Listing]

We show that any accelerating Friedmann-Robertson-Walker (FRW) cosmology with equation of state w < -1/3 (and therefore not only a de Sitter stage with w =-1) exhibits three-dimensional conformal symmetry on future constant-time hypersurfaces. We also offer an alternative derivation of this result in terms of conformal Killing vectors and show that long wavelength comoving curvature perturbations of the perturbed FRW metric are just conformal Killing motions of the FRW background. We then extend theb boundary conformal symmetry to the bulk for accelerating cosmologies. Our findings indicate that one can easily generate perturbations of scalar fields which are not only scale invariant, but also fully conformally invariant on super-Hubble scales. Measuring a scale-invariant power spectrum for the cosmological perturbation does not automatically imply that the universe went through a de Sitter stage.

### The Aquarius Co-Moving Group is Not a Disrupted Classical Globular Cluster

We present a detailed analysis of high-resolution, high S/N spectra for 5 Aquarius stream stars observed with the MIKE spectrograph on the Magellan Clay telescope. Our sample represents one third of the 15 known members in the stream. We find the stream is not mono-metallic: the metallicity ranges from [Fe/H] = -0.63 to -1.58. No anti-correlation in Na-O abundances is present, and we find a strong positive Mg-Al relationship, similar to that observed in the thick disk. We find no evidence that the stream is a result of a disrupted classical globular cluster, contrary to a previously published claim. High [(Na, Ni, alpha)/Fe] and low [Ba/Y] abundance ratios in the stream suggests it is not a tidal tail from a disrupted dwarf galaxy, either. The stream is chemically indistinguishable from Milky Way field stars with the exception of one candidate, C222531-145437. From its position, velocity, and detailed chemical abundances, C222531-145437 is likely a star that was tidally disrupted from omega-Centauri. We propose the Aquarius stream is Galactic in origin, and could be the result from a disk-satellite perturbation in the Milky Way thick disk on the order of a few Gyr ago: derived orbits, UVW velocities, and angular momenta of the Aquarius members offer qualitative support for our hypothesis. Assuming C222531-145437 is a tidally disrupted member of omega-Centauri, this system is the most likely disk perturber. In the absence of compelling chemical and/or dynamical evidence that the Aquarius stream is the tidal tail of a disrupted satellite, we advocate the "Aquarius group" as a more appropriate description. Like the Canis Major over-density, as well as the Hercules and Monoceros groups, the Aquarius group joins the list of kinematically-identified substructures that are not actually accreted material: they are simply part of the rich complexity of the Milky Way structure.

### Intensity interferometry for observation of dark objects [Replacement]

We analyze an intensity interferometry measurement carried out with two point-like detectors facing a distant source (e.g., a star) that may be partially occluded by an absorptive object (e.g., a planet). Such a measurement, based on the perturbation of the observed covariance function due to the object’s presence, can provide information of the object complementary to a direct optical intensity measurement. In particular, one can infer the orientation of the object’s transient trajectory. We identify the key parameters that impact this perturbation and show that its magnitude is equal to the magnitude of the intensity variation caused by the same object. In astronomy applications, this value may be very small, so a differential measurement may be necessary. Finally, we discuss the signal-to-noise ratio that may be expected in this type of measurement.

### Intensity interferometry for observation of dark objects [Cross-Listing]

We analyze an intensity interferometry measurement carried out with two point-like detectors facing a distant source (e.g., a star) that may be partially occluded by an absorptive object (e.g., a planet). Such a measurement, based on the perturbation of the observed covariance function due to the object’s presence, can provide information of the object complementary to a direct optical intensity measurement. In particular, one can infer the orientation of the object’s transient trajectory. We identify the key parameters that impact this perturbation and show that its magnitude is equal to the magnitude of the intensity variation caused by the same object. In astronomy applications, this value may be very small, so a differential measurement may be necessary. Finally, we discuss the signal-to-noise ratio that may be expected in this type of measurement.

### Viscous Kelvin-Helmholtz instabilities in highly ionised plasmas

Transport coefficients in highly ionised plasmas like the intra-cluster medium (ICM) are still ill-constrained. They influence various processes, among them the mixing at shear flow interfaces due to the Kelvin-Helmholtz instability (KHI). The observed structure of potential mixing layers can be used to infer the transport coefficients, but the data interpretation requires a detailed knowledge of the long-term evolution of the KHI under different conditions. Here we present the first systematic numerical study of the effect of constant and temperature-dependent isotropic viscosity over the full range of possible values. We show that moderate viscosities slow down the growth of the KHI and reduce the height of the KHI rolls and their rolling-up. Viscosities above a critical value suppress the KHI. The effect can be quantified in terms of the Reynolds number Re = U{\lambda}/{\nu}, where U is the shear velocity, {\lambda} the perturbation length, and {\nu} the kinematic viscosity. We derive the critical Re for constant and temperature dependent, Spitzer-like viscosities, an empirical relation for the viscous KHI growth time as a function of Re and density contrast, and describe special behaviours for Spitzer-like viscosities and high density contrasts. Finally, we briefly discuss several astrophysical situations where the viscous KHI could play a role, i.e., sloshing cold fronts, gas stripping from galaxies, buoyant cavities, ICM turbulence, and high velocity clouds.

### A resolved debris disk around the candidate planet-hosting star HD95086

Recently, a new planet candidate was discovered on direct images around the young (10-17 Myr) A-type star HD95086. The strong infrared excess of the system indicates that, similarly to HR8799, {\ss} Pic, and Fomalhaut, the star harbors a circumstellar disk. Aiming to study the structure and gas content of the HD95086 disk, and to investigate its possible interaction with the newly discovered planet, here we present new optical, infrared and millimeter observations. We detected no CO emission, excluding the possibility of an evolved gaseous primordial disk. Simple blackbody modeling of the spectral energy distribution suggests the presence of two spatially separate dust belts at radial distances of 6 and 64 AU. Our resolved images obtained with the Herschel Space Observatory reveal a characteristic disk size of ~6.0×5.4 arcsec (540×490 AU) and disk inclination of ~25 degree. Assuming the same inclination for the planet candidate’s orbit, its re-projected radial distance from the star is 62 AU, very close to the blackbody radius of the outer cold dust ring. The structure of the planetary system at HD95086 resembles the one around HR8799. Both systems harbor a warm inner dust belt and a broad colder outer disk and giant planet(s) between the two dusty regions. Modelling implies that the candidate planet can dynamically excite the motion of planetesimals even out to 270 AU via their secular perturbation if its orbital eccentricity is larger than about 0.4. Our analysis adds a new example to the three known systems where directly imaged planet(s) and debris disks co-exist.

### Hemispherical Power Asymmetry from Scale-Dependent Modulated Reheating [Replacement]

We propose a new model for the hemispherical power asymmetry of the CMB based on modulated reheating. Non-Gaussianity from modulated reheating can be small enough to satisfy the bound from Planck if the dominant modulation of the inflaton decay rate is linear in the modulating field $\sigma$. $\sigma$ must then acquire a spatially-modulated power spectrum with a red scale-dependence. This can be achieved if the primordial perturbation of $\sigma$ is generated via tachyonic growth of a complex scalar field. Modulated reheating due to $\sigma$ then produces a spatially modulated and scale-dependent sub-dominant contribution to the adiabatic density perturbation. We show that it is possible to account for the observed asymmetry while remaining consistent with bounds from quasar number counts, non-Gaussianity and the CMB temperature quadupole. The model predicts that the adiabatic perturbation spectral index and its running will be modified by the modulated reheating component.

### Hemispherical Power Asymmetry from Scale-Dependent Modulated Reheating

We propose a new model for the hemispherical power asymmetry of the CMB based on modulated reheating. Non-Gaussianity from modulated reheating can be small enough to satisfy the bound from Planck if the dominant modulation of the inflaton decay rate is linear in the modulating field $\sigma$. $\sigma$ must then acquire a spatially-modulated power spectrum with a red scale-dependence. This can be achieved if the primordial perturbation of $\sigma$ is generated via tachyonic growth of a complex scalar field. Modulated reheating due to $\sigma$ then produces a spatially modulated and scale-dependent sub-dominant contribution to the adiabatic density perturbation. We show that it is possible to account for the observed asymmetry while remaining consistent with bounds from quasar number counts, non-Gaussianity and the CMB temperature quadupole. The model predicts that the adiabatic perturbation spectral index and its running will be modified by the modulated reheating component.

### Hemispherical Power Asymmetry from Scale-Dependent Modulated Reheating [Replacement]

We propose a new model for the hemispherical power asymmetry of the CMB based on modulated reheating. Non-Gaussianity from modulated reheating can be small enough to satisfy the bound from Planck if the dominant modulation of the inflaton decay rate is linear in the modulating field $\sigma$. $\sigma$ must then acquire a spatially-modulated power spectrum with a red scale-dependence. This can be achieved if the primordial perturbation of $\sigma$ is generated via tachyonic growth of a complex scalar field. Modulated reheating due to $\sigma$ then produces a spatially modulated and scale-dependent sub-dominant contribution to the adiabatic density perturbation. We show that it is possible to account for the observed asymmetry while remaining consistent with bounds from quasar number counts, non-Gaussianity and the CMB temperature quadupole. The model predicts that the adiabatic perturbation spectral index and its running will be modified by the modulated reheating component.

### Formation and internal structure of superdense dark matter clumps and ultracompact minihaloes

We discuss the formation mechanisms and structure of the superdense dark matter clumps (SDMC) and ultracompact minihaloes (UCMH) and outline the differences between these types of DM objects. We define as SDMC the gravitationally bounded DM objects which have come into virial equilibrium at the radiation-dominated (RD) stage of the universe evolution. Such objects can form from the isocurvature (entropy) density perturbations or from the peaks in the spectrum of curvature (adiabatic) perturbation. The axion miniclusters (Kolb and Tkachev 1994) are the example of the former model. The system of central compact mass (e.g. in the form of SDMC or primordial black hole (PBH)) with the outer DM envelope formed in the process of secondary accretion we refer to as UCMH. Therefore, the SDMC can serve as the seed for the UCMH in some scenarios. Recently, the SDMC and UCMH were considered in the many works, and we try to systematize them here. We consider also the effect of asphericity of the initial density perturbation in the gravitational evolution, which decreases the SDMC amount and, as the result, suppresses the gamma-ray signal from DM annihilation.

### Viable f(T) models are practically indistinguishable from LCDM

We investigate the cosmological predictions of several f(T) models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric SnIa, CMB and BAO and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance Lambda cosmology at the background level. In addition we constrain the growth index gamma predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for gamma. The evolution of the best fit effective Newton constant, which incorporates the f(T)-gravity effects is also obtained along with the corresponding 1sigma error regions. We show that all the viable parameter sectors of the f(T) gravity models considered, practically reduce these models to LCDM. Thus, the degrees of freedom that open up to LCDM in the context of f(T) gravity models are not utilized by the cosmological data leading to an overall disfavor of these models.

### Viable f(T) models are practically indistinguishable from LCDM [Replacement]

We investigate the cosmological predictions of several f(T) models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric SnIa, CMB and BAO and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance Lambda cosmology at the background level. In addition we constrain the growth index gamma predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for gamma. The evolution of the best fit effective Newton constant, which incorporates the f(T)-gravity effects is also obtained along with the corresponding 1sigma error regions. We show that all the viable parameter sectors of the f(T) gravity models considered, practically reduce these models to LCDM. Thus, the degrees of freedom that open up to LCDM in the context of f(T) gravity models are not utilized by the cosmological data leading to an overall disfavor of these models.

### Viable f(T) models are practically indistinguishable from LCDM [Replacement]

We investigate the cosmological predictions of several f(T) models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric SnIa, CMB and BAO and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance Lambda cosmology at the background level. In addition we constrain the growth index gamma predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for gamma. The evolution of the best fit effective Newton constant, which incorporates the f(T)-gravity effects is also obtained along with the corresponding 1sigma error regions. We show that all the viable parameter sectors of the f(T) gravity models considered, practically reduce these models to LCDM. Thus, the degrees of freedom that open up to LCDM in the context of f(T) gravity models are not utilized by the cosmological data leading to an overall disfavor of these models.

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