# Posts Tagged perturbation

## Recent Postings from perturbation

### Negative running prevents eternal inflation

Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 \sigma$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $\alpha < 0$, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{\rm S}$ from Planck, this corresponds to an upper bound of the running $\alpha < – 4 \times 10^{-5}$, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as $10^4$ e-folds.

### Conserved Quantities in Lemaitre-Tolman-Bondi Cosmology

We study linear perturbations to a Lemaitre-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, {\zeta}, which is conserved on all scales. We then briefly extend our discussion to the Lemaitre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.

### Conserved Quantities in Lemaitre-Tolman-Bondi Cosmology [Replacement]

We study linear perturbations to a Lemaitre-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, {\zeta}, which is conserved on all scales. We then briefly extend our discussion to the Lemaitre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.

### BICEP2, the curvature perturbation and supersymmetry

The tensor fraction $r\simeq 0.16$ found by BICEP2 corresponds to a Hubble parameter $H\simeq 1.0\times 10^{14}\GeV$ during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than $10\%$ of the curvature perturbation $\zeta$, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating $\zeta$ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed $r$ as well as the observed spectral index $\ns$. The shift symmetry does not require supersymmetry. Also, the big $H$ may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC. It therefore seems quite possible that the quantum field theory chosen by Nature is not supersymmetric.

### BICEP2, the curvature perturbation and supersymmetry [Cross-Listing]

The tensor fraction $r\simeq 0.16$ found by BICEP2 corresponds to a Hubble parameter $H\simeq 1.0\times 10^{14}\GeV$ during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than $10\%$ of the curvature perturbation $\zeta$, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating $\zeta$ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed $r$ as well as the observed spectral index $\ns$. The shift symmetry does not require supersymmetry. Also, the big $H$ may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC. It therefore seems quite possible that the quantum field theory chosen by Nature is not supersymmetric.

### BICEP2, the curvature perturbation and supersymmetry [Cross-Listing]

The tensor fraction $r\simeq 0.16$ found by BICEP2 corresponds to a Hubble parameter $H\simeq 1.0\times 10^{14}\GeV$ during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than $10\%$ of the curvature perturbation $\zeta$, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating $\zeta$ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed $r$ as well as the observed spectral index $\ns$. The shift symmetry does not require supersymmetry. Also, the big $H$ may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC. It therefore seems quite possible that the quantum field theory chosen by Nature is not supersymmetric.

### Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature

In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and $f^2(R)$, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the time perturbation is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.

### Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature [Cross-Listing]

In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and $f^2(R)$, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the time perturbation is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.

### Hall Viscosity and Angular Momentum in Gapless Holographic Models [Cross-Listing]

We use the holographic approach to compare the Hall viscosity $\eta_H$ and the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of $\eta_H$ and ${\cal J}$ shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, $\eta_H$ depends only on infrared physics, while ${\cal J}$ receives contributions from degrees of freedom at all scales.

### Hall Viscosity and Angular Momentum in Gapless Holographic Models

We use the holographic approach to compare the Hall viscosity $\eta_H$ and the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of $\eta_H$ and ${\cal J}$ shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, $\eta_H$ depends only on infrared physics, while ${\cal J}$ receives contributions from degrees of freedom at all scales.

### The Knotted Sky II: Does BICEP2 require a nontrivial primordial power spectrum?

An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with $l\lesssim 100$, and this effect — together with a prior on the form of the scalar perturbations — was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and Planck for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a "broken" spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses.

### The Knotted Sky II: Does BICEP2 require a nontrivial primordial power spectrum? [Cross-Listing]

An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with $l\lesssim 100$, and this effect — together with a prior on the form of the scalar perturbations — was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and Planck for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a "broken" spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses.

### The Knotted Sky II: Does BICEP2 require a nontrivial primordial power spectrum? [Cross-Listing]

An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with $l\lesssim 100$, and this effect — together with a prior on the form of the scalar perturbations — was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and Planck for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a "broken" spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses.

### Reheating the universe once more -- the dissipation of acoustic waves as a novel probe of primordial inhomogeneities on even smaller scales

We provide a simple but robust bound on the primordial curvature perturbation in the range 10^4/Mpc < k < 10^5/Mpc, which has not been constrained so far unlike low wavenumber modes. Perturbations on these scales dissipate the energy of their acoustic oscillations by the Silk damping after primordial nucleosynthesis but before the redshift z ~ 2 \times 10^6 and reheat the photon bath without invoking CMB distortions. This acoustic reheating results in the decrease of the baryon-photon ratio. By combining independent measurements probing the nucleosynthesis era and around the recombination epoch, we find an upper bound on the amplitude of the curvature perturbation over the above wavenumber range as {\cal P}_\zeta < 0.02. Implications for super massive black holes are also discussed.

### Reheating the universe once more -- the dissipation of acoustic waves as a novel probe of primordial inhomogeneities on even smaller scales [Cross-Listing]

We provide a simple but robust bound on the primordial curvature perturbation in the range 10^4/Mpc < k < 10^5/Mpc, which has not been constrained so far unlike low wavenumber modes. Perturbations on these scales dissipate the energy of their acoustic oscillations by the Silk damping after primordial nucleosynthesis but before the redshift z ~ 2 \times 10^6 and reheat the photon bath without invoking CMB distortions. This acoustic reheating results in the decrease of the baryon-photon ratio. By combining independent measurements probing the nucleosynthesis era and around the recombination epoch, we find an upper bound on the amplitude of the curvature perturbation over the above wavenumber range as {\cal P}_\zeta < 0.02. Implications for super massive black holes are also discussed.

### Constrained analytical interrelations in neutrino mixing

Hermitian squared mass matrices of charged leptons and light neutrinos in the flavor basis are studied under general additive lowest order perturbations away from the tribimaximal (TBM) limit in which a weak basis with mass diagonal charged leptons is chosen. Simple analytical expressions are found for the three measurable TBM-deviants in terms of perturbation parameters appearing in the neutrino and charged lepton eigenstates in the flavor basis. Taking unnatural cancellations to be absent and charged lepton perturbation parameters to be small, constrained analytical and testable interrelations are derived among neutrino masses, mixing angles and the amount of CP-violation, posing the challenge of verification to forthcoming experiments at the intensity frontier.

### Detection of planets in extremely weak central perturbation microlensing events via next-generation ground-based surveys

Even though the recently discovered high-magnification event MOA-2010-BLG-311 had complete coverage over the peak, confident planet detection did not happen due to extremely weak central perturbations (fractional deviations of $\lesssim 2\%$). For confident detection of planets in extremely weak central perturbation (EWCP) events, it is necessary to have both high cadence monitoring and high photometric accuracy better than those of current follow-up observation systems.The next-generation ground-based observation project, KMTNet (Korea Microlensing Telescope Network), satisfies the conditions. We estimate the probability of occurrence of EWCP events with fractional deviations of $\leq 2\%$ in high-magnification events and the efficiency of detecting planets in the EWCP events using the KMTNet. From this study, we find that the EWCP events occur with a frequency of $> 50\%$ in the case of $\lesssim 100\ M_{\rm E}$ planets with separations of $0.2\ {\rm AU} \lesssim d \lesssim 20\ {\rm AU}$. We find that for main-sequence and subgiant source stars, $\gtrsim 1\ M_{\rm E}$ planets in EWCP events with the deviations $\leq 2\%$ can be detected $> 50\%$ in a certain range that changes with the planet mass. However, it is difficult to detect planets in EWCP events of bright stars like giant stars, because it is easy for KMTNet to be saturated around the peak of the events with a constant exposure time. EWCP events are caused by close, intermediate, and wide planetary systems with low-mass planets and close and wide planetary systems with massive planets. Therefore, we expect that a much greater variety of planetary systems than those already detected, which are mostly intermediate planetary systems regardless of the planet mass, will be significantly detected in the near future.

### Baryonic matter perturbations in decaying vacuum cosmology

We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $\Lambda(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of $5\%$ independently of the dark-matter abundance which is of the order of $32\%$ for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.

### Baryonic matter perturbations in decaying vacuum cosmology [Cross-Listing]

We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $\Lambda(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of $5\%$ independently of the dark-matter abundance which is of the order of $32\%$ for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.

### Baryonic matter perturbations in decaying vacuum cosmology [Cross-Listing]

We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $\Lambda(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of $5\%$ independently of the dark-matter abundance which is of the order of $32\%$ for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.

### Effects to sin\theta_{12} from perturbation of the neutrino mixing matrix with the partially degenerated neutrino masses

We consider a situation where the leading-order neutrino mass matrix is derived by the theoretical ansatz and reproduces the experimental data well, but not preciously. Then, the next stage is to try to perfectly reproduce the data by adding small perturbation terms. In this paper, we obtain the analytical method to diagonalize the mass matrix and find a consistency condition that parameters should satisfy not to change sin\theta_{12} much. This condition could require parameter-tuning and plays a crucial role to relate the added perturbation terms with the prediction analytically, in particular, for the case of the partially-quasi-degenerated neutrino masses (m_2 \simeq m_1) where neutrinoless double beta decays would be observed in the phase-II experiments.

### Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity

In this paper, we continue our previous work of studying viscous generalized Chaplygin gas (VGCG) as a unified dark fluid but including the bulk viscosity perturbation. By using the currently available cosmic observational data from SNLS3, BAO, HST and recently released Planck, we gain the constraint on bulk viscosity coefficient: $\zeta_0=0.0000138_{- 0.0000105- 0.0000138- 0.0000138}^{+ 0.00000614+ 0.0000145+ 0.0000212}$ in $1, 2, 3\sigma$ regions respectively via Markov Chain Monte Carlo method. The result shows that when considering perturbation of bulk viscosity, the currently cosmic observations favor a smaller bulk viscosity coefficient.

### Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity [Replacement]

In this paper, we continue our previous work of studying viscous generalized Chaplygin gas (VGCG) as a unified dark fluid but including the bulk viscosity perturbation. By using the currently available cosmic observational data from SNLS3, BAO, HST and recently released Planck, we gain the constraint on bulk viscosity coefficient: $\zeta_0=0.0000138_{- 0.0000105- 0.0000138- 0.0000138}^{+ 0.00000614+ 0.0000145+ 0.0000212}$ in $1, 2, 3\sigma$ regions respectively via Markov Chain Monte Carlo method. The result shows that when considering perturbation of bulk viscosity, the currently cosmic observations favor a smaller bulk viscosity coefficient.

### Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity [Replacement]

In this paper, we continue our previous work of studying viscous generalized Chaplygin gas (VGCG) as a unified dark fluid but including the bulk viscosity perturbation. By using the currently available cosmic observational data from SNLS3, BAO, HST and recently released Planck, we gain the constraint on bulk viscosity coefficient: $\zeta_0=0.0000138_{- 0.0000105- 0.0000138- 0.0000138}^{+ 0.00000614+ 0.0000145+ 0.0000212}$ in $1, 2, 3\sigma$ regions respectively via Markov Chain Monte Carlo method. The result shows that when considering perturbation of bulk viscosity, the currently cosmic observations favor a smaller bulk viscosity coefficient.

### Perturbative photon production in a dispersive medium [Cross-Listing]

We investigate photon pair-creation in a dispersive dielectric medium induced by the presence of a spacetime varying dielectric constant. Our aim is to examine the possibility to observe new phenomena of pair creation induced by travelling dielectric perturbations e.g. created by laser pulses by means of the Kerr effect. In this perspective, we adopt a semi-phenomenological version of the Hopfield model in which a space-time dependent dielectric susceptibility appears. We focus our attention on perturbation theory, and provide general formulas for the photon production induced by a local but arbitrarily spacetime dependent refractive index perturbation. As an example, we further explore the case of an uniformly travelling perturbation, and provide examples of purely time-dependent perturbations.

### Second order density perturbations for dust cosmologies

We present simple expressions for the relativistic first and second order fractional density perturbations for FL cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two non-elementary functions, the so-called growth supression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.

### Stochastic perturbation of the two-body problem [Cross-Listing]

We study the impact of a stochastic perturbation on the classical two-body problem in particular concerning the preservation of first integrals and the Hamiltonian structure. Numerical simulations are performed which illustrate the dynamical behavior of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.

### Cosmological perturbations in the models of dark energy and modified gravity [Cross-Listing]

The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated enough so far. In this paper, the oscillating solutions, which have a possibility to unveil the difference between the models of the late-time accelerated expansion of the Universe, are also mentioned by using appropriate approximations.

### Baryon Asymmetry, Dark Matter, and Density Perturbation from PBH

We investigate the consistency of a scenario in which the baryon asymmetry, dark matters, as well as the cosmic density perturbation are generated simultaneously through the evaporation of primordial black holes (PBHs). This scenario can explain the coincidence of the dark matter and the baryon density of the universe, and is free from the isocurvature perturbation problem. We show that this scenario predicts the masses of PBHs, right-handed neutrinos and dark matters, the Hubble scale during inflation, the non-gaussianity and the running of the spectral index. We also discuss the testability of the scenario by detecting high frequency gravitational waves from PBHs.

### Baryon Asymmetry, Dark Matter, and Density Perturbation from PBH [Replacement]

We investigate the consistency of a scenario in which the baryon asymmetry, dark matters, as well as the cosmic density perturbation are generated simultaneously through the evaporation of primordial black holes (PBHs). This scenario can explain the coincidence of the dark matter and the baryon density of the universe, and is free from the isocurvature perturbation problem. We show that this scenario predicts the masses of PBHs, right-handed neutrinos and dark matters, the Hubble scale during inflation, the non-gaussianity and the running of the spectral index. We also discuss the testability of the scenario by detecting high frequency gravitational waves from PBHs.

### Perturbation of the Kerr Metric

A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. By comparison with the exterior Hartle-Thorne metric, it is showed that it could be matched to an interior solution. This metric may represent the spacetime of an astrophysical object.

### Perturbation of the Kerr Metric [Cross-Listing]

A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. By comparison with the exterior Hartle-Thorne metric, it is showed that it could be matched to an interior solution. This metric may represent the spacetime of an astrophysical object.

### 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 $z \lesssim 2$.

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

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 [Replacement]

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 [Replacement]

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 [Replacement]

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

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 [Replacement]

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.

### Sharp parameter bounds for certain maximal point lenses [Replacement]

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.

### 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 [Replacement]

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

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.

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

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.