## Recent Postings from Cosmology and Extragalactic

### Relaxing the Electroweak Scale: the Role of Broken dS Symmetry

Recently, a novel mechanism to address the hierarchy problem has been proposed [1], where the hierarchy between weak scale physics and any putative cutoff’ $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $\epsilon$ associated with the breaking of dS symmetry, and the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.

### Relaxing the Electroweak Scale: the Role of Broken dS Symmetry [Cross-Listing]

Recently, a novel mechanism to address the hierarchy problem has been proposed [1], where the hierarchy between weak scale physics and any putative cutoff’ $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $\epsilon$ associated with the breaking of dS symmetry, and the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.

### Relaxing the Electroweak Scale: the Role of Broken dS Symmetry [Cross-Listing]

Recently, a novel mechanism to address the hierarchy problem has been proposed [1], where the hierarchy between weak scale physics and any putative `cutoff’ $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $\epsilon$ associated with the breaking of dS symmetry, and the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.

### The squeezed limit of the bispectrum in multi-field inflation [Cross-Listing]

We calculate the squeezed limit of the bispectrum produced by inflation with multiple light fields. To achieve this we allow for different horizon exit times for each mode and calculate the intrinsic field-space three-point function in the squeezed limit using soft-limit techniques. We then use the $\delta N$ formalism from the time the last mode exits the horizon to calculate the bispectrum of the primordial curvature perturbation. We apply our results to calculate the spectral index of the halo bias, $n_{\delta b}$, an important observational probe of the squeezed limit of the primordial bispectrum and compare our results with previous formulae. We give an example of a curvaton model with $n_{\delta b} \sim {\cal O}(n_s-1)$ for which we find a 20% correction to observable parameters for squeezings relevant to future experiments. For completeness, we also calculate the squeezed limit of three-point correlation functions involving gravitons for multiple field models.

### The squeezed limit of the bispectrum in multi-field inflation

We calculate the squeezed limit of the bispectrum produced by inflation with multiple light fields. To achieve this we allow for different horizon exit times for each mode and calculate the intrinsic field-space three-point function in the squeezed limit using soft-limit techniques. We then use the $\delta N$ formalism from the time the last mode exits the horizon to calculate the bispectrum of the primordial curvature perturbation. We apply our results to calculate the spectral index of the halo bias, $n_{\delta b}$, an important observational probe of the squeezed limit of the primordial bispectrum and compare our results with previous formulae. We give an example of a curvaton model with $n_{\delta b} \sim {\cal O}(n_s-1)$ for which we find a 20% correction to observable parameters for squeezings relevant to future experiments. For completeness, we also calculate the squeezed limit of three-point correlation functions involving gravitons for multiple field models.

### The $\nu$ generation: present and future constraints on neutrino masses from cosmology and laboratory experiments

We perform a joint analysis of current data from cosmology and laboratory experiments to constrain the neutrino mass parameters in the framework of bayesian statistics, also accounting for uncertainties in nuclear modeling, relevant for neutrinoless double $\beta$ decay ($0\nu2\beta$) searches. We find that a combination of current oscillation, cosmological and $0\nu2\beta$ data constrains $m_{\beta\beta}~<~0.04\,(0.06)$ eV at 95\% C.L. for normal (inverted) hierarchy. This result is not affected by uncertainties in nuclear modeling. We then perform forecasts for forthcoming and next-generation experiments, and find that in the case of normal hierarchy, and given a total mass of $0.1\,$ eV, it will be possible to measure the total mass itself, the effective Majorana mass and the effective electron mass with an accuracy (at 95\% C.L.) of $0.05$, $0.015$, $0.02$ eV respectively, as well as to be sensitive to one of the Majorana phases. We argue that more precise nuclear modeling will be crucial to improve these sensitivities.

### The $\nu$ generation: present and future constraints on neutrino masses from cosmology and laboratory experiments [Cross-Listing]

We perform a joint analysis of current data from cosmology and laboratory experiments to constrain the neutrino mass parameters in the framework of bayesian statistics, also accounting for uncertainties in nuclear modeling, relevant for neutrinoless double $\beta$ decay ($0\nu2\beta$) searches. We find that a combination of current oscillation, cosmological and $0\nu2\beta$ data constrains $m_{\beta\beta}~<~0.04\,(0.06)$ eV at 95\% C.L. for normal (inverted) hierarchy. This result is not affected by uncertainties in nuclear modeling. We then perform forecasts for forthcoming and next-generation experiments, and find that in the case of normal hierarchy, and given a total mass of $0.1\,$ eV, it will be possible to measure the total mass itself, the effective Majorana mass and the effective electron mass with an accuracy (at 95\% C.L.) of $0.05$, $0.015$, $0.02$ eV respectively, as well as to be sensitive to one of the Majorana phases. We argue that more precise nuclear modeling will be crucial to improve these sensitivities.

### A non-parametric method for measuring the local dark matter density

We present a new method for determining the local dark matter density using kinematic data for a population of tracer stars. The Jeans equation in the $z$-direction is integrated to yield an equation that gives the velocity dispersion as a function of the total mass density, tracer density, and terms describing the couplings of vertical-radial and vertical-axial motions. Using MultiNest we can then fit a dark matter mass profile to tracer density and velocity dispersion data, and derive credible regions on the dark matter density profile. Our method avoids numerical differentiation, leading to lower numerical noise, and is able to deal with the tilt term while remaining one dimensional. In this study we present the method and perform initial tests on idealised mock data. We also demonstrate the crucial importance of dealing with the tilt term for tracers that sample $\gtrsim 1$ kpc above the disc plane. If ignored, this results in a systematic overestimation of the dark matter density.

### Regular and chaotic dynamics of non-spherical bodies. Zeldovich's pancakes and emission of very long gravitational waves [Cross-Listing]

In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time evolution of semi-axes of a uniformly rotating, three-axis, uniform-density ellipsoid. First, we apply this approach to investigate dynamic stability of non-spherical bodies. We solve the equations that describe, in a simplified way, the Newtonian dynamics of a self-gravitating non-rotating spheroidal body. We find that, after loss of stability, a contraction to a singularity occurs only in a pure spherical collapse, and deviations from spherical symmetry prevent the contraction to the singularity through a stabilizing action of nonlinear non-spherical oscillations. The development of instability leads to the formation of a regularly or chaotically oscillating body, in which dynamical motion prevents the formation of the singularity. We find regions of chaotic and regular pulsations by constructing a Poincare diagram. A real collapse occurs after damping of the oscillations because of energy losses, shock wave formation or viscosity. We use our approach to investigate approximately the first stages of collapse during the large scale structure formation. The theory of this process started from ideas of Ya. B. Zeldovich, concerning the formation of strongly non-spherical structures during nonlinear stages of the development of gravitational instability, known as ‘Zeldovich’s pancakes’. In this paper the collapse of non-collisional dark matter and the formation of pancake structures are investigated approximately. We estimate an emission of very long gravitational waves during the collapse, and discuss the possibility of gravitational lensing and polarization of the cosmic microwave background by these waves.

### Regular and chaotic dynamics of non-spherical bodies. Zeldovich's pancakes and emission of very long gravitational waves

In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time evolution of semi-axes of a uniformly rotating, three-axis, uniform-density ellipsoid. First, we apply this approach to investigate dynamic stability of non-spherical bodies. We solve the equations that describe, in a simplified way, the Newtonian dynamics of a self-gravitating non-rotating spheroidal body. We find that, after loss of stability, a contraction to a singularity occurs only in a pure spherical collapse, and deviations from spherical symmetry prevent the contraction to the singularity through a stabilizing action of nonlinear non-spherical oscillations. The development of instability leads to the formation of a regularly or chaotically oscillating body, in which dynamical motion prevents the formation of the singularity. We find regions of chaotic and regular pulsations by constructing a Poincare diagram. A real collapse occurs after damping of the oscillations because of energy losses, shock wave formation or viscosity. We use our approach to investigate approximately the first stages of collapse during the large scale structure formation. The theory of this process started from ideas of Ya. B. Zeldovich, concerning the formation of strongly non-spherical structures during nonlinear stages of the development of gravitational instability, known as ‘Zeldovich’s pancakes’. In this paper the collapse of non-collisional dark matter and the formation of pancake structures are investigated approximately. We estimate an emission of very long gravitational waves during the collapse, and discuss the possibility of gravitational lensing and polarization of the cosmic microwave background by these waves.

### Gravitational Lensing in Plasmic Medium [Cross-Listing]

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.

### Gravitational Lensing in Plasmic Medium

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.

### Consistency relations for sharp features in the primordial spectra [Cross-Listing]

We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c_s (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c_s and H) holds, including models in which features in the spectra are both sudden and resonant.

### Consistency relations for sharp features in the primordial spectra

We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c_s (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c_s and H) holds, including models in which features in the spectra are both sudden and resonant.

### Consistency relations for sharp features in the primordial spectra [Cross-Listing]

We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c_s (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c_s and H) holds, including models in which features in the spectra are both sudden and resonant.

### Consistency relations for sharp features in the primordial spectra [Cross-Listing]

We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c_s (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c_s and H) holds, including models in which features in the spectra are both sudden and resonant.

### Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model [Cross-Listing]

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice a modification of gauge boson dispersion relation at sub-leading order.

### Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice a modification of gauge boson dispersion relation at sub-leading order.

### Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model [Cross-Listing]

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice a modification of gauge boson dispersion relation at sub-leading order.

### Clustering of intermediate redshift quasars using the final SDSS III-BOSS sample

We measure the two-point clustering of spectroscopically confirmed quasars from the final sample of the Baryon Oscillation Spectroscopic Survey (BOSS) on comoving scales of 4 < s < 22 Mpc/h. The sample covers 6950 deg^2 (~ 19 (Gpc/h)^3) and, over the redshift range 2.2 < z < 2.8, contains 55,826 homogeneously selected quasars, which is twice as many as in any similar work. We deduce b_Q = 3.54 +/- 0.10 ; the most precise measurement of quasar bias to date at these redshifts. This corresponds to a host halo mass of ~ 2 x 10^12 ~ M_sun/h with an implied quasar duty cycle of ~1 percent. The real-space projected correlation function is well-fit by a power law of index -2 and correlation length r0 = (8.12 +/- 0.22), Mpc/h over scales of 4 < rp < 25 ~ Mpc/h. To better study the evolution of quasar clustering at moderate redshift, we extend the redshift range of our study to z ~ 3.4 and measure the bias and correlation length of three subsamples over 2.2 < z < 3.4. We find no significant evolution of r0 or bias over this range, implying that the host halo mass of quasars decreases somewhat with increasing redshift. We find quasar clustering remains similar over a decade in luminosity, contradicting a scenario in which quasar luminosity is monotonically related to halo mass at z ~ 2.5. Our results are broadly consistent with previous BOSS measurements, but they yield more precise constraints based upon a larger and more uniform data set.

### Power spectrum oscillations from Planck-suppressed operators in monodromy inflation [Cross-Listing]

We consider a phenomenological model of monodromy inflation where the inflaton is the phase of a complex scalar field $\Phi$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\left \langle \Phi \right \rangle$ at first order in the decay constant $f$, which adds a first-order periodic term to the definition of the canonically normalized inflaton $\phi$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the monodromy potential $V \sim \theta^p$. We derive the same result in a toy scenario where the vacuum $\left \langle \Phi \right \rangle$ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale $k$ and provide a possible mechanism for differentiating EFT-motivated monodromy inflation from models where the angular shift symmetry is a gauge symmetry.

### Power spectrum oscillations from Planck-suppressed operators in monodromy inflation

We consider a phenomenological model of monodromy inflation where the inflaton is the phase of a complex scalar field $\Phi$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\left \langle \Phi \right \rangle$ at first order in the decay constant $f$, which adds a first-order periodic term to the definition of the canonically normalized inflaton $\phi$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the monodromy potential $V \sim \theta^p$. We derive the same result in a toy scenario where the vacuum $\left \langle \Phi \right \rangle$ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale $k$ and provide a possible mechanism for differentiating EFT-motivated monodromy inflation from models where the angular shift symmetry is a gauge symmetry.

### Power spectrum oscillations from Planck-suppressed operators in monodromy inflation [Cross-Listing]

We consider a phenomenological model of monodromy inflation where the inflaton is the phase of a complex scalar field $\Phi$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\left \langle \Phi \right \rangle$ at first order in the decay constant $f$, which adds a first-order periodic term to the definition of the canonically normalized inflaton $\phi$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the monodromy potential $V \sim \theta^p$. We derive the same result in a toy scenario where the vacuum $\left \langle \Phi \right \rangle$ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale $k$ and provide a possible mechanism for differentiating EFT-motivated monodromy inflation from models where the angular shift symmetry is a gauge symmetry.

### Power spectrum oscillations from Planck-suppressed operators in monodromy inflation [Cross-Listing]

We consider a phenomenological model of monodromy inflation where the inflaton is the phase of a complex scalar field $\Phi$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\left \langle \Phi \right \rangle$ at first order in the decay constant $f$, which adds a first-order periodic term to the definition of the canonically normalized inflaton $\phi$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the monodromy potential $V \sim \theta^p$. We derive the same result in a toy scenario where the vacuum $\left \langle \Phi \right \rangle$ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale $k$ and provide a possible mechanism for differentiating EFT-motivated monodromy inflation from models where the angular shift symmetry is a gauge symmetry.

### No galaxy left behind: accurate measurements with the faintest objects in the Dark Energy Survey

Accurate statistical measurement with large imaging surveys has traditionally required throwing away a sizable fraction of the data. This is because most measurements have have relied on selecting nearly complete samples, where variations in the composition of the galaxy population with seeing, depth, or other survey characteristics are small. We introduce a new measurement method that aims to minimize this wastage, allowing precision measurement for any class of stars or galaxies detectable in an imaging survey. We have implemented our proposal in Balrog, a software package which embeds fake objects in real imaging in order to accurately characterize measurement biases. We demonstrate this technique with an angular clustering measurement using Dark Energy Survey (DES) data. We first show that recovery of our injected galaxies depends on a wide variety of survey characteristics in the same way as the real data. We then construct a flux-limited sample of the faintest galaxies in DES, chosen specifically for their sensitivity to depth and seeing variations. Using the synthetic galaxies as randoms in the standard Landy-Szalay correlation function estimator suppresses the effects of variable survey selection by at least two orders of magnitude. With this correction, our measured angular clustering is found to be in excellent agreement with that of a matched sample drawn from much deeper, higher-resolution space-based COSMOS imaging; over angular scales of $0.004^{\circ} < \theta < 0.2^{\circ}$, we find a best-fit scaling amplitude between the DES and COSMOS measurements of $1.00 \pm 0.09$. We expect this methodology to be broadly useful for extending the statistical reach of measurements in a wide variety of coming imaging surveys.

### Explaining the CMS excesses, baryogenesis and neutrino masses in $E_{6}$ motivated $U(1)_{N}$ model [Cross-Listing]

We study the superstring inspired $E_{6}$ model motivated $U(1)_{N}$ extension of the supersymmetric standard model to explore the possibility of explaining the recent excess CMS events and the baryon asymmetry of the universe in eight possible variants of the model. In light of the hints from short-baseline neutrino experiments at the existence of one or more light sterile neutrinos, we also study the neutrino mass matrices dictated by the field assignments and the discrete symmetries in these variants. We find that all the variants can explain the excess CMS events via the exotic slepton decay, while for a standard choice of the discrete symmetry four of the variants have the feature of allowing high scale baryogenesis (leptogenesis). For one other variant three body decay induced soft baryogenesis mechanism is possible which can induce baryon number violating neutron-antineutron oscillation. We also point out a new discrete symmetry which has the feature of ensuring proton stability and forbidding tree level flavor changing neutral current processes while allowing for the possibility of high scale leptogenesis for two of the variants. On the other hand, neutrino mass matrix of the $U(1)_{N}$ model variants naturally accommodates three active and two sterile neutrinos which acquire masses through their mixing with extra neutral fermions giving rise to interesting textures for neutrino masses.

### Explaining the CMS excesses, baryogenesis and neutrino masses in $E_{6}$ motivated $U(1)_{N}$ model [Cross-Listing]

We study the superstring inspired $E_{6}$ model motivated $U(1)_{N}$ extension of the supersymmetric standard model to explore the possibility of explaining the recent excess CMS events and the baryon asymmetry of the universe in eight possible variants of the model. In light of the hints from short-baseline neutrino experiments at the existence of one or more light sterile neutrinos, we also study the neutrino mass matrices dictated by the field assignments and the discrete symmetries in these variants. We find that all the variants can explain the excess CMS events via the exotic slepton decay, while for a standard choice of the discrete symmetry four of the variants have the feature of allowing high scale baryogenesis (leptogenesis). For one other variant three body decay induced soft baryogenesis mechanism is possible which can induce baryon number violating neutron-antineutron oscillation. We also point out a new discrete symmetry which has the feature of ensuring proton stability and forbidding tree level flavor changing neutral current processes while allowing for the possibility of high scale leptogenesis for two of the variants. On the other hand, neutrino mass matrix of the $U(1)_{N}$ model variants naturally accommodates three active and two sterile neutrinos which acquire masses through their mixing with extra neutral fermions giving rise to interesting textures for neutrino masses.

### Explaining the CMS excesses, baryogenesis and neutrino masses in $E_{6}$ motivated $U(1)_{N}$ model

We study the superstring inspired $E_{6}$ model motivated $U(1)_{N}$ extension of the supersymmetric standard model to explore the possibility of explaining the recent excess CMS events and the baryon asymmetry of the universe in eight possible variants of the model. In light of the hints from short-baseline neutrino experiments at the existence of one or more light sterile neutrinos, we also study the neutrino mass matrices dictated by the field assignments and the discrete symmetries in these variants. We find that all the variants can explain the excess CMS events via the exotic slepton decay, while for a standard choice of the discrete symmetry four of the variants have the feature of allowing high scale baryogenesis (leptogenesis). For one other variant three body decay induced soft baryogenesis mechanism is possible which can induce baryon number violating neutron-antineutron oscillation. We also point out a new discrete symmetry which has the feature of ensuring proton stability and forbidding tree level flavor changing neutral current processes while allowing for the possibility of high scale leptogenesis for two of the variants. On the other hand, neutrino mass matrix of the $U(1)_{N}$ model variants naturally accommodates three active and two sterile neutrinos which acquire masses through their mixing with extra neutral fermions giving rise to interesting textures for neutrino masses.

### Dark Matter, Shared Asymmetries, and Galactic Gamma Ray Signals

We introduce a novel dark matter scenario where the visible sector and the dark sector share a common asymmetry. The two sectors are connected through an unstable mediator with baryon number one, allowing the standard model baryon asymmetry to be shared with dark matter via semi-annihilation. The present-day abundance of dark matter is then set by thermal freeze-out of this semi-annihilation process, yielding an asymmetric version of the WIMP miracle as well as promising signals for indirect detection experiments. As a proof of concept, we find a viable region of parameter space consistent with the observed Fermi excess of GeV gamma rays from the galactic center.

### Dark Matter, Shared Asymmetries, and Galactic Gamma Ray Signals [Cross-Listing]

We introduce a novel dark matter scenario where the visible sector and the dark sector share a common asymmetry. The two sectors are connected through an unstable mediator with baryon number one, allowing the standard model baryon asymmetry to be shared with dark matter via semi-annihilation. The present-day abundance of dark matter is then set by thermal freeze-out of this semi-annihilation process, yielding an asymmetric version of the WIMP miracle as well as promising signals for indirect detection experiments. As a proof of concept, we find a viable region of parameter space consistent with the observed Fermi excess of GeV gamma rays from the galactic center.

### CMB Lensing and Scale Dependent New Physics

Cosmic microwave background lensing has become a new cosmological probe, carrying rich information on the matter power spectrum and distances over the redshift range $z\approx1$-4. We investigate the role of scale dependent new physics, such as from modified gravity, neutrino mass, and cold (low sound speed) dark energy, and its signature on CMB lensing. The distinction between different scale dependences, and the different redshift dependent weighting of the matter power spectrum entering into CMB lensing and other power spectra, imply that CMB lensing can probe simultaneously a diverse range of physics. We highlight the role of arcminute resolution polarization experiments for distinguishing between physical effects.

### HeCS-SZ: The Hectospec Survey of Sunyaev-Zeldovich Selected Clusters

We estimate cluster masses and velocity dispersions for 123 clusters from optical spectroscopy to compare the Sunyaev-Zeldovich (SZ) mass proxy and dynamical masses. Our new survey, HeCS-SZ (Hectospec Cluster Survey of SZ-selected clusters), includes 7,721 new or remeasured redshifts from MMT/Hectospec observations of 24 SZ-selected clusters at redshifts $z$=0.05-0.20 and not in previous surveys. We supplement the Hectospec data with spectra from the Sloan Digital Sky Survey (SDSS) and cluster data from the Cluster Infall Regions in SDSS (CIRS) project and the Hectospec Cluster Survey (HeCS), our Hectospec survey of clusters selected by X-ray flux. We measure the scaling relation between velocity dispersion and SZ mass estimates from the integrated Compton parameter for an SZ complete sample of 83 clusters. The observed relation agrees very well with a simple virial scaling from mass (based on SZ) to velocity dispersion. The SZ mass estimates (calibrated with hydrostatic X-ray mass estimates) are not significantly biased. Further, the velocity dispersion of cluster galaxies is consistent with the expected velocity dispersion of dark matter particles, indicating that galaxies are good dynamical tracers (i.e., velocity bias is small). Significant mass bias in SZ mass estimates could relieve tension between cosmological results from Planck SZ cluster counts and Planck CMB data. However, the excellent agreement between our measured velocity dispersions and those predicted from a virial scaling relation suggests that any SZ mass bias is too small to reconcile SZ and CMB results. In principle, SZ mass bias and velocity bias of galaxies could conspire to yield good agreement, but the required velocity bias is $\sigma_{galaxy}\approx 0.77\sigma_{DM}$, outside the range of plausible models of velocity bias in the literature.

### A Test of Cosmological Models using high-z Measurements of H(z) [Cross-Listing]

The recently constructed Hubble diagram using a combined sample of SNLS and SDSS-II Type Ia SNe, and an application of the Alcock-Paczynski (AP) test using model-independent Baryon Acoustic Oscillation data, have suggested that the principal constraint underlying the cosmic expansion is the total equation-of-state of the cosmic fluid, rather than that of its dark energy. These studies have focused on the critical redshift range (0 < z < 2) within which the transition from decelerated to accelerated expansion is thought to have occurred, and they suggest that the cosmic fluid has zero active mass, consistent with a constant expansion rate. The evident impact of this conclusion on cosmological theory calls for an independent confirmation. In this paper, we carry out this crucial one-on-one comparison between the R_h=ct Universe (an FRW cosmology with zero active mass) and wCDM/LCDM, using the latest high-z measurements of H(z). Whereas the Type Ia SNe yield the integrated luminosity distance, while the AP diagnostic tests the geometry of the Universe, the Hubble parameter directly samples the expansion rate itself. We find that the model-independent cosmic chronometer data prefer R_h}=ct over wCDM/LCDM with a BIC likelihood of ~95% versus only ~5%, in strong support of the earlier SNeIa and AP results. This contrasts with a recent analysis of H(z) data based solely on BAO measurements which, however, strongly depend on the assumed cosmology. We discuss why the latter approach is inappropriate for model comparisons, and emphasize again the need for truly model-independent observations to be used in cosmological tests.

### A Test of Cosmological Models using high-z Measurements of H(z)

The recently constructed Hubble diagram using a combined sample of SNLS and SDSS-II Type Ia SNe, and an application of the Alcock-Paczynski (AP) test using model-independent Baryon Acoustic Oscillation data, have suggested that the principal constraint underlying the cosmic expansion is the total equation-of-state of the cosmic fluid, rather than that of its dark energy. These studies have focused on the critical redshift range (0 < z < 2) within which the transition from decelerated to accelerated expansion is thought to have occurred, and they suggest that the cosmic fluid has zero active mass, consistent with a constant expansion rate. The evident impact of this conclusion on cosmological theory calls for an independent confirmation. In this paper, we carry out this crucial one-on-one comparison between the R_h=ct Universe (an FRW cosmology with zero active mass) and wCDM/LCDM, using the latest high-z measurements of H(z). Whereas the Type Ia SNe yield the integrated luminosity distance, while the AP diagnostic tests the geometry of the Universe, the Hubble parameter directly samples the expansion rate itself. We find that the model-independent cosmic chronometer data prefer R_h}=ct over wCDM/LCDM with a BIC likelihood of ~95% versus only ~5%, in strong support of the earlier SNeIa and AP results. This contrasts with a recent analysis of H(z) data based solely on BAO measurements which, however, strongly depend on the assumed cosmology. We discuss why the latter approach is inappropriate for model comparisons, and emphasize again the need for truly model-independent observations to be used in cosmological tests.

### Pure de Sitter Supergravity [Cross-Listing]

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

### Pure de Sitter Supergravity

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

### Pure de Sitter Supergravity [Cross-Listing]

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

### Pure de Sitter Supergravity [Cross-Listing]

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

### Light sterile neutrinos

The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, Gallium and LSND anomalies are briefly described and interpreted as indications of the existence of short-baseline oscillations which require the existence of light sterile neutrinos. The global fits of short-baseline oscillation data in 3+1 and 3+2 schemes are discussed, together with the implications for beta-decay and neutrinoless double-beta decay. The cosmological effects of light sterile neutrinos are briefly reviewed and the implications of existing cosmological data are discussed. The review concludes with a summary of future perspectives.

### Light sterile neutrinos [Cross-Listing]

The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, Gallium and LSND anomalies are briefly described and interpreted as indications of the existence of short-baseline oscillations which require the existence of light sterile neutrinos. The global fits of short-baseline oscillation data in 3+1 and 3+2 schemes are discussed, together with the implications for beta-decay and neutrinoless double-beta decay. The cosmological effects of light sterile neutrinos are briefly reviewed and the implications of existing cosmological data are discussed. The review concludes with a summary of future perspectives.

### Light sterile neutrinos [Cross-Listing]

The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, Gallium and LSND anomalies are briefly described and interpreted as indications of the existence of short-baseline oscillations which require the existence of light sterile neutrinos. The global fits of short-baseline oscillation data in 3+1 and 3+2 schemes are discussed, together with the implications for beta-decay and neutrinoless double-beta decay. The cosmological effects of light sterile neutrinos are briefly reviewed and the implications of existing cosmological data are discussed. The review concludes with a summary of future perspectives.

### The near-infrared radiation background, gravitational wave background and star formation rate of Pop III and Pop II during cosmic reionization

In this paper, we obtain the NIRB and SBGWs from the early stars, which are constrained by the observation of reionization and star formation rate. We study the transition from Pop III to Pop II stars via the star formation model of different population, which takes into account the reionization and the metal enrichment evolution. We calculate the two main metal pollution channels arising from the supernova-driven protogalactic outflows and "genetic channel". We obtain the SFRs of Pop III and Pop II and their NIRB and SBGWs radiation. We predict that the upper limit of metallicity in metal-enriched IGM (the galaxies whose polluted via "genetic channel") reaches $Z_{\rm crit}=10^{-3.5}Z_{\odot}$ at $z\sim13$ ($z\sim11$), which is consistent with our star formation model. We constrain on the SFR of Pop III stars from the observation of reionization. The peak intensity of NIRB is about $0.03-0.2~nW m^{-2}{sr}^{-1}$ at $\sim 1 \mu m$ for $z>6$. The prediction of NIRB signal is consistent with the metallicity evolution. We also obtain the gravitational wave background from the black holes formed by these early stars. The predicted gravitational wave background has a peak amplitude of $\Omega_{GW}\simeq8\times10^{-9}$ at $\nu=158$ Hz for Pop II star remnants. However, the background generated by Pop III.2 stars is much less than Pop II stars, with a peak amplitude of $\Omega_{GW}\simeq1.2\times10^{-11}$ at $\nu=28~Hz$. The background of Pop III.1 shifts to lower frequencies, and the amplitude of $\Omega _{GW}$ for Pop III.1 stars shows a minimum value at $\nu\simeq 10$ Hz, due to the lack of gravitational wave signals from the stars with $140~M_{\odot}<M_\ast<260~M_{\odot}$.

### Running of the scalar spectral index in bouncing cosmologies [Cross-Listing]

We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.

### Running of the scalar spectral index in bouncing cosmologies

We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.

### Running of the scalar spectral index in bouncing cosmologies [Cross-Listing]

We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.

### Clustering and Bias Measurements of SDSS Voids

Using a void catalog from the SDSS survey, we present the first measurements of void clustering and the corresponding void bias. Over the range 30-200 Mpc/h the void auto-correlation is detected at 5-sigma significance for voids of radius 15-20 Mpc/h. We also measure the void-galaxy cross-correlation at higher signal-to-noise and compare the inferred void bias with the autocorrelation results. Void bias is constant with scale for voids of a given size, but its value falls from 5.6 +/- 1.0 to below zero as the void radius increases from 15 to 30 Mpc/h. The comparison of our measurements with carefully matched galaxy mock catalogs, with no free parameters related to the voids, shows that model predictions can be reliably made for void correlations. We study the dependence of void bias on tracer density and void size with a view to future applications. In combination with our previous lensing measurements of void mass profiles, these clustering measurements provide another step towards using voids as cosmological tracers.

### Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs et al. 2014 that give an LMC distance modulus of (m-M)_{0}=18.49 \pm 0.13 (median and 1\sigma symmetrized error). Central estimates found from weighted mean and median statistics are used to construct the error distributions. The weighted mean error distribution is non-Gaussian — flatter and broader than Gaussian — with more (less) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of unaccounted-for systematic uncertainties. The median statistics error distribution, which does not make use of the individual measurement errors, is also non-Gaussian — more peaked than Gaussian — with less (more) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of publication bias and/or the non-independence of the measurements.

### Lens galaxies in the Illustris simulation: power-law models and the bias of the Hubble constant from time-delays

The combination of dynamical and strong gravitational lensing studies of massive galaxies shows that their total density profile in the central region (i.e. up to a few half-light radius) can be described by a power law, $\rho(r)\propto r^{-\gamma}$. Therefore, such a power-law model is employed for a large number of strong-lensing applications, including the so-called time-delay technique used to infer the Hubble constant $H_0$. However, since the radial scale at which strong lensing features are formed (i.e., the Einstein radius) corresponds to the transition from the dominance of baryonic matter to dark matter, there is no known reason why galaxies should follow a power law in density. The assumption of a power law artificially breaks the mass-sheet degeneracy, a well-known invariance transformation in gravitational lensing which affects the product of Hubble constant and time delay and can therefore cause a bias in the determination of $H_0$ from the time-delay technique. In this paper, we use the Illustris hydrodynamical simulations to estimate the amplitude of this bias, and to understand how it is related to observational properties of galaxies. Investigating a large sample of Illustris galaxies that have velocity dispersion $\sigma_{\rm SIE} \geqslant 160$ km/s at redshifts below $z=1$, we find that the bias on $H_0$ introduced by the power-law assumption can reach 20%-50%, with a scatter of 10%-30% (rms). However, we find that by selecting galaxies with an inferred power-law model slope close to isothermal, it is possible to reduce the bias on $H_0$ to <5%, and the scatter to <10%. This could potentially be used to form less biased statistical samples for $H_0$ measurements in the upcoming large survey era.

### A rise in the ionizing photons in star-forming galaxies over the past 5 billion years

We investigate the change in ionizing photons in galaxies between 0.2<z<0.6 using the F2 field of the SHELS complete galaxy redshift survey. We show, for the first time, that while the [OIII]/Hb and [OIII]/[OII] ratios rise, the [NII]/H-alpha and [SII]/H-alpha ratios fall significantly over the 0.2<z<0.35 redshift range for stellar masses between 9.2<log(M/Msun)<10.6. The [OIII]/H-beta and [OIII]/[OII] ratios continue to rise across the full 0.2<z<0.6 redshift range for stellar masses between 9.8<log(M/Msun)<10.0. We conclusively rule out AGN contamination, a changing ISM pressure, and a change in the hardness of the EUV radiation field as the cause of the change in the line ratios between 0.2<z<0.35. We find that the ionization parameter rises significantly with redshift (by 0.1 to 0.25 dex depending on the stellar mass of the sample). We show that the ionization parameter is strongly correlated with the fraction of young-to-old stars, as traced by the H-beta equivalent width. We discuss the implications of this result on higher redshift studies, and we consider the implications on the use of standard optical metallicity diagnostics at high redshift.

### The Megamaser Cosmology Project. VII. Investigating disk physics using spectral monitoring observations

We use single-dish radio spectra of known 22 GHz H$_2$O megamasers, primarily gathered from the large dataset observed by the Megamaser Cosmology Project, to identify Keplerian accretion disks and to investigate several aspects of the disk physics. We test a mechanism for maser excitation proposed by Maoz & McKee (1998), whereby population inversion arises in gas behind spiral shocks traveling through the disk. Though the flux of redshifted features is larger on average than that of blueshifted features, in support of the model, the high-velocity features show none of the predicted systematic velocity drifts. We find rapid intra-day variability in the maser spectrum of ESO 558-G009 that is likely the result of interstellar scintillation, for which we favor a nearby ($D \approx 70$ pc) scattering screen. In a search for reverberation in six well-sampled sources, we find that any radially-propagating signal must be contributing $\lesssim$10% of the total variability. We also set limits on the magnetic field strengths in seven sources, using strong flaring events to check for the presence of Zeeman splitting. These limits are typically 200–300 mG ($1\sigma$), but our most stringent limits reach down to 73 mG for the galaxy NGC 1194.