• #### Light Dark Matter: Models and Constraints

We study the direct detection prospects for a representative set of simplified models of sub-GeV dark matter (DM), accounting for existing terrestrial, astrophysical and cosmological constraints. We focus on dark matter lighter than an MeV, where these constraints are most stringent, and find three scenarios with accessible direct detection cross sections: (i) DM interacting via an ultralight kinetically mixed dark photon, (ii) a DM sub-component interacting with nucleons or electrons through a light scalar or vector mediator, and (iii) DM coupled with nucleons via a mediator heavier than ~ 100 keV.
Dark matterStandard ModelBig bang nucleosynthesisDark sectorLight mediatorThermalisationHidden photonDegree of freedomRed giantStar...
• #### Particle-hole symmetry and composite fermions in fractional quantum Hall states

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write down an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi liquid description, we demonstrate the appearance of the Girvin--Macdonlald--Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the HLR theory is particle-hole symmetric, correlation functions obtained from HLR are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the HLR theory violate it.
Particle-hole symmetryFractional quantum Hall stateComposite fermionsDirac fermionTwo-point correlation functionFermi liquidFilling fractionGalilean invarianceEffective field theoryTheory...
• #### The Mass Profile and Accretion History of Cold Dark Matter Halos

We use the Millennium Simulation series to study the relation between the accretion history (MAH) and mass profile of cold dark matter halos. We find that the mean density within the scale radius, r_{-2} (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the main progenitor's virial mass equals the mass enclosed within r_{-2}. Scaled to these characteristic values of mass and density, the mean MAH, expressed in terms of the critical density of the Universe, M(\rho_{crit}(z)), resembles that of the enclosed density profile, M(<\rho >), at z=0. Both follow closely the NFW profile, suggesting that the similarity of halo mass profiles originates from the mass-independence of halo MAHs. Support for this interpretation is provided by outlier halos whose accretion histories deviate from the NFW shape; their mass profiles show correlated deviations from NFW and are better approximated by Einasto profiles. Fitting both M(<\rho >) and M(\rho_{crit}) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work linking the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only halos whose accretion histories differ greatly from the NFW shape show noticeable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter halos, which do not form hierarchically, and for fluctuation power spectra other than CDM. Our findings, however, predict a subtle but systematic dependence of mass profile shape on accretion history which, if confirmed, would provide strong support for the link between accretion history and halo structure we propose here.
Navarro-Frenk-White profileAccretionVirial massEinasto profileMass profileCritical densityDark matter haloCold dark matterMean mass densityHalo accretion history...
• #### The Mass-Concentration-Redshift Relation of Cold Dark Matter Halos

We use the Millennium Simulation series to investigate the mass and redshift dependence of the concentration of equilibrium cold dark matter (CDM) halos. We extend earlier work on the relation between halo mass profiles and assembly histories to show how the latter may be used to predict concentrations for halos of all masses and at any redshift. Our results clarify the link between concentration and the collapse redshift'' of a halo as well as why concentration depends on mass and redshift solely through the dimensionless peak height'' mass parameter, $\nu(M,z)=\delta_{\rm crit}(z)/\sigma(M,z)$. We combine these results with analytic mass accretion histories to extrapolate the $c(M,z)$ relations to mass regimes difficult to reach through direct simulation. Our model predicts that, at given $z$, $c(M)$ should deviate systematically from a simple power law at high masses, where concentrations approach a constant value, and at low masses, where concentrations are substantially lower than expected from extrapolating published empirical fits. This correction may reduce the expected self-annihilation boost factor from substructure by about one order of magnitude. The model also reproduces the $c(M,z)$ dependence on cosmological parameters reported in earlier work, and thus provides a simple and robust account of the relation between cosmology and the mass-concentration-redshift relation of CDM halos.
Halo accretion historyNavarro-Frenk-White profileVirial massMass profileCold dark matterConcentration-mass relationCosmological parametersAccretionCosmologyMillennium Run...
• #### High-redshift post-reionisation cosmology with 21cm intensity mapping

We investigate the possibility of performing cosmological studies in the redshift range $2.5<z<5$ through suitable extensions of existing and upcoming radio-telescopes like CHIME, HIRAX and FAST. We use the Fisher matrix technique to forecast the bounds that those instruments can place on the growth rate, the Alcock-Paczynski parameters, the sum of the neutrino masses and the number of relativistic degrees of freedom at decoupling, $N_{\rm eff}$. We point out that quantities that depend on the amplitude of the 21cm power spectrum, like $f\sigma_8$, are completely degenerate with $\Omega_{\rm HI}$ and $b_{\rm HI}$, and propose several strategies to independently constraint them through cross-correlations with other probes. Assuming $5\%$ priors on $\Omega_{\rm HI}$ and $b_{\rm HI}$, $k_{\rm max}=0.2~h{\rm Mpc}^{-1}$ and the primary beam wedge, we find that a HIRAX extension can constrain, within bins of $\Delta z=0.1$: 1) the value of $f\sigma_8$ at $\simeq4\%$, 2) the value of $D_A$ and $H$ at $\simeq1\%$. In combination with data from Euclid-like galaxy surveys and CMB S4, the sum of the neutrino masses can be constrained with an error equal to $23$ meV ($1\sigma$), while $N_{\rm eff}$ can be constrained within 0.02 ($1\sigma$). We derive similar constraints for the extensions of the other instruments. We study in detail the dependence of our results on the instrument, amplitude of the HI bias, the foreground wedge coverage, the nonlinear scale used in the analysis, uncertainties in the theoretical modeling and the priors on $b_{\rm HI}$ and $\Omega_{\rm HI}$. We conclude that 21cm intensity mapping surveys operating in this redshift range can provide extremely competitive constraints on key cosmological parameters.
Neutrino massLine intensity mappingFisher information matrixGalaxyCosmological parametersEuclid missionLarge scale structure surveyBaryon acoustic oscillationsRedshift-space distortionRedshift bins...
• #### The impact of ultra-light axion self-interactions on the large scale structure of the Universe

Ultra-light axions have sparked attention because their tiny mass $m\sim 10^{-22}$ eV, which leads to a Kiloparsec-scale de Broglie wavelength comparable to the size of dwarf galaxy, could alleviate the so-called small-scale crisis of massive cold dark matter (CDM) candidates.However, recent analyses of the Lyman-$\alpha$ forest power spectrum set a tight lower bound on their mass of $m\gtrsim 10^{-21}$ eV which makes them much less relevant from an astrophysical point of view. An important caveat to these numerical studies is that they do not take into account attractive self-interactions among ultra-light axions, which can counteract the quantum "pressure" induced by the strong delocalization of the particles. In this work, we show that even a tiny attractive interaction among ultra-light axions can have a significant impact on the stability of cosmic structures at low redshift. After a brief review of known results about solitons in the absence of gravity, we discuss the stability of filamentary and pancake-like solutions when quantum pressure, attractive interactions and gravity are present. The analysis based on one degree of freedom, namely the breathing mode, reveals that pancakes are stable, while filaments are unstable if the mass per unit length is larger than a critical value. However, we show that pancakes are unstable against transverse perturbations. We expect this to be true for halos and filaments as well. Finally, we also assess whether these instabilities can leave a detectable signature in the Lyman-$\alpha$ forest. We find that unstable filaments could be seen as absorption lines with column densities of neutral hydrogen $N_\text{HI}\lesssim 10^{17}$ cm$^{-2}$ even for an axion decay constant as large as $f\lesssim 10^{16}$ GeV. We hope our work motivates future numerical studies of the impact of axion self-interactions on cosmic structure formation.
SolitonAxionHamiltonianDark matterLyman-alpha forestInstabilityCold dark matterLight bosonIntergalactic mediumLarge scale structure...
• #### Characteristics of Chiral Anomaly in View of Various Applications

In view of the recent applications of chiral anomaly to various fields beyond particle physics, we discuss some basic aspects of chiral anomaly which may help deepen our understanding of chiral anomaly in particle physics also. It is first shown that Berry's phase for the Weyl model $H =v_{F} \vec{\sigma}\cdot \vec{p}(t)$ assumes a monopole form at the exact adiabatic limit but deviates from it off the adiabatic limit and vanishes quadratically $\sim 1/\omega^{2}$ in the high frequency limit of the Fourier transform of $\vec{p}(t)$. An effective action which is consistent with the non-adiabatic limit of Berry's phase and BJL prescription gives normal equal-time space-time commutators and no chiral anomaly. In contrast, an effective action with a monopole at the origin of the momentum space, which describes Berry's phase in the precise adiabatic limit but fails off the adiabatic limit, gives anomalous space-time commutators and a covariant anomaly to the gauge current. We regard this anomaly as an artifact of the postulated monopole and not a consequence of Berry's phase. As for the recent application of the chiral anomaly to the description of effective Weyl fermions in condensed matter and nuclear physics, which is closely related to the formulation of lattice chiral fermions, we point out that the chiral anomaly for each species doubler separately vanishes for a finite lattice spacing, contrary to the common assumption. Instead a general form of pair creation associated with the spectral flow for the Dirac sea with finite depth takes place. This view is supported by the Ginsparg-Wilson fermion, which defines a single Weyl fermion without doublers on the lattice and gives a well-defined index (anomaly) even for a finite lattice spacing. A different use of anomaly in analogy to PCAC is also mentioned, which could lead to an effect without fermion number non-conservation.
Quantum anomalyChiral anomalyBerry phaseMagnetic monopoleMomentum spaceWeyl fermionSpectral flowGinsparg-Wilson fermionWilson fermionEffective action...
• #### Spacetime and Euclidean Geometryver. 2

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
• #### The variance of dispersion measure of high-redshift transient objects as a probe of ionized bubble size during reionization

The dispersion measure (DM) of high-redshift $(z \gtrsim 6)$ transient objects such as Fast Radio Bursts can be a powerful tool to probe the intergalactic medium during the Epoch of Reionization. In this paper, we study the variance of the DMs of objects with the same redshift as a potential probe of the size distribution of ionized bubbles. We calculate the DM variance with a simple model with randomly-distributed spherical bubbles. It is found that the DM variance reflects the characteristics of the probability distribution of the bubble size. We find the variance can be measured precisely enough to obtain the information on the typical size with a few hundred sources at a single redshift.
Dispersion measureFast Radio BurstsReionizationEpoch of reionizationIntergalactic mediumLine of sightGalaxyNumerical simulationHost galaxyQuasar...
• #### An Overview of the MHONGOOSE Survey: Observing Nearby Galaxies with MeerKAT

MHONGOOSE is a deep survey of the neutral hydrogen distribution in a representative sample of 30 nearby disk and dwarf galaxies with HI masses from 10^6 to ~10^{11} M_sun, and luminosities from M_R ~ -12 to M_R ~ -22. The sample is selected to uniformly cover the available range in log(M_HI). Our extremely deep observations, down to HI column density limits of well below 10^{18} cm^{-2} - or a few hundred times fainter than the typical HI disks in galaxies - will directly detect the effects of cold accretion from the intergalactic medium and the links with the cosmic web. These observations will be the first ever to probe the very low-column density neutral gas in galaxies at these high resolutions. Combination with data at other wavelengths, most of it already available, will enable accurate modelling of the properties and evolution of the mass components in these galaxies and link these with the effects of environment, dark matter distribution, and other fundamental properties such as halo mass and angular momentum. MHONGOOSE can already start addressing some of the SKA-1 science goals and will provide a comprehensive inventory of the processes driving the transformation and evolution of galaxies in the nearby universe at high resolution and over 5 orders of magnitude in column density. It will be a Nearby Galaxies Legacy Survey that will be unsurpassed until the advent of the SKA, and can serve as a highly visible, lasting statement of MeerKAT's capabilities.
GalaxyMeerKATStar formationAccretionNearby galaxiesTHINGS surveyIntergalactic mediumCosmic webSquare Kilometre ArrayInterstellar medium...
• #### Using spin to understand the formation of LIGO's black holes

With the detection of four candidate binary black hole (BBH) mergers by the Advanced LIGO detectors thus far, it is becoming possible to constrain the properties of the BBH merger population in order to better understand the formation of these systems. Black hole (BH) spin orientations are one of the cleanest discriminators of formation history, with BHs in dynamically formed binaries in dense stellar environments expected to have spins distributed isotropically, in contrast to isolated populations where stellar evolution is expected to induce BH spins preferentially aligned with the orbital angular momentum. In this work we propose a simple, model-agnostic approach to characterizing the spin properties of LIGO's BBH population. Using measurements of the effective spin of the binaries, which is LIGO's best constrained spin parameter, we introduce a simple parameter to quantify the fraction of the population that is isotropically distributed, regardless of the spin magnitude distribution of the population. Once the orientation characteristics of the population have been determined, we show how measurements of effective spin can be used to directly constrain the underlying BH spin magnitude distribution. Although we find that the majority of the current effective spin measurements are too small to be informative, with LIGO's four BBH candidates we find a slight preference for an underlying population with aligned spins over one with isotropic spins (with an odds ratio of 1.1). We argue that it will be possible to distinguish symmetric and anti-symmetric populations at high confidence with tens of additional detections, although mixed populations may take significantly more detections to disentangle. We also derive preliminary spin magnitude distributions for LIGO's black holes, under the assumption of aligned or isotropic populations.
Laser Interferometer Gravitational-Wave ObservatoryBinary black hole systemBlack holeBlack hole spinOdds ratioOrbital angular momentum of lightOrientationLIGO GW151226 eventGravitational waveSpin orientation...
• #### Distance measures in gravitational-wave astrophysics and cosmology

We present quantities which characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances. In particular, we introduce and generalize the horizon, range, response, and reach distances. These quantities incorporate a number of important effects, including cosmologically well-defined distances and volumes, cosmological redshift, cosmological time dilation, and rate density evolution. In addition, these quantities incorporate unique aspects of gravitational wave detectors, such as the variable sky sensitivity of the detectors and the scaling of the sensitivity with inverse distance. An online calculator (http://gwc.rcc.uchicago.edu) and python notebook (https://github.com/hsinyuc/distancetool) to determine GW distances are available. We provide answers to the question: "How far can gravitational-wave detectors hear?"
FramesHorizonLuminosity distanceInclinationOrientationStar formation rateGravitational wave detectorGravitational waveLaser Interferometer Gravitational-Wave ObservatoryTime dilation...

In this paper, we introduce and investigate monadic NM-algebras: a variety of NM-algebras equipped with universal quantifiers. Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. Besides, we show that the variety of monadic NM-algebras faithfully the axioms on quantifiers in monadic predicate NM logic. Furthermore, we discuss relations between monadic NM-algebras and some related structures, likeness modal NM-algebras and rough approximation spaces. In addition, we investigate monadic filters in monadic NM-algebras. In particular, we characterize simple and subdirectly irreducible monadic NM-algebras and obtain a representation theorem for monadic NM-algebras. Finally, we present monadic NM-logic and prove the (chain) completeness of monadic NM-logic based on monadic NM-algebras. These results constitute a crucial first step for providing a solid algebraic foundation for the monadic predicate NM logic.
Boolean algebraCompletenessFuzzy logicMessier 5Residuated latticeDouble negationAlgebraic semanticsNilpotentMonoidMessier 4...
• #### How to confirm the existence of population III stars by observations of gravitational waves

We propose a method for confirmation of the existence of Population III (Pop III) stars with massive black hole binaries as GW150914 in gravitational wave (GW) observation. When we get enough number of events, we want to determine which model is closer to reality, with and without Pop III stars. We need to prepare various "Pop I/II models" and various "Pop I/II/III models" and investigate which model is consistent with the events. To demonstrate our analysis, we simulate detections of GW events for some examples of population synthesis models with and without Pop III stars. We calculate the likelihood ratio with the realistic number of events and evaluate the probability of identifying the existence of Pop III stars. In typical cases, our analysis can distinguish between Pop I/II model and Pop I/II/III model with 90% probability by 22 GW signals from black hole-black hole binary mergers.
Gravitational waveStarInitial mass functionPopulation IIIStandard ModelSignal to noise ratioMass distributionStar formation ratePopulation IBlack hole...
• #### The Mass-Concentration-Redshift Relation of Cold and Warm Dark Matter Halosver. 2

We use a suite of cosmological simulations to study the mass-concentration-redshift relation, $c({\rm M},z)$, of dark matter halos. Our simulations include standard $\Lambda$-cold dark matter (CDM) models, and additional runs with truncated power spectra, consistent with a thermal warm dark matter (WDM) scenario. We find that the mass profiles of CDM and WDM halos are self-similar and well approximated by the Einasto profile. The $c({\rm M},z)$ relation of CDM halos is monotonic: concentrations decrease with increasing virial mass at fixed redshift, and decrease with increasing redshift at fixed mass. The mass accretion histories (MAHs) of CDM halos are also scale-free, and can be used to infer concentrations directly. These results do not apply to WDM halos: their MAHs are not scale-free because of the characteristic scale imposed by the power-spectrum suppression. Further, the WDM $c({\rm M},z)$ relation is non-monotonic: concentrations peak at a mass scale dictated by the truncation scale, and decrease at higher and lower masses. We show that the assembly history of a halo can still be used to infer its concentration, provided that the total mass of its progenitors is considered (the "collapsed mass history"; CMH), rather than just that of its main ancestor. This exploits the scale-free nature of CMHs to derive a simple scaling that reproduces the mass-concentration-redshift relation of both CDM and WDM halos over a vast range of halo masses and redshifts. Our model therefore provides a robust account of the mass, redshift, cosmology and power spectrum dependence of dark matter halo concentrations.
Cold dark matterWarm dark matterHalo accretion historyVirial massMass profileNavarro-Frenk-White profileDark matter haloConcentration-mass relationCosmologyHalo concentrations...
• #### Dynamical quantum phase transitions: a review

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research.
QuenchingHamiltonianPhase transitionsQuantum phase transitionPartition functionRenormalization groupLoschmidt echoMany-body systemsTrapped ionEntanglement...
• #### Renormalization of the strongly attractive inverse square potential: Taming the singularityver. 3

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0 to 1/4. This prevents the oscillations form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states).
RenormalizationRegularization schemeHamiltonianCritical valueRegularizationBound stateWavefunctionQuantum anomalyPotentialEnergy...
• #### Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length

We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically the s-wave bound states equation in terms of Heun's functions. We discuss in detail the bound states spectrum for a specific form of the generalized uncertainty relation. The minimal length may be interpreted as characterizing the dimension of the system.
Quantum mechanicsRegularizationBound stateHeun functionMomentum spaceHypergeometric functionS-waveQuantizationHydrogen atomHamiltonian...
• #### The Renormalization Group Limit Cycle for the 1/r^2 Potential

Previous work has shown that if an attractive 1/r^2 potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be a continuous function of the short-distance cutoff R, but it can also be a log-periodic function of R with finite discontinuities, corresponding to a renormalization group (RG) limit cycle. We consider the regularization with a delta-shell potential. In this case, the coupling constant is uniquely determined to be a log-periodic function of R with infinite discontinuities, and an RG limit cycle is unavoidable. In general, a regularization with an RG limit cycle is selected as the correct renormalization of the 1/r^2 potential by the conditions that the cutoff radius R can be made arbitrarily small and that physical observables are reproduced accurately at all energies much less than hbar^2/mR^2.
Renormalization groupRenormalizationBound stateRegularizationCoupling constantWavefunctionCritical valueQuantum chromodynamicsQuantum mechanicsScale factor...
• #### Anomaly in conformal quantum mechanics: From molecular physics to black holesver. 2

A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of dimensional scales, and an SO(2,1) symmetry algebra. Examples from molecular physics to black holes are provided and discussed within a unified treatment. When such systems are physically realized in the appropriate strong-coupling regime,the occurrence of quantum symmetry breaking is possible. This anomaly is revealed by the failure of the symmetry generators to close the algebra in a manner shown to be independent of the renormalization procedure.
RenormalizationBlack holeHorizonQuantum mechanicsBound stateHamiltonianSymmetry breakingConformal invarianceRegularizationExpectation Value...
• #### Solving differential equations for Feynman integrals by expansions near singular points

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. nontrivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer implementation of our algorithm in a simple example of four-loop generalized sun-set integrals with three equal non-zero masses. Our code provides values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter $\epsilon$.
Path integralPolylogarithmRegularizationComplex planeSunIterated integralElliptic functionPropagatorComputer algebra systemColumn vector...
• #### KiDS-450: Cosmological Constraints from Weak Lensing Peak Statistics-I: Inference from Analytical Prediction of high Signal-to-Noise Ratio Convergence Peaks

This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using $\sim 450~\rm deg^2$ of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: $\nu$) weak lensing convergence peaks in the range of $3<\nu<5$, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate the impacts of other potential astrophysical systematics including the projection effects of large scale structures, intrinsic galaxy alignments, as well as residual measurement uncertainties in the shear and redshift calibration. Assuming a flat $\Lambda$CDM model, we find constraints for $S_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.5}=0.746^{+0.046}_{-0.107}$ according to the degeneracy direction of the cosmic shear analysis and $\Sigma_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.38}=0.696^{+0.048}_{-0.050}$ based on the derived degeneracy direction of our high-SNR peak statistics. The difference between the power index of $S_{\rm 8}$ and in $\Sigma_{\rm 8}$ indicates that combining the two probes has the potential to break the degeneracy in $\sigma_{\rm 8}$ and $\Omega_{\rm m}$. Our results are consistent with the cosmic shear tomographic correlation analysis of the same dataset and $\sim 2\sigma$ lower than the Planck 2016 results.
Weak lensingKiDS surveySignal to noise ratioGalaxyCosmic shearStatisticsLarge scale structureDark matter haloCosmological constraintsPlanck mission...
• #### An effective description of dark energy: from theory to phenomenology

In the last decades, a cosmological model that fits observations through a vast range of scales emerged. It goes under the name of ${\Lambda}$CDM. However, there are still challenging questions that remain unanswered by this model, such as what causes the observed accelerated expansion of the universe, and many alternatives have been proposed. This thesis concerns an approach to test such models known as "Effective Theory of Dark Energy" . It applies to all models where general relativity is modified by adding a single scalar degree of freedom, called "scalar-tensor theories". In Chapter 1 I summarise the most general class of such theories currently known, called "Degenerate higher-Order Scalar-Tensor" (DHOST) theories. In Chapter 2, I introduce the effective theory of dark energy. The inclusion of a general coupling between matter and the gravitational sector is the subject of Chapter 3. Chapter 4 analyses in details the stability of different classes of theories. Notably, I show that the most general class of theories free from instabilities reduces to the so-called Horndeski and beyond-Horndeski theories, up to a non minimal coupling to matter. Another goal of the thesis is to study the observable effects of deviations from ${\Lambda}$CDM. In Chapter 5, I consider the possibility of an interaction between dark matter and dark energy and I analyse the constraining power of future surveys on the free parameters of the theory. Chapter 6 focuses on the observational effects of theories where a kinetic mixing between matter and the scalar field exists. This gives a peculiar and potentially observable effect, namely the weakening of gravity at large scale structure scales.
Degree of freedomScalar fieldDark energyEffective theoryHamiltonianExtrinsic curvatureInstabilityCosmological perturbationsCovariant derivativeFoliation...
• #### DeepSetNet: Predicting Sets with Deep Neural Networksver. 5

This paper addresses the task of set prediction using deep learning. This is important because the output of many computer vision tasks, including image tagging and object detection, are naturally expressed as sets of entities rather than vectors. As opposed to a vector, the size of a set is not fixed in advance, and it is invariant to the ordering of entities within it. We define a likelihood for a set distribution and learn its parameters using a deep neural network. We also derive a loss for predicting a discrete distribution corresponding to set cardinality. Set prediction is demonstrated on the problem of multi-class image classification. Moreover, we show that the proposed cardinality loss can also trivially be applied to the tasks of object counting and pedestrian detection. Our approach outperforms existing methods in all three cases on standard datasets.
ClassificationDeep Neural NetworksCountingArchitectureF1 scoreTraining setPoisson distributionGround truthDeep learningObject detection...
• #### Symmetry properties of finite sums involving generalized Fibonacci numbers

We extend a result of I. J. Good and prove more symmetry properties of sums involving generalized Fibonacci numbers
NonnegativeLucas numberTelescopingSymmetry...
• #### The large scale impact of offshore windfarm structures on pelagic primary production in the southern North Sea

The increasing demand for renewable energy is projected to result in a 40-fold increase in offshore wind electricity in the European Union by~2030. Despite a great number of local impact studies for selected marine populations, the regional ecosystem impacts of offshore windfarm structures are not yet well investigated nor understood. Our study investigates whether the accumulation of epifauna, dominated by the filter feeder \mytilus{}, on turbine structures affects pelagic primary production and ecosystem functioning in the southern North Sea. We estimate the anthropogenically increased potential distribution based on the current projections of turbine locations and understanding of \species{M.~edulis} settlement patterns. This distribution is integrated through the Modular Coupling System for Shelves and Coasts to state-of-the-art hydrodynamic and ecosystem models. Our simulations reveal non-negligible changes in regional annual primary production of up to a few percent, and larger changes (up to $\pm10\%$) of the phytoplankton stock, and thus water clarity, during the bloom period. Our setup and modular coupling are effective tools for system scale studies of other environmental changes arising from large-scale offshore wind-farming such as ocean physics and distribution of pelagic top predators.
EcosystemsAbundanceWind turbineFluid dynamicsClimateRemote sensingFar-fieldTime SeriesSoftwarePhysical layer...
• #### The Physics and Mathematics of the Second Law of Thermodynamicsver. 2

The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of `hotness' is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.
• #### Thermal Dark Matter Through the Dirac Neutrino Portal

We study a simple model of thermal dark matter annihilating to standard model neutrinos via the neutrino portal. A (pseudo-)Dirac sterile neutrino serves as a mediator between the visible and the dark sectors, while an approximate lepton number symmetry allows for a large neutrino Yukawa coupling and, in turn, efficient dark matter annihilation. The dark sector consists of two particles, a Dirac fermion and complex scalar, charged under a symmetry that ensures the stability of the dark matter. A generic prediction of the model is a sterile neutrino with a large active-sterile mixing angle that decays primarily invisibly. We derive existing constraints and future projections from direct detection experiments, colliders, rare meson and tau decays, electroweak precision tests, and small scale structure observations. Along with these phenomenological tests, we investigate the consequences of perturbativity and scalar mass fine tuning on the model parameter space. A simple, conservative scheme to confront the various tests with the thermal relic target is outlined, and we demonstrate that much of the cosmologically-motivated parameter space is already constrained. We also identify new probes of this scenario such as multi-body kaon decays and Drell-Yan production of $W$ bosons at the LHC.
Dark matterNeutrinoSterile neutrinoMixing angleDark sectorStandard ModelNeutrino massDark matter annihilationDark matter particle massCollider...
• #### Derivation of the Complex Unit Sphere and its Hyperbolic Analoguever. 5

We present the derivation of the 6-dimensional Eulerian Lie group of the form SO(3,C). We describe our derivation process, which involves creation of finite group by using permutation matrices, and the exponentiation of the adjoint representation of the subset representing the generators of the finite group. We take clues from the 2-dimensional complex rotation matrix to present, what we believe, is a true representation of the Lie group for the six-dimensional complex unit sphere and proceed to study its dynamics. We also derive the 6-dimensional form of the hyperbolic Lie group representing the higher dimensional exponential, apply this to special relativity considerations, and show its relation to its Eulerian counterpart. With this approach, we discover a profound link with SO(3,C) and SO(3,3) and proceed to show the isomorphism to the Lie group SU(3). The following findings will likely prove useful in mathematical physics, complex analysis and applications in deriving higher dimensional forms of similar division algebras.
PermutationDivision algebraIsomorphismSpecial relativityLie groupUnitsComplex analysisSU(3)...
• #### Chiral Symmetry and Lattice Fermionsver. 2

The subject of these summer school lectures are (i) Chiral symmetry; (ii) Anomalies; (iii) Domain wall fermions; (iv) Overlap fermions and the Ginsparg-Wilson equation
Chiral symmetryQuantum anomalyDomain wallGauge fieldWeyl fermionDirac fermionFermion massStandard ModelLattice FermionChirality...
• #### Wolfgang Pauli 1900 to 1930: His Early Physics in Jungian Perspective

Wolfgang Pauli's philosophy and physics were intertwined. His philosophy was a variety of Platonism, in which Pauli's affiliation with Carl Jung formed an integral part, but Pauli's philosophical explorations in physics appeared before he met Jung. Jung validated Pauli's psycho-philosophical perspective. Thus, the roots of Pauli's physics and philosophy are important in the history of modern physics. In his early physics, Pauli attempted to ground his theoretical physics in positivism. He then began instead to trust his intuitive visualizations of entities that formed an underlying reality to the sensible physical world. These visualizations included holistic kernels of mathematical-physical entities that later became for him synonymous with Jung's mandalas. I have connected Pauli's visualization patterns in physics during the period 1900 to 1930 to the psychological philosophy of Jung and displayed some examples of Pauli's creativity in the development of quantum mechanics. By looking at Pauli's early physics and philosophy, we gain insight into Pauli's contributions to quantum mechanics. His exclusion principle, his influence on Werner Heisenberg in the formulation of matrix mechanics, his emphasis on firm logical and empirical foundations, his creativity in formulating electron spinors, his neutrino hypothesis, and his dialogues with other quantum physicists, all point to Pauli being the dominant genius in the development of quantum theory. Because Pauli was in a difficult individuation process during his early years, his own writings on philosophy tend to be sparse and often contradictory. My analysis of Pauli's physics and philosophy is based upon published and unpublished sources, and Pauli's later reflections. A pattern has emerged. Pauli changed his mind from relying on high rationality and empiricism, to valuing intuitive metaphysical visualizations. This coupled with disturbing events in his life precipitated a breakdown and led Pauli to seek treatment at the Jung Clinic. Pauli's psychological tension diminished after 1932. His physics consistently involved symmetry and invariants. His philosophy allied with Jung's resembled a Platonism of combined psyche and physics. Pauli sought a rational unification and foundation for his philosophy, but that goal was cut short by his untimely death at the age of 58.
Quantum mechanicsNeutrinoEventPeriodateSpinorElectronTension...
• #### Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.
Gravitational waveNeutron starInstabilityPulsar glitchLow-mass X-ray binaryStarMagnetarSuperfluidAsteroseismologyLaser Interferometer Gravitational-Wave Observatory...
• #### Radio Afterglows of Gamma Ray Bursts

This review focuses on the physics of Gamma Ray Bursts probed through their radio afterglow emission. Even though radio band is the least explored of the afterglow spectrum, it has played an important role in the progress of GRB physics, specifically in confirming the hypothesized relativistic effects. Currently radio astronomy is in the beginning of a revolution. The high sensitive Square Kilometer Array (SKA) is being planned, its precursors and pathfinders are about to be operational, and several existing instruments are undergoing upgradation. Thus, the afterglow detection statistics and results from follow up programs are expected to improve in the coming years. We list a few avenues unique to radio band which if explored to full potential have the promise to greatly contribute to the future of GRB physics.
Gamma ray burstSquare Kilometre ArrayRadio astronomyStatisticsPrecursorAfterglow emissionPotential...
• #### Accelerating the Discovery of Light Dark Matter

We analyze the present status of sub-GeV thermal dark matter annihilating through Standard Model mixing and identify a small set of future experiments that can decisively test these scenarios.
Dark matterStandard ModelLight dark matterDark matter annihilationCosmic microwave backgroundVector mediatorsScalar DMRelic abundanceElectron scatteringDark matter scattering...
• #### Perfect numbers and Fibonacci primes (III)

In this article, we consider the Diophantine equation $\sigma_{2}(n)-n^2=An+B$ with $A=P^2\pm2$. For some $B$, we show that except for finitely many computable solutions in the range $n\leq(|A|+|B|)^{3}$, all the solutions are expressible in terms of Lucas sequences. Meanwhile, we obtain some results relating to other linear recurrent sequences.
Perfect numberSquare-freeLucas sequencePrime numberMersenne primeEuler's theoremEuclid missionContradiction...
• #### Semantic Composition via Probabilistic Model Theory

Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a probabilistic version of model theory. Building on this, we explain how various semantic phenomena can be recast in terms of conditional probabilities in the graphical model. This connection between formal semantics and machine learning is helpful in both directions: it gives us an explicit mechanism for modelling context-dependent meanings (a challenge for formal semantics), and also gives us well-motivated techniques for composing distributed representations (a challenge for distributional semantics). We present results on two datasets that go beyond word similarity, showing how these semantically-motivated techniques improve on the performance of vector models.
Mean fieldModel structureVector spaceModel theoryGraphical modelGraphDependency graphInferenceRankHyperparameter...
• #### Dark Sectors 2016 Workshop: Community Report

This report, based on the Dark Sectors workshop at SLAC in April 2016, summarizes the scientific importance of searches for dark sector dark matter and forces at masses beneath the weak-scale, the status of this broad international field, the important milestones motivating future exploration, and promising experimental opportunities to reach these milestones over the next 5-10 years.
Dark matterDark sectorStandard ModelHidden photonColliderBeam dumpMissing massHiggs bosonKinetic mixingWeakly interacting massive particle...
• #### Model Independent Bounds on Kinetic Mixing

New Abelian vector bosons can kinetically mix with the hypercharge gauge boson of the Standard Model. This letter computes the model independent limits on vector bosons with masses from 1 GeV to 1 TeV. The limits arise from the numerous e+e- experiments that have been performed in this energy range and bound the kinetic mixing by epsilon < 0.03 for most of the mass range studied, regardless of any additional interactions that the new vector boson may have.
Vector bosonStandard ModelKinetic mixingDark sectorHyperchargeMass eigen stateStandard Model fermionColliderDark matterDecay mode...
• #### Probing Light Thermal Dark-Matter With a Higgs Portal Mediatorver. 2

We systematically study light (< few GeV) Dark Matter (DM) models that thermalize with visible matter through the Higgs portal and identify the remaining gaps in the viable parameter space. Such models require a comparably light scalar mediator that mixes with the Higgs to avoid DM overproduction and can be classified according to whether this mediator decays (in)visibly. In a representative benchmark model with Dirac fermion DM, we find that, even with conservative assumptions about the DM-mediator coupling and mass ratio, the regime in which the mediator is heavier than the DM is fully ruled out by a combination of collider, rare meson decay, and direct detection limits; future and planned experiments including NA62 can further improve sensitivity to scenarios in which the Higgs portal interaction does not determine the DM abundance. The opposite, regime in which the mediator is lighter than the DM and the latter annihilates to pairs of visibly-decaying mediators is still viable, but much of the parameter space is covered by rare meson decay, supernova cooling, beam dump, and direct detection constraints. Nearly all of these conclusions apply broadly to the simplest variations (e.g. scalar or asymmetric DM). Future experiments including SHiP, NEWS, and Super-CDMS SNOLAB can greatly improve coverage to this class of models.
Dark matterStandard ModelHiggs bosonHiggs portalFreeze-outMixing angleMass ratioRare meson decayLight scalarPlanned experiment...
• #### Light dark matter in neutrino beams: production modelling and scattering signatures at MiniBooNE, T2K and SHiPver. 3

We analyze the prospects for detection of light sub-GeV dark matter produced in experiments designed to study the properties of neutrinos, such as MiniBooNE, T2K, SHiP, DUNE etc. We present an improved production model, when dark matter couples to hadronic states via a dark photon or baryonic vector mediator, incorporating bremsstrahlung of the dark vector. In addition to elastic scattering, we also study signatures of light dark matter undergoing deep inelastic or quasi-elastic NC$\pi^0$-like scattering in the detector producing neutral pions, which for certain experiments may provide the best sensitivity. An extensive appendix provides documentation for a publicly available simulation tool {\tt BdNMC} that can be applied to determine the hidden sector dark matter production and scattering rate at a range of proton fixed target experiments.
Dark matterMiniBooNE experimentDark matter particleSHiP experimentNeutrinoLight dark matterT2K experimentBremsstrahlungPionRejection sampling...
• #### US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report

This white paper summarizes the workshop "U.S. Cosmic Visions: New Ideas in Dark Matter" held at University of Maryland on March 23-25, 2017.
Dark matterMaryland
• #### Viscous Self Interacting Dark Matter and Cosmic Acceleration

Self interacting dark matter (SIDM) provides us with a consistent solution to certain astrophysical observations in conflict with collision-less cold DM paradigm. In this work we estimate the shear viscosity $(\eta)$ and bulk viscosity $(\zeta)$ of SIDM, within kinetic theory formalism, for galactic and cluster size SIDM halos. To that extent we make use of the recent constraints on SIDM crossections for the dwarf galaxies, LSB galaxies and clusters. We also estimate the change in solution of Einstein's equation due to these viscous effects and find that $\sigma/m$ constraints on SIDM from astrophysical data provide us with sufficient viscosity to account for the observed cosmic acceleration at present epoch, without the need of any additional dark energy component. Using the estimates of dark matter density for galactic and cluster size halo we find that the mean free path of dark matter $\sim$ few Mpc. Thus the smallest scale at which the viscous effect start playing the role is cluster scale. Astrophysical data for dwarf, LSB galaxies and clusters also seems to suggest the same. The entire analysis is independent of any specific particle physics motivated model for SIDM.
Self-interacting dark matterVolume viscosityDark matterDark matter haloCosmic accelerationViscosityMean free pathKinetic theoryDissipationCold dark matter...
• #### Testing Feedback-Modified Dark Matter Haloes with Galaxy Rotation Curves: Estimation of Halo Parameters and Consistency with $\Lambda$CDMver. 2

Cosmological $N$-body simulations predict dark matter (DM) haloes with steep central cusps (e.g. NFW, Navarro et al. 1996). This contradicts observations of gas kinematics in low-mass galaxies that imply the existence of shallow DM cores. Baryonic processes such as adiabatic contraction and gas outflows can, in principle, alter the initial DM density profile, yet their relative contributions to the halo transformation remain uncertain. Recent high resolution, cosmological hydrodynamic simulations (Di Cintio et al. 2014, DC14) predict that inner density profiles depend systematically on the ratio of stellar to DM mass (M$_*$/M$_{\text{halo}}$). Using a Markov Chain Monte Carlo approach, we test the NFW and the M$_*$/M$_{\text{halo}}$-dependent DC14 halo models against a sample of 147 galaxy rotation curves from the new {\it Spitzer} Photometry and Accurate Rotation Curves (SPARC) data set. These galaxies all have extended H{\small I} rotation curves from radio interferometry as well as accurate stellar mass density profiles from near-infrared photometry. The DC14 halo profile provides markedly better fits to the data compared to the NFW profile. Unlike NFW, the DC14 halo parameters found in our rotation curve fits naturally fall within two standard deviations of the mass-concentration relation predicted by $\Lambda$CDM and the stellar mass-halo mass relation inferred from abundance matching with few outliers. Halo profiles modified by baryonic processes are therefore more consistent with expectations from $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology and provide better fits to galaxy rotation curves across a wide range of galaxy properties than do halo models that neglect baryonic physics. Our results offer a solution to the decade long cusp-core discrepancy.
GalaxyNavarro-Frenk-White profileRotation CurveHalo modelDark matter haloDark matterMonte Carlo Markov chainConcentration-mass relationMass to light ratioStellar mass...
• #### Charles Peirce on the Classification of Dyadic Relations and the Implications for Mathematical Logic

Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems of mathematical logic. Our aim in this essay is to reconstruct and examine central features of the classificatory system that he develops. Given the complexity of the system, we will focus our attention on the classification and explanation of of degenerate and genuine dyadic relations, and we will take up the discussion of triadic relations elsewhere. One of our reasons for wanting to explore this account of relations is to better understand how it informed the later development of relations as they figure in the history of mathematical logic. The earlier work of Peirce on dyadic relations influenced the development of the account of dyadic logical relations in works of Ernst Schroder, Leopold Lowenheim, Thoralf Skolem and Alfred Tarski. As such, our primary aim in this essay is to trace the early development of these ideas about the formal relation of the dyad for the sake of better understanding how it might have influenced these later developments.
Mathematical logicClassification
• #### On relativistic harmonic oscillator

A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time dependent) mass. This mass is quantized and is given by $m_{*n}^2=m_\omega^2\left(n_r^2-1-\beta\,\left(n+1\right)\right)\,,$ where $m_\omega=\frac{\hbar\omega}{c^2}\,,$ $\beta=\frac{2mc^2}{\hbar\,\omega}\,$, $n$, is the oscillator index, and $n_r$ is the refractive index in which the oscillator travels. The harmonic oscillator in 3+1 dimensions is found to have a total energy of $E_{*n}=(n+1)\,\hbar\,\omega$, where $\omega$ is the oscillator frequency. A Lorentz invariant solution for the oscillator is also obtained. The time coordinate is found to contribute a term $-\frac{1}{2}\,\hbar\,\omega$ to the total energy. The squared interval of a massive oscillator (wave) depends on the medium in which it travels. Massless oscillators have null light cone. The interval of a quantum oscillator is found to be determined by the equation, $c^2t^2-r^2=\lambda^2_c(1-n_r^2)$, where $\lambda_c$ is the Compton wavelength. The space-time inside a medium appears to be curved for a massive wave (field) propagating in it.
Harmonic oscillatorQuantum harmonic oscillatorQuantum mechanicsIndex of refractionQuaternionsLorentz invariantHamiltonianWave equationQuantizationCompton wavelength...