Point Function Research Articles

Improving the line of sight for the anisotropic 3-point correlation function of galaxies: Centroid and Unit-Vector-Average methods scaling as 𝒪 (N2)

ABSTRACT The 3-point correlation function (3PCF) is a powerful tool for the current era of high-data volume, high-precision cosmology. It goes beyond the Gaussian cosmological perturbations probed by the 2-point correlation function, including late-time non-Gaussianities, and encodes information about peculiar velocities, which distort observed positions of galaxies along the line of sight away from their true positions. To access this information, we must track the 3PCF’s dependence not only on each triangle’s shape, but also on its orientation with respect to the line of sight. Consequently, different choices for the line of sight will affect the measured 3PCF. Up to now, the line of sight has been taken as the direction to a single triplet member, but which triplet member is used impacts the 3PCF by ∼20 per cent of the statistical error for a BOSS-like survey. For DESI (5× more precise) this would translate to ∼100 per cent of the statistical error. We propose a new method that is fully symmetric between the triplet members, and uses either the average of the three galaxy position vectors, or the average of their unit vectors. We prove that these methods are equivalent to $\mathcal {O}(\theta ^2)$, where θ is the angle subtended at the observer by any triangle side. By harnessing the solid harmonic shift theorem, we show how these methods can be evaluated scaling as N2, with N the number of objects. We expect that they can be used to make a robust, systematics-free measurement of the anisotropic 3PCF of upcoming redshift surveys such as DESI.

Effects of peculiar velocities on the morphological properties of large-scale structure

It is known that the large-scale structure (LSS) mapped by a galaxy redshift survey is subject to distortions by galaxies' peculiar velocities. Besides the signatures generated in common N-point statistics, such as the anisotropy in the galaxy 2-point correlation function, the peculiar velocities also induce distinct features in LSS's morphological properties, which are fully described by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated mean curvature and Euler characteristic (or genus). In this work, by using large suite of N-body simulations, we present and analyze these important features in the MFs of LSS on both (quasi-)linear and non-linear scales, with a focus on the latter. We also find the MFs can give competitive constraints on cosmological parameters compared to the power spectrum, probablly due to the non-linear information contained. For galaxy number density similar to the DESI BGS galaxies, the constraint on $\sigma_8$ from the MFs with one smoothing scale can be better by $\sim 50\%$ than from the power spectrum. These findings are important for the cosmological applications of MFs of LSS, and probablly open up a new avenue for studying the peculiar velocity field itself.

Quantum instability of gauge theories on κ -Minkowski space

We consider a gauge theory on the 5-d $\kappa$-Minkowski which can be viewed as the noncommutative analog of a $U(1)$ gauge theory. We show that the Hermiticity condition obeyed by the gauge potential $A_\mu$ is necessarily twisted. Performing a BRST gauge-fixing with a Lorentz-type gauge, we carry out a first exploration of the one loop quantum properties of this gauge theory. We find that the gauge-fixed theory gives rise to a non-vanishing tadpole for the time component of the gauge potential, while there is no non-vanishing tadpole 1-point function for the spatial components of $A_\mu$. This signals that the classical vacuum of the theory is not stable against quantum fluctuations. Possible consequences regarding the symmetries of the gauge model and the fate of the tadpole in other gauges of non-covariant type are discussed.

Ringing the universe with cosmic emptiness: void properties through a combined analysis of stacked weak gravitational and Doppler lensing

ABSTRACT An essential aspect of cosmic voids is that these underdense regions provide complementary information about the properties of our Universe. Unlike dense regions, voids are avoided by matter and are less contaminated by baryonic processes. The first step to understanding the properties of cosmic voids is to correctly infer their mass profiles. In the literature, various techniques have been implemented. In this paper, we review them and implement a new technique that is based on Doppler lensing. We use a relativistic N-body code, Gevolution, to generate cosmological mass perturbations and implement a three-dimensional (3D) ray-tracing technique that follows the evolution of ray-bundles. We focus on the various properties of cosmic voids (e.g. void size function, 2-point correlation function, and the density profile of voids), and compare the results with their universal trends. We show that when weak lensing is combined with the Doppler lensing we obtain even tighter constraints than weak lensing alone. We also obtain better agreement between density profiles within central parts of voids inferred from lensing and density profiles inferred from halo tracers. The implication of the result relevant to the ongoing and prospective low-redshift spectroscopic surveys is briefly discussed.

Full wCDM analysis of KiDS-1000 weak lensing maps using deep learning

We present a full forward-modeled $w\mathrm{CDM}$ analysis of the KiDS-1000 weak lensing maps using graph-convolutional neural networks (GCNN). Utilizing the cosmogrid, a novel massive simulation suite spanning six different cosmological parameters, we generate almost one million tomographic mock surveys on the sphere. Due to the large dataset size and survey area, we perform a spherical analysis while limiting our map resolution to HEALPix ${n}_{\mathrm{side}}=512$. We marginalize over systematics such as photometric redshift errors, multiplicative calibration and additive shear bias. Furthermore, we use a map-level implementation of the nonlinear intrinsic alignment model along with a novel treatment of baryonic feedback to incorporate additional astrophysical nuisance parameters. We also perform a spherical power spectrum analysis for comparison. The constraints of the cosmological parameters are generated using a likelihood-free inference method called Gaussian process approximate Bayesian computation (GPABC). Finally, we check that our pipeline is robust against choices of the simulation parameters. We find constraints on the degeneracy parameter of ${S}_{8}\ensuremath{\equiv}{\ensuremath{\sigma}}_{8}\sqrt{{\mathrm{\ensuremath{\Omega}}}_{M}/0.3}=0.7{8}_{\ensuremath{-}0.06}^{+0.06}$ for our power spectrum analysis and ${S}_{8}=0.7{9}_{\ensuremath{-}0.05}^{+0.05}$ for our GCNN analysis, improving the former by 16%. This is consistent with earlier analyses of the 2-point function, albeit slightly higher. Baryonic corrections generally broaden the constraints on the degeneracy parameter by about 10%. These results offer great prospects for full machine learning based analyses of ongoing and future weak lensing surveys.

Nuclear two point correlation functions on a quantum computer

The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly-correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this work we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.

Additive manufacturing: A machine learning model of process-structure-property linkages for machining behavior of Ti-6Al-4V

Prior studies in metal additive manufacturing (AM) of parts have shown that various AM methods and post-AM heat treatment result in distinctly different microstructure and machining behavior when compared with conventionally manufactured parts. There is a crucial knowledge gap in understanding this process-structure-property (PSP) linkage and its relationship to material behavior. In this study, the machinability of metallic Ti-6Al-4V AM parts was investigated to better understand this unique PSP linkage through a novel data science-based approach, specifically by developing and validating a new machine learning (ML) model for material characterization and material property, that is, machining behavior. Heterogeneous material structures of Ti-6Al-4V AM samples fabricated through laser powder bed fusion and electron beam powder bed fusion in two different build orientations and post-AM heat treatments were quantitatively characterized using scanning electron microscopy, electron backscattered diffraction, and residual stress measured through X-ray diffraction. The reduced dimensional representation of material characterization data through chord length distribution (CLD) functions, 2-point correlation functions, and principal component analysis was found to be accurate in quantifying the complexities of Ti-6Al-4V AM structures. Specific cutting energy was the response variable for the Taguchi-based experimentation using force dynamometer. A low-dimensional S-P linkage model was established to correlate material structures of metallic AM and machining properties through this novel ML model. It was found that the prediction accuracy of this new PSP linkage is extremely high (>99%, statistically significant at 95% confidence interval). Findings from this study can be seamlessly integrated with P-S models to identify AM processing conditions that will lead to desired material behaviors, such as machining behavior (this study), fatigue behavior, and corrosion resistance.

Ringing non-Gaussianity from inflation with a step in the second derivative of the potential

Inflationary model driven by a scalar field whose potential has a step in the second derivative with respect to the field is considered. For the best-fit potential parameter values, the 3-point function and the non-Gaussianity associated with the featured model is calculated. We study the shape and scale dependence of the 3-point function. The distinctive feature of this model is its characteristic ringing behaviour of \(f_{\mathrm {NL}}\). We can see that the oscillations in \(f_{\mathrm {NL}}\) in this model last for a much longer range of k values, than the previously studied models. In that sense, this model is potentially distinguishable from models with other features in the potential.

Quantization of Generalized Abelian Gauge Field Theory under Rotor Model

This paper is a follow-up work of the previous study of the generalized abelian gauge field theory under rotor model of order $n$ of higher order derivatives. We will study the quantization of this theory using path integral approach and find out the Feynman propagator (2-point correlation function) of this generalized theory. We also investigate the generalized Proca action under rotor model and derive the Feynman propagator for the massive case.

Spinors and conformal correlators

In conformal field theory, momentum eigenstates can be parameterized by a pair of real spinors, in terms of which special conformal transformations take a simpler form. This well-known fact allows to express 2-point functions of primary operators in the helicity basis, exposing the consequences of unitarity. What is less known is that the same pair of spinors can be used, together with a pair of scalar quantities, to parameterize 3-point functions. We develop this formalism in 3 dimensions and show that it provides a simple realization of the operator product expansion (OPE) for scalar primary operators acting on the vacuum.

Analytical computation of quantum corrections to a nontopological soliton within the saddle-point approximation

Schr\"{o}dinger field theory with an attractive self-interaction possess non-topological extended solutions with a finite energy in both finite and infinite-volume cases, namely, bright solitons. The analytical form of the solution itself is well-known, though analytical investigation of the quantum fluctuations in this background still requires more thorough investigation, for instance, analytical computation of quantum corrections to this background within the saddle-point approximation. In the present work this gap is filled. Both 2-point Green's function and quantum corrections to the background are analytically computed and properly renormalized by means of momentum cut-off procedure. It is deduced that quantum corrections are indeed small provided that particle number is large. Also, we see that perturbation modes of continuum spectrum at bright soliton background generate a gap in the energy spectrum. Moreover, it turns out that the whole spectrum is continuous modulo zero-modes, which is similar to Sine-Gordon solitons.

Non-perturbative renormalization for the neural network-QFT correspondence

In a recent work (Halverson et al 2021 Mach. Learn.: Sci. Technol. 2 035002), Halverson, Maiti and Stoner proposed a description of neural networks (NNs) in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory while finite N corrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for NNs (since inputs can be arbitrary), however, the renormalization group (RG) provides natural notions of locality and scaling. Moreover, we comment on several subtleties, for example, that data components may not have a permutation symmetry: in that case, we argue that random tensor field theories could provide a natural generalization. Second, we improve the perturbative Wilsonian renormalization from Halverson et al (2021 Mach. Learn.: Sci. Technol. 2 035002) by providing an analysis in terms of the non-perturbative RG using the Wetterich-Morris equation. An important difference with usual non-perturbative RG analysis is that only the effective infrared 2-point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate NNs behavior beyond the large-width limit (i.e. far from Gaussian limit) in a non-perturbative fashion. A major result of our analysis is that changing the standard deviation of the NN weight distribution can be interpreted as a renormalization flow in the space of networks. We focus on translations invariant kernels and provide preliminary numerical results.

Structure of holographic BCFT correlators from geodesics

We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a Karch-Randall brane -- a rigid boundary in the bulk AdS space. Geodesic approximation requires the inclusion of paths reflecting off of this brane, which we show in detail. For the 1-point function, we find agreement between geodesic approximation and the harder $\Delta$-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-point function, we find a factorization phase transition and a mysterious set of anomalous boundary-localized BCFT operators. We also discuss some puzzles concerning these operators.

Cosmic Voids and BAO with relative baryon-CDM perturbations

ABSTRACT We study the statistics of various large-scale structure tracers in gravity-only cosmological simulations including baryons and cold dark matter (CDM) initialized with two different transfer functions, and simulated as two distinct fluids. This allows us to study the impact of baryon-CDM relative perturbations on these statistics. In particular, we focus on the statistics of cosmic voids, as well as on the matter and halo real-space 2-point correlation function and baryon acoustic oscillations (BAO) peak. We find that the void size function is affected at the 1–2 per cent level at maximum, and that the impact is more important at higher redshift, while the void density profile and void bias are roughly unaffected. We do not detect a sizeable impact of relative baryon-CDM perturbations on the real-space correlation functions of matter and haloes or the BAO peak, which is in line with results from previous works. Our results imply that it would be hard to use voids or real-space correlation functions to constrain baryon-CDM relative perturbations, but also that we might not have to include them in models for the analysis of future cosmological surveys data.

A new analysis of galaxy 2-point functions in the BOSS survey, including full-shape information and post-reconstruction BAO

We present a new method for consistent, joint analysis of the pre- and post-reconstruction galaxy two-point functions of the BOSS survey. The post-reconstruction correlation function is used to accurately measure the distance-redshift relation and expansion history, while the pre-reconstruction power spectrum multipoles constrain the broad-band shape and the rate-of-growth of large-scale structure. Our technique uses Lagrangian perturbation theory to self-consistently work at the level of two-point functions, i.e. directly with the measured data, without approximating the constraints with summary statistics normalized by the drag scale. Combining galaxies across the full redshift range and both hemispheres we constrain Ωm = 0.303 ± 0.0082, H 0 = 69.23 ± 0.77 and σ8 = 0.733 ± 0.047 within the context of ΛCDM. These constraints are consistent both with the Planck primary CMB anisotropy data and recent cosmic shear surveys.

Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.

Harmonic analysis of isotropic fields on the sphere with arbitrary masks

Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from the diagonal and introduces coupling between modes. In this paper, we derive a custom eigenbasis adapted to any particular survey geometry so that all information is retained on the diagonal. At the expense of a somewhat complex pixel- and selection-function-window, the result is a diagonal 2-point function with a simple shot noise, and a diagonal covariance matrix in the case of a Gaussian random field. We derive the basis on the surface of a sphere, and we use it to construct a 3D spherical Fourier-Bessel power spectrum estimator assuming a survey geometry that is separable in the angular and radial directions.

Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models

We continue the investigation of coupled Sachdev-Ye-Kitaev (SYK) models without Schwarzian action dominance. Like the original SYK, at large N and low energies these models have an approximate reparametrization symmetry. However, the dominant action for reparametrizations is non-local due to the presence of irrelevant local operator with small conformal dimension. We semi-analytically study different thermodynamic properties and the 4-point function and demonstrate that they significantly differ from the Schwarzian prediction. However, the residual entropy and maximal chaos exponent are the same as in Majorana SYK. We also discuss chain models and finite N corrections.

H i IM correlation function from UNIT simulations: BAO and observationally induced anisotropy

ABSTRACT We study the clustering of H i intensity maps (IM) produced from simulations with a focus on baryonic acoustic oscillations (BAOs) and the effects induced by telescope beam smoothing and foreground cleaning. We start by creating an H i catalogue at z = 1.321 based on the Semi-Analytic Galaxy Evolution (SAGE) model applied to the UNIT simulations. With this catalogue, we investigate the relation between model H i and the dark matter haloes and we also study the abundance of H i, $\Omega _\rm{H \small {\rm I}}$, predicted by this model. We then create synthetic H i IM with a nearest-grid-point approach. In order to simulate the telescope beam effect, a Gaussian smoothing is applied on the plane perpendicular to the line of sight. The effect of foreground removal methods is simulated by exponentially damping the largest wavelength Fourier modes on the radial direction. We study the anisotropic 2-point correlation function (2PCF) ξ(r⊥, r∥) and how it is affected by the aforementioned observational effects. In order to better isolate the BAO signal, we study several 2PCF μ-wedges (with a restricted range of orientations μ) tailored to address the systematics effects and we compare them with different definitions of radial 2PCFs. Finally, we discuss our findings in the context of an SKA-like survey, finding a clear BAO signal in most of the estimators here proposed.

Constraints on f(R) and normal-branch Dvali-Gabadadze-Porrati modified gravity model parameters with cluster abundances and galaxy clustering

We present forecasted cosmological constraints from combined measurements of galaxy cluster abundances from the Simons Observatory and galaxy clustering from a DESI-like experiment on two well-studied modified gravity models, the chameleon-screened $f(R)$ Hu-Sawicki model and the nDGP braneworld Vainshtein model. A Fisher analysis is conducted using $\sigma_8$ constraints derived from thermal Sunyaev-Zel'dovich (tSZ) selected galaxy clusters, as well as linear and mildly non-linear redshift-space 2-point galaxy correlation functions. We find that the cluster abundances drive the constraints on the nDGP model while $f(R)$ constraints are led by galaxy clustering. The two tracers of the cosmological gravitational field are found to be complementary, and their combination significantly improves constraints on the $f(R)$ in particular in comparison to each individual tracer alone. For a fiducial model of $f(R)$ with $\text{log}_{10}(f_{R0})=-6$ and $n=1$ we find combined constraints of $\sigma(\text{log}_{10}(f_{R0}))=0.48$ and $\sigma(n)=2.3$, while for the nDGP model with $n_{\text{nDGP}}=1$ we find $\sigma(n_{\text{nDGP}})=0.087$. Around a fiducial General Relativity (GR) model, we find a $95\%$ confidence upper limit on $f(R)$ of $f_{R0}\leq5.68\times 10^{-7}$. Our results present the exciting potential to utilize upcoming galaxy and CMB survey data available in the near future to discern and/or constrain cosmic deviations from GR.