Point Correlation Function Research Articles

Measuring the matter fluctuations in the Local Universe with the ALFALFA catalogue

Abstract The standard model of cosmology describes the matter fluctuations through the matter power spectrum, where σ8 ≡ σ8, 0 ≡ σ8(z = 0), defined at the scale of 8 h−1 Mpc, acts as a normalisation parameter. Currently, the literature reports measurements of σ8 analysing different cosmic tracers, where some of these results were obtained assuming a fiducial cosmology. In this study we measure, in a model-independent approach, the matter fluctuations in the Local Universe using HI extragalactic sources mapped by the ALFALFA survey. Our analyses allow us to test the standard cosmological model under extreme conditions in the highly non-linear Local Universe, quantifying the amplitude of the matter fluctuations there. Our work directly measures σ8 using the 3-dimensional distances of the HI sources determined by the ALFALFA survey without assuming a fiducial cosmology, resulting in a robust model-independent measurement of σ8. Our methodology involves the construction of suitable mock catalogues to simulate the large scale structure features observed in the data, applying the 2-point correlation function, and making use of Markov Chain Monte Carlo methods to estimate the parameters. Analysing these data we measure σ8 = 0.78 ± 0.04 for h = 0.6727, σ8 = 0.80 ± 0.05 for h = 0.698, and σ8 = 0.83 ± 0.05 for h = 0.7304. Considering the data pairs (σ8, H0) from the Planck CMB and ACT CMB-lensing analyses, our measurement agrees with them within 1 σ confidence level. From a model-independent perspective, we find that the scale where the matter fluctuation is 1, is R = 7.2 ± 1.5 Mpc.

Quantization of Carrollian conformal scalar theories

In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional (2D) magnetic scalar and three-dimensional (3D) electric and magnetic scalars. We discuss two different quantization schemes, depending on the choice of the vacuum. We show that the standard canonical quantization corresponding to the induced vacuum yields a unitary Hilbert space and the 2-point correlation functions in this scheme match exactly with the ones computed from the path integral. In the canonical quantization, the BMS symmetry can be realized without anomaly. On the other hand, for the quantization based on the highest-weight vacuum, it does not have a unitary Hilbert space. In 2D, the correlators in the highest-weight vacuum agree with the ones obtained by taking the c→0 limit of the 2D CFT, and there is an anomalous term in the commutation relations between the Virasoso generators, whose form is similar to the one in 2D CFT. In 3D, there is no good definition of the highest-weight vacuum without breaking the rotational symmetry. In our study, we find that the usual state-operator correspondence in CFT does not hold in the Carrollian case. Published by the American Physical Society 2024

Using relativistic effects in large-scale structure to constrain astrophysical properties of galaxy populations

Upcoming large-scale structure surveys will be able to measure new features in the galaxy two point correlation function. Relativistic effects appear on large scales as subtle corrections to redshift-space distortions, showing up as a dipole and octupole when cross-correlating two different tracers of dark matter.The dipole and octupole are very sensitive to the evolution and magnification biases of the observed tracers which are hard to model accurately as they depend upon the derivative of the luminosity function at the flux limit of the survey.We show that splitting a galaxy population into bright and faint samples allows us to cross-correlate these and constrain both the evolution bias and magnification bias of the two samples — using the relativistic odd multipoles of the correlation function, together with the even Newtonian multipoles.Although the octupole has much lower signal-to-noise than the dipole, it significantly improves the constraints by breaking parameter degeneracies.We illustrate this in the case of a futuristic survey with the Square Kilometre Array, and demonstrate how splitting the samples in different ways can help improve constraints.This method is quite general and can be used on different types of tracers to improve knowledge of their luminosity functions. Furthermore, the signal-to-noise of the dipole and octupole peaks on intermediate scales, which means that they can deliver a clean measurement of the magnification bias and evolution bias without contamination from local primordial non-Gaussianities or from systematics on very large scales.

Modeling the 3-point correlation function of projected scalar fields on the sphere

One of the main obstacles for the signal extraction of the three point correlation function using photometric surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST), will be the prohibitive computation time required for dealing with a vast quantity of sources. Brute force algorithms, which naively scales as 𝒪(N 3) with the number of objects, can be further improved with tree methods but not enough to deal with large scale correlations of Rubin's data. However, a harmonic basis decomposition of these higher order statistics reduces the time dramatically, to scale as a two-point correlation function with the number of objects, so that the signal can be extracted in a reasonable amount of time. In this work, we aim to develop the framework to use these expansions within the Limber approximation for scalar (or spin-0) fields, such as galaxy counts, weak lensing convergence or aperture masses. We develop an estimator to extract the signal from catalogs and different phenomenological and theoretical models for its description. The latter includes halo model and standard perturbation theory, to which we add a simple effective field theory prescription based on the short range of non-locality of cosmic fields, significantly improving the agreement with simulated data. In parallel to the modeling of the signal, we develop a code that can efficiently calculate three points correlations of more than 200 million data points (a full sky simulation with Nside=4096) in ∼40 minutes, or even less than 10 minutes using an approximation in the searching algorithm, on a single high-performance computing node, enabling a feasible analysis for the upcoming LSST data.

Holographic zero sound for [formula omitted] SCFTs in 4d

We build up the notion of metallic holography for N=2 SCFTs in four dimensions, in the presence of a finite U(1) chemical potential. We compute two point correlation functions and study their properties in the regime of low frequency and low momentum. The color sector reveals gapless excitations, one of which propagates with a finite phase velocity while the other mode attenuates through scattering. The flavour sector, on the other hand, reveals spectrum that contains quasiparticle excitations which propagate with a definite phase velocity together with modes that propagate with a finite group velocity which quantum attenuates quite similar in spirit as that of Landau's zero sound modes. We also compute associated AC conductivities, which exhibit different characteristics for different (color and flavour) sectors of N=2 SCFTs.

Investigation of pion-nucleon contributions to nucleon matrix elements

We investigate contributions of excited states to nucleon matrix elements computed in lattice QCD by employing, in addition to the standard nucleon interpolating operator, pion-nucleon (π−N) operators. We solve a generalized eigenvalue problem (GEVP) to obtain an optimal interpolating operator that minimizes overlap with the π−N states. We derive a variant of the standard application of the GEVP method, which allows for constructing 3-point correlation functions using the optimized interpolating operator without requiring the computationally demanding combination that includes π−N operators in both sink and source. We extract nucleon matrix elements using two twisted mass fermion ensembles, one ensemble generated using pion mass of 346 MeV and one ensemble tuned to reproduce the physical value of the pion mass. Especially, we determine the isoscalar and isovector scalar, pseudoscalar, vector, axial, and tensor matrix elements. We include results obtained using a range of kinematic setups, including momentum in the sink. Our results using this variational approach are compared with previous results obtained using the same ensembles and multistate fits without GEVP improvement. We find that for the physical mass point ensemble, the improvement, in terms of suppression of excited states using this method, is most significant for the case of the matrix elements of the isovector axial and pseudoscalar currents. Published by the American Physical Society 2024

Inverse problem of correlation functions in holography

This paper shows that the bulk metric of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of two probe scalar operators by solving Gel’fand-Levitan-Marchenko integral equation. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes a new method to “measure” the corresponding holographic spacetime for a material that has holographic dual but also provides an approach to experimentally check if a system has holographic dual.

Quantifying the impact of AGN feedback on the large-scale matter distribution using two- and three-point statistics

Abstract Feedback from active galactic nuclei (AGN) plays a critical role in shaping the matter distribution on scales comparable to and larger than individual galaxies. Upcoming surveys such as Euclid and LSST aim to precisely quantify the matter distribution on cosmological scales, making a detailed understanding of AGN feedback effects essential. Hydrodynamical simulations provide an informative framework for studying these effects, in particular by allowing us to vary the parameters that determine the strength of these feedback processes and, consequently, to predict their corresponding impact on the large-scale matter distribution. We use the EAGLE simulations to explore how changes in subgrid viscosity and AGN heating temperature affect the matter distribution, quantified via 2- and 3-point correlation functions, as well as higher order cumulants of the matter distribution. We find that varying viscosity has a small impact ($\approx 10~{{\%}}$) on scales larger than 1h−1 Mpc, while changes to the AGN heating temperature lead to substantial differences, with up to 70% variation in gas clustering on small scales (≲ 1h−1 Mpc). By examining the suppression of the power spectrum as a function of time, we identify the redshift range z = 1.5 − 1 as a key epoch where AGN feedback begins to dominate in these simulations. The 3-point function provides complementary insight to the more familiar 2-point statistics, and shows more pronounced variations between models on the scale of individual haloes. On the other hand, we find that effects on even larger scales are largely comparable.

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

In this paper, we develop a momentum super space formalism for N = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N = 1, 2 theories. We discover interesting double copy relations in N = 1 super-correlators. Further, we discovered super double copy relations that take us from N = 1 to N = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Loops in AdS: from the spectral representation to position space. Part III

We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-Nf conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in 1Nf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N_f} $$\\end{document}. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as “blob diagrams”. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a k-loop ladder diagram.

Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as the Lévy-Lorentz gas. To gain insight into the microscopic properties of such a stochastically complex system, deterministic dynamics known as the slicer map and fly-and-die dynamics are used. We analytically derive the generalized position autocorrelation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single-parameter-dependent scaling and compare it with the numerically estimated 3-point position autocorrelation of the Lévy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position autocorrelations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems. Published by the American Physical Society 2024

Averages of products of characteristic polynomials and the law of real eigenvalues for the real Ginibre ensemble

We review an elementary derivation of the Borodin–Sinclair–Forrester–Nagao Pfaffian point process, which characterizes the law of real eigenvalues for the real Ginibre ensemble in the large matrix size limit, in terms of averages of products of characteristic polynomials. This derivation relies on a number of interesting structures associated with the real Ginibre ensemble such as the hidden symplectic symmetry of the statistics of real eigenvalues. It leads to a representation for the [Formula: see text]-point correlation function for any [Formula: see text] in terms of an integral over the symmetric space [Formula: see text] and this paper gives the proof of asymptotic exactness for this integral.

Equation and solution for the 4-point correlation function of galaxies in the Gaussian approximation and its parity-odd part

Equation and solution for the 4-point correlation function of galaxies in the Gaussian approximation and its parity-odd part

Cosmological constraints from the EFT power spectrum and tree-level bispectrum of 21 cm intensity maps

We explore the information content of 21 cm intensity maps in redshift space using the 1-loop Effective Field Theory power spectrum model and the bispectrum at tree level. The 21 cm signal contains signatures of dark matter, dark energy and the growth of large-scale structure in the Universe. These signatures are typically analysed via the 2-point correlation function or power spectrum. However, adding the information from the 3-point correlation function or bispectrum will be crucial to exploiting next-generation intensity mapping experiments. The bispectrum could offer a unique opportunity to break key parameter degeneracies that hinder the measurement of cosmological parameters and improve on the precision. We use a Fisher forecast analysis to estimate the constraining power of the HIRAX survey on cosmological parameters, dark energy and modified gravity.

The DESI one-per cent survey: exploring the halo occupation distribution of luminous red galaxies and quasi-stellar objects with AbacusSummit

ABSTRACT We present the first comprehensive halo occupation distribution (HOD) analysis of the Dark Energy Spectroscopic Instrument (DESI) One-Percent Survey luminous red galaxy (LRG) and Quasi Stellar Object (QSO) samples. We constrain the HOD of each sample and test possible HOD extensions by fitting the redshift-space galaxy 2-point correlation functions in 0.15 < r < 32 h−1 Mpc in a set of fiducial redshift bins. We use AbacusSummit cubic boxes at Planck 2018 cosmology as model templates and forward model galaxy clustering with the AbacusHOD package. We achieve good fits with a standard HOD model with velocity bias, and we find no evidence for galaxy assembly bias or satellite profile modulation at the current level of statistical uncertainty. For LRGs in 0.4 < z < 0.6, we infer a satellite fraction of $f_\mathrm{sat} = 11\pm 1~{y{\ \mathrm{per\,cent}}}$, a mean halo mass of $\log _{10}\overline{M}_h/M_\odot =13.40^{+0.02}_{-0.02}$, and a linear bias of $b_\mathrm{lin} = 1.93_{-0.04}^{+0.06}$. For LRGs in 0.6 < z < 0.8, we find $f_\mathrm{sat}=14\pm 1~{{\ \mathrm{per\,cent}}}$, $\log _{10}\overline{M}_h/M_\odot =13.24^{+0.02}_{-0.02}$, and $b_\mathrm{lin}=2.08_{-0.03}^{+0.03}$. For QSOs, we infer $f_\mathrm{sat}=3^{+8}_{-2}\mathrm{per\,cent}$, $\log _{10}\overline{M}_h/M_\odot = 12.65^{+0.09}_{-0.04}$, and $b_\mathrm{lin} = 2.63_{-0.26}^{+0.37}$ in redshift range 0.8 < z < 2.1. Using these fits, we generate a large suite of high fidelity galaxy mocks, forming the basis of systematic tests for DESI Y1 cosmological analyses. We also study the redshift-evolution of the DESI LRG sample from z = 0.4 up to z = 1.1, revealling significant and interesting trends in mean halo mass, linear bias, and satellite fraction.

A comparative study of two correlation functions applying to the quantitative characterization of the pore structure within hardened concrete

The paper presents a comparative study between the autocorrelation function (ACF) and the 2-point correlation function (2PCF) for the quantitative analysis of the pore structure within hardened concrete via the image analysis technique. This work was carried out on five cross-sectional images of concrete specimens with varying area porosities ranging from 2.6% to 21.2%. This research indicates that: (i) the ACF provides a comprehensive and effective tool that is capable of capturing the contribution of the area porosity, size, and orientation of the pores in quantifying the pore structure within hardened concrete, while the 2PCF only enables quantifying the size and spacing between the pores; (ii) the ACF requires the cross-sectional images to be square, whereas the 2PCF can analyze images of any size and shape; (iii) for an area porosity below 20%, the characteristic size of the pore structure within hardened concrete, determined by both the ACF and 2PCF approaches, is not significantly different; (iv) on average, the correlation length estimated by 2PCF is more than 1.6 times greater than the corresponding value determined by ACF; and (v) the characteristic size provides a more accurate and comprehensive quantification of the pore structure within hardened concrete specimens than the correlation length.

Wave-optics limit of the stochastic gravitational wave background

The stochastic gravitational wave background (SGWB) is a rich resource of cosmological information, encoded both in its source statistics and anisotropies induced by propagation effects. We provide a theoretical description of it, without employing tools which rely on the geometric optics assumption. Our formalism is based on the so-called classical matter approximation and it is able to capture wave-optics effects, such as interference and diffraction. We show that the interaction between the gravitational waves and the cosmic structures along the line-of-sight produce observable scalar and vector polarization modes, on top of modulating the tensorial ones. We build the two point correlation function describing the statistics of the SGWB, and introduce the intensity and gravitational Stokes parameters for all its components. In the case of an unpolarized, Gaussian and statistically homogeneous SGWB, we show that the interaction with matter modulates its intensity and does not generate a net difference between left- and right-helicity tensor and vector modes, as expected. We demonstrate that, in order to produce QT- and UT-tensor polarization modes the background must possess a hexadecapole anisotropy, while a quadrupole anisotropy can source the vector QV- and UV-Stokes parameters.

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes, fX NL, with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via the Ulagam suite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs to σ(f NL eq) ≈ 110, σ(f NL or, lss) ≈ 120, σ(f NL loc) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z ≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release the Ulagam suite to enable more survey-focused analyses.

Effective field theory of particle mixing

We introduce an effective field theory to study mixing of two fields induced by their couplings to a common decay channel in a medium. The extension of the method of Lee, Oehme, and Yang, the cornerstone of analysis of CP violation in flavored mesons, to include the mixing of particles with different masses provides a guide to and benchmark for the effective field theory. The analysis reveals subtle caveats in the description of mixing in terms of the widely used non-Hermitian effective Hamiltonian, more acute in the nondegenerate case. The effective field theory describes the dynamics of field mixing where the common intermediate states populate a bath in thermal equilibrium, as an . We obtain the effective action up to second order in the couplings, where indirect mixing is a consequence of off-diagonal self-energy components. We find that if only one of the mixing fields features an initial expectation value, indirect mixing induces an expectation value of the other field. The equal time two point correlation functions exhibit an asymptotic approach to a stationary thermal state, and the emergence of long-lived coherence which displays quantum beats as a consequence of interference of quasinormal modes in the medium. The amplitudes of the quantum beats are resonantly enhanced in the nearly degenerate case with potential observational consequences. Published by the American Physical Society 2024

The sound horizon scale at the baryon drag epoch

We study how to measure the sound horizon scale at the baryon drag epoch, rs , a parameter considered a cosmological standard ruler, from the 2-point correlation function analysis. This important parameter is originated in the baryon acoustic oscillations (BAO) phenomenon, which supports the large-scale structure scenario of the ΛCDM cosmological model, and provides valuable information of the dynamical evolution of the Universe. For this, one of the aims of current astronomical surveys is to know this parameter with high precision. Here we study how to correctly extract the BAO sound horizon scale in case where the signature is weak because there are few correlated pairs, sourced from the BAO phenomenon, probably due to non-linear evolution processes.