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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Precise cosmological constraints from BOSS galaxy clustering with a simulation-based emulator of the wavelet scattering transform

For this study, we perform a reanalysis of the BOSS CMASS DR12 galaxy dataset using a simulation-based emulator for the wavelet scattering transform (WST) coefficients. Moving beyond our previous works, which laid the foundation for the first galaxy clustering application of this estimator, we construct a neural net-based emulator for the cosmological dependence of the WST coefficients and the 2-point correlation function multipoles, trained from the state-of-the-art suite of abacussummit simulations combined with a flexible halo occupation distribution (HOD) galaxy model. In order to confirm the accuracy of our pipeline, we subject it to a series of thorough internal and external mock parameter recovery tests, before applying it to reanalyze the CMASS observations in the redshift range 0.46 < z < 0.57. We find that a joint WST+2-point correlation function likelihood analysis allows us to obtain marginalized 1⁢σ errors on the Λ⁢ CDM parameters that are tighter by a factor of 2.5–6, compared to the 2-point correlation function, and by a factor of 1.4–2.5 compared to the WST-only results. This corresponds to a competitive 0.9%, 2.3% and 1% level of determination for parameters ω c , ⁢σ 8 &n s , respectively, and also to a 0.7% and 2.5% constraint on derived parameters h and ƒ⁡(z)⁢⁢σ 8 ⁡(z), in agreement with the Planck 2018 results. Our results reaffirm the constraining power of the WST and highlight the exciting prospect of employing higher-order statistics in order to fully exploit the power of upcoming stage-IV spectroscopic observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dynamics-based halo model for large scale structure

Accurate modeling of the one-to-two halo transition has long been difficult to achieve. Here, we demonstrate that physically motivated halo definitions that respect the bimodal phase-space distribution of dark matter particles near halos resolves this difficulty. Specifically, the two phase-space components are overlapping and correspond to (1) particles orbiting the halo and (2) particles infalling into the halo for the first time. Motivated by this decomposition, García et al. [Mon. Not. R. Astron. Soc. 521, 2464 (2023)] advocated for defining halos as the collection of particles orbiting their self-generated potential. This definition identifies the traditional one-halo term of the halo-mass correlation function with the distribution of orbiting particles around a halo, while the two-halo term governs the distribution of infalling particles. We use dark matter simulations to demonstrate that the distribution of orbiting particles is finite and can be characterized by a single physical scale 𝑟 h , which we refer to as the halo radius. The two-halo term is described using a simple yet accurate empirical model based on the Zel’dovich correlation function. We further demonstrate that the halo radius imprints itself on the distribution of infalling particles at small scales. Our final model for the halo-mass correlation function is accurate at the ≈ 2% level for 𝑟∈ [0.1, 50] ℎ −1 Mpc. The Fourier transform of our best-fit model describes the halo-mass power spectrum with comparable accuracy for 𝑘 ∈ [0.06, 6.0] ℎ Mpc −1 .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Investigation of K + K – interactions via femtoscopy in Pb-Pb collisions at s N N = 2.76 TeV at the CERN Large Hadron Collider

Femtoscopic correlations of nonidentical charged kaons (K + K – ) are studied in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision $\sqrt{s_{NN}}$=2.76 TeV by ALICE at the CERN Large Hadron Collider. One-dimensional K + K – correlation functions are analyzed in three centrality classes and eight intervals of particle-pair transverse momentum. The Lednický and Luboshitz interaction model used in the K + K – analysis includes the final-state Coulomb interactions between kaons and the final-state interaction through a 0 (980) and f 0 (980) resonances. The mass of f 0 (980) and coupling were extracted from the fit to K + K – correlation functions using the femtoscopic technique. The measured mass and width of the f 0 (980) resonance are consistent with other published measurements. The height of the $\phi$(1020) meson peak present in the K + K – correlation function rapidly decreases with increasing source radius, qualitatively in agreement with an inverse volume dependence. A phenomenological fit to this trend suggests that the $\phi$(1020) meson yield is dominated by particles produced directly from the hadronization of the system. The small fraction subsequently produced by final-state interactions could not be precisely quantified with data presented in this paper and will be assessed in future work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

A Lagrangian perturbation theory in the presence of massive neutrinos

We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to third order in perturbation theory. Once the neutrinos become non-relativistic, their density fluctuations are modeled as being proportional to the CDM density fluctuations, with a scale-dependent proportionality factor. This yields a gravitational back-reaction that introduces additional scales to the linear growth function, which is accounted for in the higher order LPT kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we ensure that our theory has a well behaved large scale behavior free of unwanted UV divergences, which are common when neutrino and CDM densities are not treated on an equal footing, and in resummation schemes that manifestly break Galilean invariance. We use our theory to construct correlation functions for both the underlying matter field, as well as for biased tracers using ConvolutionLPT. Redshift-space distortions effects are modeled using the Gaussian Streaming Model. When comparing our analytical results to simulated data from the Quijote 1 simulation suite, we find good accuracy down to r = 20 Mpc h -1 at redshift z = 0.5, for the real space and redshift space monopole particle correlation functions with no free parameters. The same accuracy is reached for the redshift space quadrupole if we additionally consider an effective field theory parameter that shifts the pairwise velocity dispersion. For modeling the correlation functions of tracers we adopt a simple Lagrangian biasing scheme with only density and curvature operators, which we find sufficient to reach down to r = 20 Mpc h -1 when comparing to simulated halos.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Velocity correlations of galaxy clusters

We determine the velocity correlation function, pairwise peculiar velocity difference, and rms pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: Omega = 1 and Omega = 0.3 cold dark matter (CDM), and Omega = 0.3 primeval baryonic isocurvature (PBI) models (all flat and Cosmic Background Explorer (COBE)-normalized). We find that close cluster pairs, with separation r is less than or equal to 10/h Mpc, exhibit strong attractive peculiar velocities in all models; the cluster pairwise velocities depend sensitively on the model. The mean pairwise attractive velocity of clusters on 5/h Mpc scale ranges from approximately 1700 km/s for Omega = 1 CDM to approximately 1000 km/s for PBI to approximately 700 km/s for Omega = 0.3 CDM. The small-scale pairwise velocities depend also on cluster mass: richer, more massive clusters exhibit stronger attractive velocities than less massive clusters. On large scales, from approximately 20 to 200/h Mpc, the cluster peculiar velocities are increasingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function is negative on small scales for Omega = 1 and Omega = 0.3 CDM, indicating strong pairwise motion relative to bulk motion on small scales; PBI exhibits relatively larger bulk motions. The cluster velocity correlation function is positive on very large scales, from r approximately 10/h Mpc to r approximately 200/h Mpc, for all models. These positive correlations, which decrease monotonically with scale, indicate significant bulk motions of clusters up to approximately 200/h Mpc. The strong dependence of the cluster velocity functions on models, especially at small separations, makes them useful tools in constraining cosmological models when compared with observations.

Cen, Renyue↗
DOE OSTI2016

A cumulant functional for static and dynamic correlation

A functional for the cumulant energy is introduced. The functional is composed of a pair-correction and static and dynamic correlation energy components. The pair-correction and static correlation energies are functionals of the natural orbitals and the occupancy transferred between near-degenerate orbital pairs, rather than the orbital occupancies themselves. The dynamic correlation energy is a functional of the statically correlated on-top two-electron density. The on-top density functional used in this study is the well-known Colle-Salvetti functional. Using the cc-pVTZ basis set, the functional effectively models the bond dissociation of H{sub 2}, LiH, and N{sub 2} with equilibrium bond lengths and dissociation energies comparable to those provided by multireference second-order perturbation theory. The performance of the cumulant functional is less impressive for HF and F{sub 2}, mainly due to an underestimation of the dynamic correlation energy by the Colle-Salvetti functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Simulating cosmologies beyond ΛCDM with PINOCCHIO

We present a method that extends the capabilities of the PINpointing Orbit-Crossing Collapsed HIerarchical Objects (PINOCCHIO) code, allowing it to generate accurate dark matter halo mock catalogues in cosmological models where the linear growth factor and the growth rate depend on scale. Such cosmologies comprise, among others, models with massive neutrinos and some classes of modified gravity theories. We validate the code by comparing the halo properties from PINOCCHIO against N-body simulations, focusing on cosmologies with massive neutrinos: νΛCDM. We analyse the halo mass function, halo two-point correlation function and halo power spectrum, showing that PINOCCHIO reproduces the results from simulations with the same level of precision as the original code (∼ 5–10%). We demonstrate that the abundance of halos in cosmologies with massless and massive neutrinos from PINOCCHIO matches very well the outcome of simulations, and point out that PINOCCHIO can reproduce the Ω{sub ν}–σ{sub 8} degeneracy that affects the halo mass function. We finally show that the clustering properties of the halos from PINOCCHIO matches accurately those from simulations both in real and redshift-space, in the latter case up to k = 0.3 h Mpc{sup −1}. We emphasize that the computational time required by PINOCCHIO to generate mock halo catalogues is orders of magnitude lower than the one needed for N-body simulations. This makes this tool ideal for applications like covariance matrix studies within the standard ΛCDM model but also in cosmologies with massive neutrinos or some modified gravity theories.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

We investigate the response of large inertial particle to turbulent fluctuations in an inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding particle dynamics and may permit stochastic process modelization using two-time models (for instance, Sawford’s). As particles are tracked over long times in the quasi-totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.

42 ENGINEERING↗
DOE OSTI2022

A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems

Here, we introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of $20 \sim 50 \times $ in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F 2 demonstrates favorable agreements with standard quantum-chemical calculations Bytautas et al (2007 J. Chem. Phys. 127 164317).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Hyper Suprime-Cam Year 3 results: Cosmology from galaxy clustering and weak lensing with HSC and SDSS using the minimal bias model

Here, we present cosmological parameter constraints from a blind joint analysis of three two-point correlation functions measured from the Year 3 Hyper Suprime-Cam (HSC-Y3) imaging data, covering about 416 deg 2 , and the SDSS DR11 spectroscopic galaxies spanning the redshift range [0.15, 0.70]. We subdivide the SDSS galaxies into three luminosity-cut, and therefore nearly volume-limited samples separated in redshift, each of which acts as a large-scale structure tracer characterized by the measurement of the projected correlation function, w p ⁡(R). We also use the measurements of the galaxy-galaxy weak-lensing signal Δ⁢Σ⁡(R) for each of these SDSS samples which act as lenses for a secure sample of source galaxies selected from the HSC-Y3 shape catalog based on their photometric redshifts. We combine these measurements with the cosmic shear correlation functions, ξ ± ⁡($\vartheta$) measured for our HSC source sample. We model these observables with the minimal bias model of the galaxy clustering observables in the context of a flat Λ⁢CDM cosmology. We use conservative scale cuts, R >12 and 8⁢ℎ -1 Mpc for Δ⁢Σ and w p , respectively, where the minimal bias model is valid, in addition to conservative prior on the residual bias in the mean redshift of the HSC photometric source galaxies. We present various validation tests of our model as well as analysis methods. Our baseline analysis yields S 8 = $0.77⁢5^{+0.043}_{-0.038}$ (68% C.I.) for the Λ⁢CDM model, after marginalizing over uncertainties in other parameters. Our value of S 8 is consistent with that from the Planck 2018 data, but the credible interval of our result is still relatively large. We show that various internal consistency tests based on different splits of the data are passed. Our results are statistically consistent with those of a companion paper, which extends this analysis to smaller scales with an emulator-based halo model, using Δ⁢Σ⁡(R) and w p ⁡(R) down to R >3 and 2⁢ℎ -1 Mpc, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Numerical evaluation of the bispectrum in multiple field inflation—the transport approach with code

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or 'in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with | f {sub NL}| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Clustering with general photo- z uncertainties: application to Baryon Acoustic Oscillations

ABSTRACT Photometric data can be analysed using the 3D correlation function ξp to extract cosmological information via e.g. measurement of the Baryon Acoustic Oscillations (BAO). Previous studies modeled ξp assuming a Gaussian photo-z approximation. In this work we improve the modeling by incorporating realistic photo-z distribution. We show that the position of the BAO scale in ξp is determined by the photo-z distribution and the Jacobian of the transformation. The latter diverges at the transverse scale of the separation s⊥, and it explains why ξp traces the underlying correlation function at s⊥, rather than s, when the photo-z uncertainty σz/(1+ z) ≳ 0.02. We also obtain the Gaussian covariance for ξp. Due to photo-z mixing, the covariance of ξp shows strong off-diagonal elements. The high correlation of the data causes some issues to the data fitting. None the less, we find that either it can be solved by suppressing the largest eigenvalues of the covariance or it is not directly related to the BAO. We test our BAO fitting pipeline using a set of mock catalogs. The data set is dedicated for Dark Energy Survey Year 3 (DES Y3) BAO analyses and includes realistic photo-z distributions. The theory template is in good agreement with mock measurement. Based on the DES Y3 mocks, ξp statistic is forecast to constrain the BAO shift parameter α to be 1.001 ± 0.023, which is well consistent with the corresponding constraint derived from the angular correlation function measurements. Thus, ξp offers a competitive alternative for the photometric data analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Constraints on large-scale clustering from the autocorrelation properties of the X-ray background

Expectations for the angular correlation function of intensity fluctuations of the extragalacitc 2-10 keV X-ray background are discussed in relation to the two-point spatial correlation functions, xi(r), of X-ray sources. A simple analytic formula for the amplitude of intensity correlations, Gamma(theta), holding in the low-redshift, small-separation approximation, is derived. The HEAO 1 A-2 upper limits on Gamma(theta) have been exploited to derive constraints on the local xi(r) functions of rich clusters of galaxies, of AGNs, and on the AGN-cluster cross-correlation, as well as on evolution of the correlation functions with cosmic time. X-ray data are found to be compatible with the Bahcall and Soneira estimates of xi(cluster-cluster) as well as with the results of recent studies of quasar clustering.

De Zotti, G.↗
DOE OSTI2016

Can quantum transition state theory be defined as an exact t = 0 + limit?

Here, the definition of the classical transition state theory (TST) as a t → 0 + limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) recently suggested that a true QTST can be defined as the exact t → 0 + limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0 + limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA’s proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0 + limit of HA’s QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals. In conclusion, it is shown that the t → 0 + limit of the new rate expression vanishes in the exact quantum limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Hyper Open-Shell Excited Spin States of Transition-Metal Compounds: FeF 2 , FeF 2 ···Ethane, and FeF 2 ···Ethylene

Spin-state energetics are important for understanding properties that involve more than one spin state, for example, catalysis occurring on two or more potential energy surfaces corresponding to different electronic spins. Very often, multiple-spin processes involve transition-metal compounds, and therefore, it is important to understand the electronic structure and energetics of such compounds in different spin states. In this work, we benchmark relative spin-state energies of FeF 2 with respect to the quintet ground spin state using both singleconfigurational and multi-configurational methods, and we examine how they are affected by the binding of ethane and ethylene to the iron center. We also benchmark the binding energies of the complexes. The single-configurational methods used in this work are the Hartree–Fock method, 32 exchange–correlation functionals, and the CCSD(T) coupled-cluster method in both restricted and unrestricted formalisms. The multi-configurational methods that have been used are CASSCF, CASPT2, CASPT3, MRCI, MRCI+Q, and MR-ACPF. The spin-state splitting energies depend on the functional chosen and of the 32 exchange-correlation functionals investigated here we find that for the septet and spin-projected triplet states of FeF 2 , the M06 functional is the best when compared to our best estimates from multi-reference calculations. If all the nine excitation energies are considered, where there are three excited spin states (singlet, triplet, and septet) for each of the three systems (FeF 2 , FeF 2 ···ethane, and FeF 2 ···ethylene), the three best performing functionals are HLE16, SOGGA11-X, and M06-2X. We find that the binding of ethane perturbs the relative spin-state energy of FeF 2 by only a small amount, but the stronger binding of ethylene has a larger effect. For the spin-state splitting energies of FeF 2 using single-reference CCSD(T), we found the predicted results depend very strongly on precisely how the calculations are done, in particular, on the spin-restricted or spin-unrestricted character of the SCF reference state, which can differ even by around 50 kcal/mol for the SCF reference state and the subsequent CCSD(T) calculations. Furthermore, on analyzing the wave functions of both the spinrestricted or spin-unrestricted formalisms, we find that the lowest-energy singlet and triplet states of the complexes, just like FeF 2 in isolation, can have more unpaired electrons than they are usually assumed to have, i.e. they can be hyper open-shell electronic configurations, and that this can significantly lower the energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Frequency-Bessel Transform Method for Effective Imaging of Higher-Mode Rayleigh Dispersion Curves From Ambient Seismic Noise Data

It has been widely recognized that the cross-correlation function of ambient seismic noise data recorded at two stations approximates to the part of Greens function between two stations. Therefore, the cross-correlation function should include higher modes, aside from the fundamental mode. However, the problem of measuring or extracting overtones from ambient seismic noise data remains. In this paper, we propose the frequency-Bessel transform method (F-J method) for extracting the dispersion curves of higher modes from ambient seismic noise data. We then assess the validity, accuracy, and applicability of the F-J method by conducting extensive numerical simulations and processing the observed ambient seismic noise data of the USArray. As demonstrated in this study, the F-J method is a convenient, practical, and accurate method for extracting the dispersion curves of multimodes from ambient seismic noise data and therefore has significant potentiality in the field of ambient seismic noise tomography.

58 GEOSCIENCES↗