arXiv subjects

Zachary Slepian

Publications and source records attributed to Zachary Slepian.

At least 19 recordsLinked to original sources

arXiv2026

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm I}$: 1-Loop Corrections involving Second-Order Densities

Analytical templates for the covariance matrix of the 4-Point Correlation Function (4PCF) have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the first non-Gaussian calculation of the 4PCF covariance, incorporating 1-loop corrections using the second-order density contrast. Furthermore, we introduce a non-trivial galaxy bias scheme at second order. To simplify the calculation, we decompose the covariance into five distinct structures, and then exploit the isotropic basis functions of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals naively involved, enabling the angular parts to be performed and leaving us with low-dimensional radial integrals. This analytical template will provide a more accurate characterization of the statistical errors on the 4PCF, improving both the parity-odd and parity-even analyses. This is the first paper in a two-part series.

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arXiv2026

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm II}$: 1-Loop Corrections with Third-Order Densities

Analytical templates for the 4-Point Correlation Function (4PCF) covariance matrix have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the second part of the beyond GRF calculation of the 4PCF covariance, incorporating 1-loop corrections stemming from the third-order density contrast. Furthermore, we introduce a non-trivial galaxy biasing scheme at third order. To simplify the calculation, we decompose the covariance into three distinct structures and leverage the isotropic basis of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals that would be naively involved, enabling the angular parts to be performed and leaving us with low-dimensional radial integrals. This analytical template could provide a more accurate characterization of the statistical errors on the 4PCF in future surveys, improving our ability to probe both its parity-even and parity-odd modes. This is the second and final paper in a two-part series.

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arXiv2026

A Two-Dimensional Test of Cosmological Parity Violation with the 3-Point Correlation Function

Searches for parity violation (PV) in the Universe's large-scale structure have recently been carried out using parity-odd modes of the galaxy 4-Point Correlation Function (4PCF). Here, we introduce a new estimator for a 3-Point Correlation Function (3PCF) that is sensitive to PV. The construction exploits the handedness of triangles formed on 2D spherical shells, where mirror-image configurations cannot be related by proper rotations within the surface. By dotting the oriented area vector with an externally-defined normal vector to the shell, we obtain sensitivity to PV. We present a discrete estimator for this statistic and also show how to correct for the survey geometry. This parity-odd 3PCF provides a complementary test of PV in galaxy surveys and a potential cross-check of PV 4PCF measurements.

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arXiv2026

A Finely-Binned Measurement of the Connected Even-Parity Galaxy 4-Point Correlation Function of DESI Year 1 Luminous Red Galaxies

We present the connected even-parity galaxy 4-Point Correlation Function (4PCF) of DESI Year 1 (Y1) Luminous Red Galaxies (LRGs). This is one of the first measurements of the connected 4PCF on data, and shows a clear detection at $\sim$12 to 17$σ$ in the full-sky analysis. We test the robustness of the signal by varying three factors: hemisphere (north vs. south), redshift range (either the full range $0.4 < z < 1.1$ or the higher-number-density interval $0.4 < z < 0.8$), and sample completeness (the full sample vs. only the most complete regions within the number density-motivated cut). Finally, we cross-correlate different patches that are spatially well-separated, and thus should have largely independent noise. This approach, at leading order, is able to remove mismatch between the covariance matrix of the data and that of the mocks; however, in certain cases at the cost of sensitivity. We find $\sim$15$σ$ evidence for an even-parity 4PCF in this approach. Overall, the studies of the 4PCF presented here probe sensitively any mismatch between mock catalogs and data, and also open up the prospect of fitting a model, constraining cosmological parameters and galaxy biases, and searching for Baryon Acoustic Oscillation (BAO) features.

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arXiv2026

A Path to an All-Sky Survey with Roman

A deep, space-based, all-sky near-infrared survey carried out with the Nancy Grace Roman Space Telescope would constitute a foundational astronomical infrastructure for decades to come. In this white paper, we present a concrete and feasible path to imaging the entire sky at $\sim0.1''$ resolution, beginning with high-impact fields in Cycle 1 and scaling to ultra-wide coverage within the nominal mission. This first-epoch survey will reach $\mathrm{H}\sim25.5$ AB mag (5$σ$) and maximize synergies with contemporaneous observatories, while preserving substantial time for other ambitious Roman programs. We outline representative scheduling scenarios and an example Cycle 1 program that triples early Roman-LSST overlap and delivers high-value community data products such as LSST forced photometry, joint \textit{Gaia}-Roman astrometry, and catalogs of Galactic substructure, stong lenses, and other rare systems. The Cycle 1 program will lay the foundation for an eventual all-sky survey, while also delivering high-impact early science. We invite broad community participation in shaping and carrying out both the initial program and the long-term vision of an all-sky Roman survey.

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arXiv2026

First Detection of the Baryon Acoustic Oscillation (BAO) Feature in the 3-Point Correlation Function of DESI DR1 Luminous Red Galaxies

We present the first detection of the 3-Point Correlation Function (3PCF) Baryon Acoustic Oscillation (BAO) signal from the DESI Data Release 1 (DR1) sample of Luminous Red Galaxies (LRGs), which contains over 2.1 million galaxies. Our analysis is based on a tree-level redshift-space bispectrum template, which is then transformed to position space using the Fast Fourier Transform on Logarithmic scales (FFTLog) algorithm. We detect the BAO feature with a significance of approximately $8.1σ$ using the EZmock covariance matrix and $8.5σ$ using the analytical covariance matrix, for the full LRG redshift range ($0.4<z<1.1$), denoted as the $z_{\rm full}$ sample. We use the Abacus altMTL mocks, the most precise DESI DR1 mock catalogs currently available, to validate our model. We find that our model fits the mocks well, with a small offset of $0.6\%$ in the recovered BAO scale, which we treat as a systematic error due to modeling. We measure the angle-averaged distance, $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.88 \pm 0.27$ ($1.72\%$ precision) when using the covariance matrix estimated from EZmocks and $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.72 \pm 0.18$ ($1.12\%$ precision) when using the analytical Gaussian covariance matrix. Our results show excellent agreement with the DESI DR1 2PCF BAO measurements as well. We also explore several other ways to estimate the error and find between $1.7$--$2.2\%$ precision on the BAO scale from the EZmock covariance matrix and between $1.1$--$1.5\%$ precision from the analytical covariance matrix. This work represents the first detection of the BAO feature in the DESI 3PCF, establishing its ability to probe the expansion history of the Universe with future DESI 3PCF measurements.

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arXiv2026

Illuminating the Physics of Cosmic Origin and Evolution: A UK Space Frontiers 2035 White Paper

Understanding the Universe's origins and evolution remains one of the most fundamental challenges in modern cosmology. This white paper explores three key science priorities in this field: unravelling the physics of cosmic inflation, investigating the accelerating expansion of the Universe, and precisely measuring the sum of the neutrino masses. Achieving these goals requires a dedicated survey to map the large-scale structure at high redshift in unprecedented detail. We describe how this can be achieved through a mission concept called SIRMOS, providing a high-throughput, highly multiplexed spectroscopic capability to obtain accurate redshifts for over 100 million galaxies over a wide sky area. Such a survey would leverage the deepest existing wide-area photometric catalogues for targeting, with spectra offering continuous 1.25-2.5~$μ$m wavelength coverage at moderate resolution, allowing precise redshift measurements in the $1<z<4$ range with minimal bias. We outline the scientific opportunities this presents. Recent years have seen significant advances in instrumentation, including digital micromirror devices, complex telescope mirrors, large detector arrays, and data processing pipelines. While these technologies have been demonstrated in terrestrial applications, such a survey is a unique opportunity to apply these proven capabilities in space to address fundamental questions in cosmology. Participation in such a mission will simultaneously deliver a compelling science case, help align UK Space Agency and STFC strategies, demonstrate the UK's growing capability in end-to-end space missions, and strengthen the national space economy through high-value industrial participation.

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arXiv2025

Can the CMB be Odd? Effect of a Parity-Violating Matter 4-Point Function on the Low-$\ell$ CMB Trispectrum

Here we explore from a theoretical perspective the sensitivity of the primary CMB anisotropy trispectrum to parity violation (PV) in large-scale structure (LSS). We focus on the Sachs-Wolfe term, which dominates at $\ell < 40$, after which the Doppler term takes over. We consider a model where the PV is only present out to some maximal scale $R$ of order a few hundred Mpc/$h$, consistent with what recent LSS 4PCF measurements seem to indicate. We find that the odd CMB trispectrum must be suppressed by at least one factor of $R/χ_*$$\simeq$1\%, with $χ_*$ the distance to last scattering, relative to the input matter 4PCF. Thus, a non-detection of PV in the CMB trispectrum is \textit{not necessarily inconsistent} with a genuine detection of PV in the LSS 4PCF.

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arXiv2025

Measurement of Parity-Violating Modes of the Dark Energy Spectroscopic Instrument (DESI) Year 1 Luminous Red Galaxies' 4-Point Correlation Function

Here we report the first measurement of the parity-violating (PV) 4-Point Correlation Function (4PCF) of the Dark Energy Spectroscopic Instrument's Year 1 Luminous Red Galaxy (DESI Y1 LRG) sample, motivated by the potential detection of the PV 4PCF in the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (SDSS BOSS) galaxies. In our auto-correlation ("auto") analysis, we find a statistically significant excess of the PV signal compared to mocks without any PV, at 4-10$σ$ depending on details of the analysis. This could arise either from genuine PV or from an underestimation of the variance in the mocks; it is unlikely to arise, at the signal level, from a systematic. We then cross-correlate ("cross") the putative PV signal between different, independent patches of sky, and there find no detection of parity violation. The two measurements are in significant tension: while the cross has somewhat larger error bars than the auto, this is not sufficient to explain the discrepancy. We thus present the current work as an intriguing addition to the PV work on BOSS and as motivation for exploring further the relationship between the auto and cross PV 4PCF analyses.

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arXiv2025

From Theory to Forecast: Neutrino Mass Effects on Mode-Coupling Kernels and Their Observational Implications

We present an analytical expression that gives both the matter and tracer (halo or galaxy) power spectrum with 1-loop corrections that include the neutrino effects on the mode coupling kernels. We use the FFTLog algorithm to accelerate calculating the higher-order corrections to the power spectrum. We then use our power spectrum and bispectrum models to pursue two main goals. First, we examine the impact of neutrino mass on cosmological parameter estimation from both the power spectrum and bispectrum in real space. We create 1-loop power spectrum and bispectrum templates in real-space and fit to the \texttt{Quijote} simulation suite, including the cross-covariance between the power spectrum and the bispectrum. We show the neutrino signature kernels estimate the same cosmological parameters as the model with the SPT (Standard Perturbation Theory) kernels, even for DESI Year 5 volume, except for the galaxy bias parameters inferred from the bispectrum. Second, we investigate to what extent the bispectrum can improve parameter constraints. We perform a Fisher forecast using the power spectrum, the tree-level bispectrum, and a joint analysis that includes the cross-covariance between them. We show that including the bispectrum can substantially reduce the error bars on key parameters. For the neutrino mass in particular, the uncertainty is reduced by $\sim 20\%$

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arXiv2025

Power Spectrum, Bispectrum, 2- and 3-Point Correlation Function, and Beyond

N-Point Correlation Functions, usually with N = 2, 3, and their Fourier-space analogs power spectrum and bispectrum, are major tools used in cosmology to capture the clustering of large-scale structure. We outline how the clustering these functions capture emerges, explain that inflation produces a 2PCF or power spectrum but that subsequent evolution eventually produces a 3PCF or bispectrum, and beyond (and that inflation may do so as well at some level). Furthermore, in principle the Universe also has a 4PCF or trispectrum, and even clustering beyond. For each of these tools, we discuss the motivation, the practical details of how they are estimated, the current algorithms used to compute them, the theory behind them, and recent applications to data. Throughout, we focus on positioning the reader to find and apply these algorithms with some understanding, linking to public code for each algorithm to the fullest extent possible.

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arXiv2025

Analytic Model for Covariance Matrices of the 2-, 3-, and 4-Point Correlation Functions in the Gaussian Random Field Approximation

Analyses of the galaxy N-Point Correlation Functions (NPCFs) have a large number of degrees of freedom, meaning one cannot directly estimate an invertible covariance matrix purely from mock catalogs, as has been the standard approach for the 2PCF and power spectrum. Instead, templates are used based on assuming a Gaussian Random Field density with the true, Boltzmann-solver-computed power spectrum. The resulting covariance matrices are sparse but have notable internal structure. To understand this structure better, we seek a fully analytic, closed-form covariance matrix template, using a power law power spectrum $P(k) \propto 1/k$ and including shot noise. We obtain a simple closed-form solution for the covariance of the 2PCF, as well as closed-form solutions for the fundamental building blocks (termed ``$f$-integrals'') of the covariance matrices for the 3PCF, 4PCF, and beyond. We achieve single-digit percent level accuracy for the $f$-integrals, confirming that our power spectrum model is a suitable alternative to the true power spectrum. In the $f$-integrals, we find that the greatest contributions arise when closed triangles may be formed. When $f$-integrals are multiplied together, as needed for the covariance, the number of non-vanishing configurations reduces. We use these results to present a clearer picture of the covariance matrices' structure and sparsity, which correspond to triangular and non-triangular regions. This will be useful in guiding future NPCF analyses with spectroscopic galaxy surveys such as DESI, Euclid, Roman, and SPHEREx.

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arXiv2025

Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals

Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have seemingly detected non-zero parity-odd modes at high significance. Since gravity, the primary driver of galaxy formation and evolution is parity-even, any parity violation, if genuine, is likely to have been produced by some new parity-violating mechanism in the early Universe. Here we investigate an inflationary model with a Chern-Simons interaction between an axion and a $U(1)$ gauge field, where the axion itself is the inflaton field. Evaluating the trispectrum (Fourier-space analog of the 4PCF) of the primordial curvature perturbations is an involved calculation with very high-dimensional loop integrals. We demonstrate how to simplify these integrals and perform all angular integrations analytically by reducing the integrals to convolutions and exploiting the Convolution Theorem. This leaves us with low-dimensional radial integrals that are much more amenable to efficient numerical evaluation. This paper is the first in a series in which we will use these results to compute the full late-time 4PCF for axion inflation, thence enabling constraints from upcoming 3D spectroscopic surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, or Roman.

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arXiv2025

CMB Lensing Trispectrum as a Probe of Parity Violation in LSS

We show that the Cosmic Microwave Background (CMB) lensing trispectrum is sensitive to parity violation in Large-Scale Structure (LSS). We obtain a compact expression for the reduced lensing trispectrum that is general for any input matter trispectrum. We then present as an example a simple parity-violating toy model for the latter, and explicitly compute the parity-odd lensing trispectrum, including an estimate of the Signal-to-Noise Ratio (SNR). This work serves as a proof of principle, demonstrating how future studies of more physically motivated models can be conducted. It also provides an intuitive physical explanation of why CMB lensing is sensitive to parity. Our work is the first to point out that secondary CMB anisotropies can be used to probe parity in LSS, and will be important in enabling upcoming experiments such as Simons Observatory and CMB-S4 to contribute maximal power on parity violation.

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arXiv2025

Neutrino Mass Signatures in the Galaxy Bispectrum

In the Standard Model, neutrinos are massless. However, oscillation experiments demonstrate that they do have a small mass. Currently, only the differences of the masses squared are known, along with an upper bound on their sum. Upcoming surveys of the Universe's Large-Scale Structure (LSS) offer a promising avenue to probe neutrino mass by revealing how neutrinos influence galaxy clustering. Massive neutrinos affect mode coupling within the framework of Perturbation Theory (PT) for structure formation, leaving detectable signatures in the PT kernels. In this work, we present for the first time the explicit modifications to the kernels caused by massive neutrinos and investigate the extent of these changes in the redshift-space galaxy bispectrum. To this end, we generate synthetic data using a theoretical covariance matrix and employ Markov-Chain Monte Carlo (MCMC) to assess the impact of these new signature terms. This approach, in contrast to Fisher forecasting, allows us to see if the new terms induce shifts in the recovered central values of parameters. The synthetic data is produced to mirror two different galaxy samples. The first corresponds to the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 CMASS Luminous Red Galaxy (LRG) sample, characterized by an effective volume of $V_{\rm eff} = 3 \;[{\rm Gpc}/h]^3$ and a number density of $\bar{n} = 3 \times 10^{-4} \;h/{\rm Mpc}$. The second corresponds to the Dark Energy Spectroscopic Instrument (DESI) Year 5 LRG sample with $V_{\rm eff} = 25 \;[{\rm Gpc}/h]^3$. Our findings indicate that neglecting neutrino mass effects in the kernels can result in a central value shift equivalent to approximately $1σ$ in the galaxy biases estimated from the DESI Y5-like sample. For the BOSS CMASS volume, the shift, though not statistically significant, is non-negligible.

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arXiv2024

A Simple Analytic Treatment of Neutrino Mass Impact on the Full Power Spectrum Shape via a Two-Fluid Approximation

We present a new closed-form formula for the matter power spectrum in the presence of massive neutrinos that gives an accuracy of better than 5\% on all scales. It is the first closed-form result valid on all scales. To calculate this closed-form solution, we iteratively solve the fluid equations for cold dark matter+baryons, and neutrinos in terms of the neutrino mass fraction, $f_ν \ll 1$, using variation of parameters to construct the response of the matter to the neutrino perturbation, which in turn will source the higher-order neutrino perturbations. This analytic solution accelerates calculations of the matter power spectrum with neutrinos. Also, it enables one to calculate the cross power spectra of matter and neutrinos which in turn can be used in computing the higher-order corrections to the power spectrum. To demonstrate our formula's accuracy and utility, we perform a Fisher forecast with it and show we reproduce the forecast from the Boltzmann solver class.

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arXiv2024

A Model for the Redshift-Space Galaxy 4-Point Correlation Function

The field of cosmology is entering an epoch of unparalleled wealth of observational data thanks to galaxy surveys such as DESI, Euclid, and Roman. Therefore, it is essential to have a firm theoretical basis that allows the effective analysis of the data. With this purpose, we compute the nonlinear, gravitationally-induced connected galaxy 4-point correlation function (4PCF) at the tree level in Standard Perturbation Theory (SPT), including redshift-space distortions (RSD). We begin from the trispectrum and take its inverse Fourier transform into configuration space, exploiting the isotropic basis functions of Cahn & Slepian (2023). We ultimately reduce the configuration-space expression to low-dimensional radial integrals of the power spectrum. This model will enable the use of the BAO feature in the connected 4PCF to sharpen our constraints on the expansion history of the Universe. It will also offer an additional avenue for determining the galaxy bias parameters, and thus tighten our cosmological constraints by breaking degeneracies. Survey geometry can be corrected in the 4PCF, and many systematics are localized, which is an advantage over data analysis with the trispectrum.

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arXiv2024

First Measurements of the 4-Point Correlation Function of Magnetohydrodynamic Turbulence as a Novel Probe of the Interstellar Medium

In the Interstellar Medium (ISM), gas and dust evolve under magnetohydrodynamic (MHD) turbulence. This produces dense, non-linear structures that then seed star formation. Observationally and theoretically, turbulence is quantified by summary statistics such as the 2-Point Correlation Function (2PCF) or its Fourier-space analog the power spectrum. These cannot capture the non-Gaussian correlations coming from turbulence's highly non-linear nature. We here for the first time apply the 4-Point Correlation Function (4PCF) to turbulence, measuring it on a large suite of MHD simulations that mirror, as well as currently possible, the conditions expected in the ISM. The 4PCF captures the dependence of correlations between quadruplets of density points on the geometry of the tetrahedron they form. Using a novel functionality added to the \textsc{sarabande} code specifically for this work, we isolate the purely non-Gaussian piece of the 4PCF. We then explore simulations with a range of pressures, $P$, and magnetic fields, $B$ (but without self-gravity); these are quantified by different sonic $(M_{\rm S})$ and Alfvénic $(M_{\rm A})$ Mach numbers. We show that the 4PCF has rich behavior that can in future be used as a diagnostic of ISM conditions. We also show that a large-scale coherent magnetic field leads to parity-odd modes of the 4PCF, a clean test of magnetic field coherence with observational ramifications. All our measurements of the 4PCF (10 $M_{\rm S}, M_{\rm A}$ combinations, 9 time-slices for each, 34 4PCF modes for each) are made public for the community to explore.

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