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Patrick McDonald

Publications and source records attributed to Patrick McDonald.

At least 19 recordsLinked to original sources
arXiv2025

The Compressed 3D Lyman-Alpha Forest Bispectrum

Cosmological studies of the Lyman-Alpha (Lya) forest typically constrain parameters using two-point statistics. However, higher-order statistics, such as the three-point function (or its Fourier counterpart, the bispectrum) offer additional information and help break the degeneracy between the mean flux and power spectrum amplitude, albeit at a significant computational cost. To address this, we extend an existing highly informative compression of the bispectrum, the skew spectra, to the Lya forest. We derive the tree-level bispectrum of Lya forest fluctuations in the framework of effective field theory (EFT) directly in redshift space and validate our methodology on synthetic Lya forest data. We measure the anisotropic cross-spectra between the transmitted flux fraction and all quadratic operators arising in the bispectrum, yielding a set of 26 skew spectra. Using idealized 3D Gaussian smoothing (R=10 Mpc/h), we find good agreement (1-2 sigma level based on the statistical errors of the mocks) with the theoretical tree-level bispectrum prediction for monopole and quadrupole up to k <= 0.17 h/Mpc. To enable the cosmological analysis of Lya forest data from the currently observing Dark Energy Spectroscopic Instrument (DESI), where we cannot do 3D smoothing, we use a line-of-sight smoothing and introduce a new statistic, the shifted skew spectra. These probe non-squeezed bispectrum triangles and avoid locally applying quadratic operators to the field by displacing one copy of the field in the radial direction. Using a fixed displacement of 40 Mpc/h (and line-of-sight smoothing of 10 Mpc/h) yields a similar agreement with the theory prediction. For the special case of correlating the squared (and displaced) field with the original one, we analytically forward model the window function making this approach readily applicable to DESI data.

astro-ph.CO↗
arXiv2025

Weighted FFT estimators for 1D and 3D correlations of the Lyman-$\alpha$ forest

Correlations in the Lyman-$\alpha$ (Ly$\alpha$) forest, both as a function of line of sight separation (1D) and 3D separation, provide a unique window to the distribution of matter at redshifts not accessible by current galaxy surveys. While optimal quadratic estimators have been used to measure 1D correlations, they are computationally expensive and difficult to extend to 3D analyses. On the other hand, estimators based on the Fast Fourier Transform (FFT) are significantly faster, but are affected by missing data in the spectra (masked pixels) and so far have not used pixel weights to reduce the uncertainties in the measurement. In this publication we describe how to compute the window matrix that enables forward-modeling the impact of masked pixels and weights on the FFT-based estimators. We use Gaussian and hydrodynamical simulations with artificially masked pixels to validate the method on the measurement of 1D correlations. Finally, we show that the formalism can be extended to model the impact on 3D correlations, in particular on the cross-spectrum, the correlation of 1D Fourier modes as a function of transverse separation. This work will enable more precise clustering measurements with the Ly$\alpha$ forest dataset recently collected by the Dark Energy Spectroscopic Instrument (DESI).

astro-ph.CO↗
arXiv2025

The Spectroscopic Stage-5 Experiment

The existence, properties, and dynamics of the dark sectors of our universe pose fundamental challenges to our current model of physics, and large-scale astronomical surveys may be our only hope to unravel these long-standing mysteries. In this white paper, we describe the science motivation, instrumentation, and survey plan for the next-generation spectroscopic observatory, the Stage-5 Spectroscopic Experiment (Spec-S5). Spec-S5 is a new all-sky spectroscopic instrument optimized to efficiently carry out cosmological surveys of unprecedented scale and precision. The baseline plan for Spec-S5 involves upgrading two existing 4-m telescopes to new 6-m wide-field facilities, each with a highly multiplexed spectroscopic instrument capable of simultaneously measuring the spectra of 13,000 astronomical targets. Spec-S5, which builds and improves on the hardware used for previous cosmology experiments, represents a cost-effective and rapid approach to realizing a more than 10$\times$ gain in spectroscopic capability compared to the current state-of-the-art represented by the Dark Energy Spectroscopic Instrument project (DESI). Spec-S5 will provide a critical scientific capability in the post-Rubin and post-DESI era for advancing cosmology, fundamental physics, and astrophysics in the 2030s.

astro-ph.CO↗
arXiv2024

The 3D Lyman-$\alpha$ Forest Power Spectrum from eBOSS DR16

We measure the three-dimensional power spectrum (P3D) of the transmitted flux in the Lyman-a (Ly-a) forest using the complete extended Baryon Oscillation Spectroscopic Survey data release 16 (eBOSS DR16). This sample consists of 205,012 quasar spectra in the redshift range 2 <= z <= 4 at an effective redshift z=2.334. We propose a pair-count spectral estimator in configuration space, weighting each pair by exp(ikr), for wave vector k and pixel pair separation r, effectively measuring the anisotropic power spectrum without the need for fast Fourier transforms. This accounts for the window matrix in a tractable way, avoiding artifacts found in Fourier-transform based power spectrum estimators due to the sparse sampling transverse to the line-of-sight of Ly-a skewers. We extensively test our pipeline on two sets of mocks: (i) idealized Gaussian random fields with a sparse sampling of Ly-a skewers, and (ii) log-normal LyaCoLoRe mocks including realistic noise levels, the eBOSS survey geometry and contaminants. On eBOSS DR16 data, the Kaiser formula with a non-linear correction term obtained from hydrodynamic simulations yields a good fit to the power spectrum data in the range 0.02 <= k <= 0.35 h/Mpc at the 1-2 sigma level with a covariance matrix derived from LyaCoLoRe mocks. We demonstrate a promising new approach for full-shape cosmological analyses of Ly-a forest data from cosmological surveys such as eBOSS, the currently observing Dark Energy Spectroscopic Instrument and future surveys such as the Prime Focus Spectrograph, WEAVE-QSO and 4MOST.

astro-ph.CO↗
arXiv2024

Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results

This paper provides a comprehensive overview of how fitting of Baryon Acoustic Oscillations (BAO) is carried out within the upcoming Dark Energy Spectroscopic Instrument's (DESI) 2024 results using its DR1 dataset, and the associated systematic error budget from theory and modelling of the BAO. We derive new results showing how non-linearities in the clustering of galaxies can cause potential biases in measurements of the isotropic ($\alpha_{\mathrm{iso}}$) and anisotropic ($\alpha_{\mathrm{ap}}$) BAO distance scales, and how these can be effectively removed with an appropriate choice of reconstruction algorithm. We then demonstrate how theory leads to a clear choice for how to model the BAO and develop, implement and validate a new model for the remaining smooth-broadband (i.e., without BAO) component of the galaxy clustering. Finally, we explore the impact of all remaining modelling choices on the BAO constraints from DESI using a suite of high-precision simulations, arriving at a set of best-practices for DESI BAO fits, and an associated theory and modelling systematic error. Overall, our results demonstrate the remarkable robustness of the BAO to all our modelling choices and motivate a combined theory and modelling systematic error contribution to the post-reconstruction DESI BAO measurements of no more than $0.1\%$ ($0.2\%$) for its isotropic (anisotropic) distance measurements. We expect the theory and best-practices laid out to here to be applicable to other BAO experiments in the era of DESI and beyond.

astro-ph.CO↗
arXiv2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological $N$-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis. We also provide an optimized package for computing the power spectra and other two-point statistics of an arbitrary galaxy catalog as well as a pipeline for obtaining CV-reduced measurements on any of the AbacusSummit cubic box outputs. We make our scripts publicly available and report a speed improvement of $\sim$10 for a grid size of $N_{\rm mesh} = 256^3$ compared with \texttt{nbodykit}.

astro-ph.CO↗
arXiv2023

First Detection of the BAO Signal from Early DESI Data

We present the first detection of the baryon acoustic oscillations (BAO) signal obtained using unblinded data collected during the initial two months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). From a selected sample of 261,291 Luminous Red Galaxies spanning the redshift interval 0.4 < z < 1.1 and covering 1651 square degrees with a 57.9% completeness level, we report a ~5 sigma level BAO detection and the measurement of the BAO location at a precision of 1.7%. Using a Bright Galaxy Sample of 109,523 galaxies in the redshift range 0.1 < z < 0.5, over 3677 square degrees with a 50.0% completeness, we also detect the BAO feature at ~3 sigma significance with a 2.6% precision. These first BAO measurements represent an important milestone, acting as a quality control on the optimal performance of the complex robotically-actuated, fiber-fed DESI spectrograph, as well as an early validation of the DESI spectroscopic pipeline and data management system. Based on these first promising results, we forecast that DESI is on target to achieve a high-significance BAO detection at sub-percent precision with the completed 5-year survey data, meeting the top-level science requirements on BAO measurements. This exquisite level of precision will set new standards in cosmology and confirm DESI as the most competitive BAO experiment for the remainder of this decade.

astro-ph.CO↗
arXiv2022

The MegaMapper: A Stage-5 Spectroscopic Instrument Concept for the Study of Inflation and Dark Energy

In this white paper, we present the MegaMapper concept. The MegaMapper is a proposed ground-based experiment to measure Inflation parameters and Dark Energy from galaxy redshifts at $2<z<5$. In order to achieve path-breaking results with a mid-scale investment, the MegaMapper combines existing technologies for critical path elements and pushes innovative development in other design areas. To this aim, we envision a 6.5-m Magellan-like telescope, with a newly designed wide field, coupled with DESI spectrographs, and small-pitch robots to achieve multiplexing of at least 26,000. This will match the expected achievable target density in the redshift range of interest and provide a 10x capability over the existing state-of the art, without a 10x increase in project budget.

astro-ph.IM↗
arXiv2022

A Spectroscopic Road Map for Cosmic Frontier: DESI, DESI-II, Stage-5

In this white paper, we present an experimental road map for spectroscopic experiments beyond DESI. DESI will be a transformative cosmological survey in the 2020s, mapping 40 million galaxies and quasars and capturing a significant fraction of the available linear modes up to z=1.2. DESI-II will pilot observations of galaxies both at much higher densities and extending to higher redshifts. A Stage-5 experiment would build out those high-density and high-redshift observations, mapping hundreds of millions of stars and galaxies in three dimensions, to address the problems of inflation, dark energy, light relativistic species, and dark matter. These spectroscopic data will also complement the next generation of weak lensing, line intensity mapping and CMB experiments and allow them to reach their full potential.

astro-ph.CO↗
arXiv2021

Unified galaxy power spectrum measurements from 6dFGS, BOSS, and eBOSS

We make use of recent developments in the analysis of galaxy redshift surveys to present an easy to use matrix-based analysis framework for the galaxy power spectrum multipoles, including wide-angle effects and the survey window function. We employ this framework to derive the deconvolved power spectrum multipoles of 6dFGS DR3, BOSS DR12 and the eBOSS DR16 quasar sample. As an alternative to the standard analysis, the deconvolved power spectrum multipoles can be used to perform a data analysis agnostic of survey specific aspects, like the window function. We show that in the case of the BOSS dataset, the Baryon Acoustic Oscillation (BAO) analysis using the deconvolved power spectra results in the same likelihood as the standard analysis. To facilitate the analysis based on both the convolved and deconvolved power spectrum measurements, we provide the window function matrices, wide-angle matrices, covariance matrices and the power spectrum multipole measurements for the datasets mentioned above. Together with this paper we publish a \code{Python}-based toolbox to calculate the different analysis components. The appendix contains a detailed user guide with examples for how a cosmological analysis of these datasets could be implemented. We hope that our work makes the analysis of galaxy survey datasets more accessible to the wider cosmology community.

astro-ph.CO↗
arXiv2021

An emulator for the Lyman-$α$ forest in beyond-$Λ$CDM cosmologies

Interpreting observations of the Lyman-$α$ forest flux power spectrum requires interpolation between a small number of expensive simulations. We present a Gaussian process emulator modelling the 1D flux power spectrum as a function of the amplitude and slope of the small-scale linear matter power spectrum, and the state of the intergalactic medium at the epoch of interest ($2 < z < 4$). This parameterisation enables the prediction of the flux power spectrum in extended cosmological models that are not explicitly included in the training set, eliminating the need to construct bespoke emulators for a number of extensions to $Λ$CDM. Our emulator is appropriate for cosmologies in which the linear matter power spectrum is described to percent level accuracy by just an amplitude and slope across the epoch of interest, and in the regime probed by eBOSS/DESI data. We demonstrate this for massive neutrino cosmologies, where the emulator is able to predict the flux power spectrum in a $Σm_ν=0.3$ eV neutrino cosmology to sub-percent accuracy, without including massive neutrinos in the training simulations. Further parameters would be required to describe models with sharp features in the linear power, such as warm or light axion dark matter. This work will facilitate the combination of upcoming DESI data with observations of the cosmic microwave background, to obtain constraints on neutrino mass and other extensions to $Λ$CDM cosmology.

astro-ph.CO↗
arXiv2021

Extremizing Temperature Functions of Rods with Robin Boundary Conditions

We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one with given data, and one where the data has been symmetrized. When the Robin parameter is positive and the symmetrization is symmetric decreasing rearrangement, we prove that the solution to the symmetrized problem has larger increasing convex means. When the Robin parameter equals zero (so that we have Neumann boundary conditions) and the symmetrization is decreasing rearrangement, we similarly show that the solution to the symmetrized problem has larger convex means.

math.AP↗
arXiv2020

Massive neutrinos and degeneracies in Lyman-alpha forest simulations

Using a suite of hydrodynamical simulations with cold dark matter, baryons, and neutrinos, we present a detailed study of the effect of massive neutrinos on the 1-D and 3-D flux power spectra of the Lyman-$α$ (Ly$α$) forest. The presence of massive neutrinos in cosmology induces a scale- and time-dependent suppression of structure formation that is strongest on small scales. Measuring this suppression is a key method for inferring neutrino masses from cosmological data, and is one of the main goals of ongoing and future surveys like eBOSS, DES, LSST, Euclid or DESI. The clustering in the Ly$α$ forest traces the quasi-linear power at late times and on small scales. In combination with observations of the cosmic microwave background, the forest therefore provides some of the tightest constraints on the sum of the neutrino masses. However there is a well-known degeneracy between $Σm_ν$ and the amplitude of perturbations in the linear matter power spectrum. We study the corresponding degeneracy in the 1-D flux power spectrum of the Ly$α$ forest, and for the first time also study this degeneracy in the 3-D flux power spectrum. We show that the non-linear effects of massive neutrinos on the Ly$α$ forest, beyond the effect of linear power amplitude suppression, are negligible, and this degeneracy persists in the Ly$α$ forest observables to a high precision. We discuss the implications of this degeneracy for choosing parametrisations of the Ly$α$ forest for cosmological analysis.

astro-ph.CO↗
arXiv2019

Improved renormalization group computation of likelihood functions for cosmological data sets

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.

astro-ph.CO↗
arXiv2019

Inflation and Dark Energy from spectroscopy at $z > 2$

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at $z < 1$, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at $2 < z < 5$, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $σ(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space.

astro-ph.CO↗
arXiv2018

Renormalization group computation of likelihood functions for cosmological data sets

I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian fields, where the method allows arbitrarily close to exact computation of the likelihood function in order $\sim N$ time, even for problems with no symmetry, compared to $N^3$ for brute force linear algebra (where $N$ is the number of data points -- to be fair, methods already exist to solve the Gaussian problem in at worst $N \log N$ time, and this method will not necessarily be faster in practice). The method requires no sampling or other Monte Carlo (random) element. Non-linearity/non-Gaussianity can be accounted for to the extent that terms generated by integrating out small scale modes can be projected onto a sufficient basis, e.g., at least in the sufficiently perturbative regime. The formulas to evaluate are straightforward and require no understanding of quantum field theory, but this paper may also serve as a pedagogical introduction to Wilsonian RG for astronomers.

astro-ph.CO↗