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DOE OSTI2025

The DESI DR1 Peculiar Velocity Survey: Fundamental Plane Catalogue

Measurements of peculiar velocities in the local Universe are a powerful tool to study the nature of dark energy at low ($z < 0.1$) redshifts. Here we present the largest single set of $z<0.1$ peculiar velocity measurements to date, obtained using the Fundamental Plane (FP) of galaxies in the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). We describe the photometric and spectroscopic selection criteria used to define the sample, as well as extensive quality control checks on the photometry and velocity dispersion measurements. Additionally, we perform detailed systematics checks for the many analysis parameters in our pipeline. Our DESI DR1 catalogue contains FP-based distances and peculiar velocities for $98,292$ unique early-type galaxies, increasing the total number of $z < 0.1$ FP distances ever measured by a factor of $\sim2$. We achieve a precision of $26\%$ random error in our distance measurements which is comparable to previous surveys. A series of companion DESI papers use the distances and peculiar velocities presented in this paper to measure cosmological parameters.

Ross, C. E. [Queensland U.]↗
DOE OSTI2021

Fast radio burst dispersion measure distribution as a probe of helium reionization

Fast radio burst (FRB) discoveries are occurring rapidly, with thousands expected from upcoming surveys. The dispersion measures (DM) observed for FRB include important information on cosmological distances and the ionization state of the universe from the redshift of emission until today. Rather than considering the DM–redshift relation, we investigate the statistical ensemble of the distribution of dispersion measures. Here, we explore the use of this abundance information, with and without redshift information, to probe helium reionization through simulated data to redshift z = 6. Carrying out Monte Carlo simulations of FRB survey samples, we examine the effect of different source redshift distributions, host galaxy models, sudden vs gradual reionization, and covariance with cosmological parameters on determination of helium reionization properties. We find that a fluence limited survey with 10 4 FRBs can discriminate different helium reionization histories at ~6σ using the DM-distribution of bursts, without redshift information (and ~10σ with redshifts).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Lens Modeling of STRIDES Strongly Lensed Quasars Using Neural Posterior Estimation

Strongly lensed quasars can be used to constrain cosmological parameters through time-delay cosmography. Models of the lens masses are a necessary component of this analysis. To enable time-delay cosmography from a sample of $\mathcal{O}(10^3)$ lenses, which will soon become available from surveys like the Rubin Observatory’s Legacy Survey of Space and Time and the Euclid Wide Survey, we require fast and standardizable modeling techniques. To address this need, we apply neural posterior estimation (NPE) for modeling galaxy-scale strongly lensed quasars from the Strong Lensing Insights into the Dark Energy Survey (STRIDES) sample. NPE brings two advantages: speed and the ability to implicitly marginalize over nuisance parameters. We extend this method by employing sequential NPE to increase precision of mass model posteriors. We then fold individual lens models into a hierarchical Bayesian inference to recover the population distribution of lens mass parameters, accounting for out-of-distribution shift. After verifying our method using simulated analogs of the STRIDES lens sample, we apply our method to 14 Hubble Space Telescope single-filter observations. We find the population mean of the power-law elliptical mass distribution slope, γ lens , to be $\mathcal{M}_γ$ lens = 2.13 ± 0.06. Our result represents the first population-level constraint for these systems. This population-level inference from fully automated modeling is an important stepping stone toward cosmological inference with large samples of strongly lensed quasars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Studying the effects of overlapping objects in dark energy

Observing the clustering of galaxies allows us to calculate cosmological parameters necessary for understanding dark energy. However, as the density of observed objects increases, the probability of these objects blending likewise increases, causing multiple galaxies to be observed as one. This affects the inferred values of parameters such as the galaxy bias (b) and the matter energy density (ΩM). To see whether the bias from incorrectly inferring the galaxy count is significant, we compare the correlation functions in simulated data for “true” and “observed” data sets with one-to-one and multiple-to-one correspondences, respectively. For each data set, we create two correlation functions: one “measured” function directly relying on the galaxies’ positions using the TreeCorr python library, and one “model” derived mathematically from the galaxies’ power spectrum using the Cosmological Core Library (CCL). By minimizing the residual between these two functions, we compute the ideal values for b and ΩM across the various possible redshifts that position the galaxies in three dimensional space. This minimization is done with an Markov chain Monte Carlo (MCMC) estimate that finds one value of ΩM and ten values for b corresponding to the ten redshift bins ranging from z = 0.2 to z = 1.2. We find that neither b nor ΩM is particularly affected by inclusion of blended galaxies. Though there is room for improvement, the data suggests that the fluctuations we found are a result of noise or limitations on the modeling rather than blending explicitly.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Cosmological cross-correlations and nearest neighbour distributions

ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Improving Dark Energy Constraints Using Low-Redshift Large-Scale Structures

The primary goal of this project was to improve constraints on dark energy measurements by improving our ability to extract cosmological information from low redshift large-scale structures. PI Clowe's project's primary aim was to reduce the bias in measurements of the masses of clusters of galaxies to a level where the evolution of the cluster mass function can be used in the Vera Rubin Observatory's Legacy Survey of Space and Time Dark Energy Science Collaboration survey to improve the accuracy of the measurement of dark energy and other cosmological parameters. Co-PI Seo's project studied observational systematics affecting large-scale clustering of galaxies, which will be used to improve dark energy constraints from the Dark Energy Spectroscopic Instrument (DESI). The cluster lensing project employed a series of simulations and observations of clusters of galaxies to test numerous potential systematic errors in cluster mass measurements using weak gravitational lensing as the accuracy of current weak lensing measurements are more than order of magnitude worse than what is required to use clusters of galaxies for accurate determination of dark energy parameters. PI Clowe and group developed and analyzed simulations to test for, and correct biases introduced in, the weak lensing measurement process. Finally, PI Clowe and group developed a method of detecting clusters using galaxy overdensities and applied the method to the BLISS and DES surveys. The success of spectroscopic dark energy mission such as the extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic Instrument (DESI) will depend on a thorough understanding of various observational systematics in the target density fluctuations that would give rise to spurious, non-cosmological signals. PI Seo and group developed a deep learning, artificial neural network (ANN) technique that modeled and mitigated such effects, aimed at deriving more robust galaxy clustering signals not only for the baryon acoustic oscillation feature and redshift-space distortions but also for primordial non-Gaussianity constraint.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The cosmology dependence of galaxy clustering and lensing from a hybrid N -body–perturbation theory model

ABSTRACT We implement a model for the two-point statistics of biased tracers that combines dark matter dynamics from N-body simulations with an analytic Lagrangian bias expansion. Using Aemulus, a suite of N-body simulations built for emulation of cosmological observables, we emulate the cosmology dependence of these non-linear spectra from redshifts z = 0 to z = 2. We quantify the accuracy of our emulation procedure, which is sub-per cent at $k=1\, h \,{\rm Mpc}^{-1}$ for the redshifts probed by upcoming surveys and improves at higher redshifts. We demonstrate its ability to describe the statistics of complex tracer samples, including those with assembly bias and baryonic effects, reliably fitting the clustering and lensing statistics of such samples at redshift z ≃ 0.4 to scales of $k_{\rm max} \approx 0.6\, h\,\mathrm{Mpc}^{-1}$. We show that the emulator can be used for unbiased cosmological parameter inference in simulated joint clustering and galaxy–galaxy lensing analyses with data drawn from an independent N-body simulation. These results indicate that our emulator is a promising tool that can be readily applied to the analysis of current and upcoming data sets from galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗
DOE OSTI2022

Map-based cosmology inference with lognormal cosmic shear maps

ABSTRACT Most cosmic shear analyses to date have relied on summary statistics (e.g. ξ+ and ξ−). These types of analyses are necessarily suboptimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps – and to the extent that the convergence field can be described by the lognormal model – our map posteriors allow us to reconstruct all summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the σ8–Ωm plane by $\approx\!{30}{{\ \rm per\ cent}}$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma _8\Omega _{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on S8.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗
DOE OSTI2025

Optimal parameterizations for observational constraints on thawing dark energy

Time-varying dark energy is often modeled in observational analyses through generic parameterizations of its equation of state w(z), which typically use two free parameters {w 0 , w a } to span a broad range of behaviors as a function of redshift. However, this broad range of behaviors can only approximately capture the dynamics of any given microphysical theory of dark energy. A complementary approach is to use targeted parameterizations designed to model specific classes of dynamical dark energy with greater precision. Focusing on the class of thawing dark energy, we quantify and compare the precision with which nineteen generic and targeted parameterizations can capture the dynamics of physically motivated thawing quintessence theories. We find that a targeted parameterization derived from a Padé expansion of w is the most reliable of these, producing accurate reconstructions of w(z), the expansion history H(z), and cosmological parameters such as H 0 and Ω m for a broad range of microphysical theories.

dark energy experiments↗
DOE OSTI2023

Role of the Hubble scale in the weak lensing versus CMB tension

Here, we explore a reparametrization of the lensing amplitude tension between weak lensing (WL) and cosmic microwave background (CMB) data and its implications for a joint resolution with the Hubble tension. Specifically, we focus on the lensing amplitude over a scale of 12 Mpc in absolute distance units using a derived parameter S 12 and show its constraints from recent surveys in comparison with Planck 2018. In WL alone, we find that the absolute distance convention correlates S 12 with H 0 . Accounting for this correlation in the 3D space S 12 ×w m ×ℎ reproduces the usual levels of 2~3⁢σ tension inferred from S 8 ×Ω m . Additionally, we derive scaling relations in the S 8 ×ℎ and S 12 ×ℎ planes that are allowed by Λ⁢CDM and extrapolate target scalings needed to solve the H 0 and lensing-amplitude tensions jointly in a hypothetical beyond-Λ⁢CDM model. As a test example, we quantify how the early dark energy scenario compares with these target scalings. Useful fitting formulas for S 8 and S 12 as a function of other cosmological parameters in Λ⁢CDM are provided, with 1% precision.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The DECADE cosmic shear project IV: cosmological constraints from 107 million galaxies across 5,400 deg$^2$ of the sky

We present cosmological constraints from the Dark Energy Camera All Data Everywhere (DECADE) cosmic shear analysis. This work uses shape measurements for 107 million galaxies measured through Dark Energy Camera (DECam) imaging of $5,\!412$ deg$^2$ of sky that is outside the Dark Energy Survey (DES) footprint. We derive constraints on the cosmological parameters $S_8 = 0.791^{+0.027}_{-0.032}$ and $Ω_{\rm m} =0.269^{+0.034}_{-0.050}$ for the $Λ$CDM model, which are consistent with those from other weak lensing surveys and from the cosmic microwave background. We combine our results with cosmic shear results from DES Y3 at the likelihood level, since the two datasets span independent areas on the sky. The combined measurements, which cover $\approx\! 10,\!000$ deg$^2$, prefer $S_8 = 0.791 \pm 0.023$ and $Ω_{\rm m} = 0.277^{+0.034}_{-0.046}$ under the $Λ$CDM model. These results are the culmination of a series of rigorous studies that characterize and validate the DECADE dataset and the associated analysis methodologies (Anbajagane et. al 2025a,b,c). Overall, the DECADE project demonstrates that the cosmic shear analysis methods employed in Stage-III weak lensing surveys can provide robust cosmological constraints for fairly inhomogeneous datasets. This opens the possibility of using data that have been previously categorized as ``unusable'' for cosmic shear analyses, thereby increasing the statistical power of upcoming weak lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Neural network-based model of galaxy power spectrum: fast full-shape galaxy power spectrum analysis

ABSTRACT We present a neural network-based emulator for the galaxy redshift-space power spectrum that enables several orders of magnitude acceleration in the galaxy clustering parameter inference, while preserving 3$\sigma$ accuracy better than 0.5 per cent up to $k_{\mathrm{max}}$ = 0.25 $\, h\text{Mpc}^{-1}$ within Lambda-cold dark matter ($\Lambda$CDM) and around 0.5 per cent $w_0$–$w_a$CDM. Our surrogate model only emulates the galaxy bias-invariant terms of one-loop perturbation theory predictions, these terms are then combined analytically with galaxy bias terms, counter-terms, and stochastic terms in order to obtain the non-linear redshift-space galaxy power spectrum. This allows us to avoid any galaxy bias prescription in the training of the emulator, which makes it more flexible. Moreover, we include the redshift $z \in [0,1.4]$ in the training which further avoids the need for re-training the emulator. We showcase the performance of the emulator in recovering the cosmological parameters of $\Lambda$CDM by analysing the suite of 25 AbacusSummit simulations that mimic the Dark Energy Spectroscopic Instrument luminous red galaxies at $z=0.5$ and 0.8, together as the emission line galaxies at $z=0.8$. We obtain similar performance in all cases, demonstrating the reliability of the emulator for any galaxy sample at any redshift in $0 \lt z \lt 1.4$. We will make our emulator public at github repository.

Trusov, Svyatoslav (ORCID:0000000224146720)↗
DOE OSTI2023

Precision cosmology with primordial GW backgrounds in presence of astrophysical foregrounds

The era of Gravitational-Wave (GW) astronomy will grant the detection of the astrophysical GW background from unresolved mergers of binary black holes, and the prospect of probing the presence of primordial GW backgrounds. In particular, the low-frequency tail of the GW spectrum for causally-generated primordial signals (like a phase transition) offers an excellent opportunity to measure unambiguously cosmological parameters as the equation of state of the universe, or free-streaming particles at epochs well before recombination. We discuss whether this programme is jeopardised by the uncertainties on the astrophysical GW foregrounds that coexist with a primordial background. We detail the motivated assumptions under which the astrophysical foregrounds can be assumed to be known in shape, and only uncertain in their normalisation. In this case, the sensitivity to a primordial signal can be computed by a simple and numerically agile procedure, where the optimal filter function subtracts the components of the astrophysical foreground that are close in spectral shape to the signal. We show that the degradation of the sensitivity to the signal in presence of astrophysical foregrounds is limited to a factor of a few, and only around the frequencies where the signal is closer to the foregrounds. Our results highlight the importance of modelling the contributions of eccentric or intermediate-mass black hole binaries to the GW background, to consolidate the prospects to perform precision cosmology with primordial GW backgrounds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Sensitivity of Next-Generation CMB Surveys to Neutrinos and Other Light Relics

Neutrinos and other light relics leave characteristic imprints in the cosmic microwave background anisotropies, making their observation a sensitive probe of the particle content and thermal history of the early universe. The energy density in these relativistic species is parameterized by their effective number $N_\mathrm{eff}$. Measuring this parameter at the percent level, which is a long-standing science goal of CMB-S4 and other experiments, would test a wide range of well-motivated physics within and beyond the Standard Model of particle physics. In this paper, we present Fisher-matrix forecasts of the projected sensitivity to $N_\mathrm{eff}$ of several CMB-S4 survey configurations considered during its extensive design phase. The conceptual design reaches $σ(N_\mathrm{eff}) < 0.03$ over its seven-year observing period, while the revised configuration achieves the same precision over a longer timescale. We complement these results with a cosmic-variance-limited survey over the same multipole range to quantify the room for improvement accessible with additional instrumental, observational, and theoretical efforts. Finally, we discuss the broad implications of precise $N_\mathrm{eff}$ measurements for the radiation sector, big bang nucleosynthesis, light thermal relics, and other early-universe physics. The forecasts presented in this work are performed with the publicly released DRAFT (Dark Radiation Anisotropy Flowdown Team) tool. It provides an end-to-end pipeline from simulated foreground maps and component separation to delensing and projected sensitivities for any cosmological parameter, and it can be directly applied to other cosmic microwave background survey designs.

Trendafilova, Cynthia [Case Western Reserve U., CE↗