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DOE OSTI2026

The Stability of Nd Hydroxyl Complexes at Near Neutral to Alkaline pH from 25 to 75 °C: Implications for Monazite Solubility in Hydrothermal Aqueous Fluids

Speciation of rare earth elements (REE) in aqueous fluids controls their mobilization during fluid-rock interaction. Thermodynamic modeling provides important insights into the factors controlling REE mobility and fractionation in aqueous fluids, in which aqueous REE hydroxyl complexes are particularly important across a broad pH range. However, the stability of these REE hydroxyl complexes remains poorly determined due to limited experimental data above ambient temperature. In this work, UV–vis spectrophotometry experiments were conducted to determine the cumulative hydrolysis constants for neodymium (Nd) from 25 to 75 °C in near-neutral to alkaline solutions. The color indicator m -cresol purple was used to determine in situ pH. Alkaline NaOH-bearing aqueous solutions were doped with varying initial Nd concentrations (0 to ∼0.155 mmol/kg), which resulted in the release of protons (H + ) and pH decrease during hydrolysis of Nd 3+ according to Nd 3+ + n H 2 O = Nd(OH) n 3– n + H + . The average OH – ligand number coordinated to Nd 3+ was found to increase from 1.0 to 1.6 at 25 °C and from 1.2 to 2.8 at 75 °C over a pH range from 6.3 to 9.0. The measured speciation shows an increased predominance of Nd(OH) 3 0 over the Nd(OH) 2 + and Nd(OH) 2+ species with increased temperature and pH. The increasing cumulative formation constants (log*β° n , n = 1 to 3) retrieved from 25 to 75 °C differ by 0.1 to 1.9 logarithmic units in comparison to existing thermodynamic databases. These updated thermodynamic data have important implications for geochemical modeling of the speciation of Nd hydroxyl complexes and the solubility of monazite as a function of pH.

58 GEOSCIENCES↗

DOE OSTI2024

Shallow Soil Response to a Buried Chemical Explosion With Geophones and Distributed Acoustic Sensing

Abstract Shallow sediments can respond non‐linearly to large dynamic strains and undergo a subsequent healing phase as the material gradually recovers following the passing of seismic waves. This study focuses on the physical changes in the subsurface caused by the shaking from a buried chemical explosion detonated in a borehole in Nevada, USA, as a part of the Source Physics Experiment Phase II. The explosion damaged the shallow subsurface and modified the frequency content recorded by 491 geophones and 2240 Distributed Acoustic Sensing (DAS) channels within 2.5 km from surface ground zero. We observe a gradual shift of resonance frequencies in the 10–25 Hz frequency band in the hours following the explosion and develop a method to characterize the related logarithm‐type healing process of the shallow (i.e., upper ∼25 m) subsurface. We find that stronger levels of ground motion increase the relative degree of damage and duration of the subsurface healing; with the spall region exhibiting the largest degree of damage and longest healing recovery time. We observe coherent spatial patterns of damage with the region located to the southeast of the explosion exhibiting more damage than the southwest region. This study demonstrates that both DAS and co‐located geophones capture similar temporal changes associated with the physical processes occurring in the subsurface, with the high‐density sampling of DAS measurements enabling a new capability to monitor the fine‐scale changes of the Earth's shallow subsurface following the detonation of a buried explosion.

Viens, Loïc↗

DOE OSTI2025

The Turbulent Pressure Spectrum Within the Roughness Sublayer of a Subarctic Forest Canopy

The turbulent static pressure spectrum E pp (k x ) as a function of longitudinal wavenumber k x in the roughness sublayer of forested canopies is of interest to a plethora of problems such as pressure transport in the turbulent kinetic energy budget, pressure pumping from snow or forest floor, and coupling between flow within and above canopies. Long term static pressure measurements above a sub-arctic forested canopy for near-neutral conditions during the winter and spring were collected and analyzed for three snow cover conditions: trees and ground covered with snow, trees are snow free but the ground is covered with snow, and snow free cover. In all three cases, it is shown that E pp (k x ) obeys the attached eddy hypothesis at low wavenumbers (1/δ < k x < 1/z) —with E pp (k x ) ∝ u$^4_*$k$^{-1}_x$ and Kolmogorov scaling in the inertial subrange at higher wavenumbers—with E pp (k x ) ∝ ϵ 4/3 k x -7/3 , where u * is the friction velocity at the canopy top, is the mean turbulent kinetic energy dissipation rate, z is the distance from the snow top, and is the boundary layer depth. The implications of these two scaling laws to the normalized root-mean squared pressure C p = o p /u$^2_*$ and its newly proposed logarithmic scaling with normalized wall-normal distance z/δ are discussed for snow covered and snow free vegetation conditions. The work here also shows that k$^{-1}_x$ the in the E pp (k x ) appears more extensive and robust than its longitudinal velocity counterpart.

Aslan, Toprak [Finnish Meteorological Inst., Helsi↗

DOE OSTI2025

Deep learning forecasts the spatiotemporal evolution of fluid-induced microearthquakes

Microearthquakes generated by subsurface fluid injection record the evolving stress state and permeability of reservoirs. Forecasting their spatiotemporal evolution is therefore critical for applications such as enhanced geothermal systems, carbon dioxide sequestration and other geoengineering applications. Here we propose a transformer neural network model that ingests hydraulic stimulation history and prior microearthquake observations to forecast four key quantities: cumulative microearthquake count, cumulative logarithmic seismic moment, and the 50th- and 95th-percentile extents of the microearthquake cloud. Applied to the EGS Collab Experiment 1 dataset, the model achieves R2 > 0.98 for the 1-s forecast horizon and R2 > 0.88 for the 15-s forecast horizon across all targets, and supplies uncertainty estimates through a learned standard deviation term. These accurate, uncertainty-quantified forecasts enable real-time inference of fracture propagation and permeability evolution, demonstrating the strong potential of deep-learning approaches to improve seismic-risk assessment and guide mitigation strategies in future fluid-injection operations.

Chung, Jaehong↗

DOE OSTI2024

UV-Vis spectrophotometric determination of rare earth elements (REE) speciation at near-neutral to alkaline pH. Part I: m-cresol purple properties from 25-75 °C and Er hydrolysis

The speciation and mobility of rare earth elements (REE) strongly depends on pH which controls the formation of charged aqueous hydroxyl species. The latter potentially play an important role in controlling heavy REE adsorption on clay minerals in near-neutral to alkaline waters such as in regolith-hosted REE mineral deposits. However, accurate REE hydrolysis constants are needed for developing geochemical models that can predict the role of these charged species in natural systems. Here, we develop a robust experimental UV-Vis spectrophotometric method using m-cresol purple to determine in situ pH from 25 to 75 °C. This method is used to derive the average ligand number and hydrolysis constants of erbium (Er) at 25 °C in aqueous solutions with low ionic strength (≤ 0.001 mol/L) at pH from ~7 to 9.5 and in the presence of Er concentrations from 0 to 0.057 mM. The average ligand number ranges between 1 and 3 indicating that Er(OH) 2+ , Er(OH) 2 + and Er(OH) 3 0 control speciation in the experiments. The logarithm of the Er hydrolysis constants (log*β n ° , n= 1 to 3) derived at infinite dilution for the reaction Er 3+ + nH 2 O = Er(OH) n 3-n + nH + are: *β 1 ° = –7.22 ± 0.10, *β 2 ° = –14.52 ± 0.08, *β 3 ° = –23.24 ± 0.04. Implementation of these experimental data into a geochemical model indicates that the Er(OH) 2 + and Er(OH) 3 0 species are both stable in a much wider pH range than previously predicted. Consequently, the positively charged REE hydroxyl complexes can potentially control the fractionation of light vs. heavy REE via adsorption as observed in the formation of certain regolith-hosted REE deposits.

58 GEOSCIENCES↗

DOE OSTI2024

Rapidly convergent quantum Monte Carlo using a Chebyshev projector

The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.

Zhao, Zijun↗

DOE OSTI2024

Volatile fatty acid extraction from fermentation broth using a hydrophobic ionic liquid and in situ enzymatic esterification

Efficient recovery of volatile fatty acids (VFAs) from fermentation broth is a challenge due to low VFA titers and thus limits the commercialization of VFA production using biological routes. Liquid–liquid extraction using hydrophobic ionic liquids (ILs) shows great promise for the extraction and esterification of hydrophilic VFAs. In this study, several ILs were evaluated to select a water-immiscible and efficient extraction solvent. The selected IL, trihexyltetradecyl phosphonium dibutylphosphate ([P 666,14 ][DBP]), gave a cumulative VFA extraction of around 842.8 mg per g IL. The predicted excess enthalpy (H E ) and logarithmic activity coefficients ln(γ) using the COSMO-RS model were validated with the experimentally obtained VFA recovery from fermentation broth. To understand the extraction mechanism of VFAs, quantum theory of atoms in molecules (QTAIM) and noncovalent interaction (NCI) were performed. The results suggest that long chain fatty acids exhibit strong van der Waals interaction with the DBP anion leading to higher VFA extraction. The enzymatic esterification of VFAs with ethanol in [P 666,14 ][DBP] was optimized using the Box–Behnken response surface design of experiment. Under the optimized conditions, up to 83.7% of hexanoic acid was converted to ethyl esters, while other shorter chain VFAs have lower conversion efficiency (38.3–63.2%).

09 BIOMASS FUELS↗

DOE OSTI2026

Nanoscale control over single vortex motion in an unconventional superconductor

Precise control of superconducting vortices is crucial for studying vortex dynamics and vortex braiding. We propose a new method to pull vortex lines in the layered superconductor FeSe using a scanning tunneling microscope (STM) tip. Weak contact of the STM tip with the FeSe surface locally reduces the superconducting gap, thereby creating a tunable vortex pinning potential on the nanometer scale. This enables controlled vortex line deformation even in dense vortex lattices. Analytical modeling reveals that the deformation strength scales logarithmically with conductance and depends on tip geometry. Our findings point to local strain-induced gap suppression as the mechanism for STM-mediated vortex manipulation, providing a fundamental insight relevant to vortex behavior in the context of quantum information studies.

Song, Sang Yong [Oak Ridge National Laboratory (OR↗

DOE OSTI2025

Quantifying Distribution System Resilience From Utility Data: Large Event Risk and Benefits of Investments

We focus on blackouts in electric distribution systems that have a large cost to customers. To quantify resilience to these events, we show how to calculate risk metrics from the historical outage data routinely collected by utilities' outage management systems. Risk is defined using a customer cost exceedance curve. The exceedance curve has a heavy tail that implies large fluctuations in large blackout costs, and this makes estimating the mean large cost in the usual way impractical. To avoid this problem, we use new resilience metrics describing the large event risk; these metrics are the probability of a large cost event, the annual log cost resilience index, and the average of the logarithm of the cost of large-cost events or the slope magnitude of the tail on a log–log exceedance curve. Resilience can be improved by planned investments to upgrade system components or speed up restoration. The benefits that these investments would have had if they had been made in the past can be quantified by “rerunning history” with the effects of the investment included, and then recalculating the large event risk to find the improvement in resilience. An example using utility data shows a 2% reduction in the probability of a large cost event due to 10% wind hardening and 6%–7% reduction due to 10% faster restoration in two different areas of a distribution utility. This new data-driven approach to quantify resilience and resilience investments is realistic and much easier to apply than complicated approaches based on modeling all the phases of resilience. Moreover, an appeal to improvements to past lived experience may well be persuasive to customers and regulators in making the case for resilience investments.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

The SRG/eROSITA All-Sky Survey: Constraints on ultralight axion dark matter through galaxy cluster number counts

Ultralight axions are hypothetical scalar particles that influence the evolution of large-scale structures of the Universe. Depending on their mass, they can potentially be part of the dark matter component of the Universe as candidates commonly referred to as fuzzy dark matter. While strong constraints have been established for pure fuzzy dark matter models, the more general scenario where ultralight axions constitute only a fraction of the dark matter has been limited to only a few observational probes. In this work, we use the galaxy cluster number counts obtained from the first All-Sky Survey (eRASS1) of the SRG/eROSITA mission together with gravitational weak lensing data from the Dark Energy Survey, the Kilo-Degree Survey, and the Hyper Suprime-Cam to constrain the fraction of ultralight axions in the mass range 10 −32 eV to 10 −24 eV. We put upper bounds on the ultralight axion relic density Ω a in independent logarithmic axion mass bins by performing a full cosmological parameter inference. We find an exclusion region in the intermediate ultralight axion mass regime with the tightest bounds reported so far in the mass bins around m a = 10 −27 eV with Ω a < 0.0035 and m a = 10 −26 eV with Ω a < 0.0079; both are at a 95% confidence level. When combined with cosmic microwave background probes, these bounds are tightened to Ω a < 0.0030 in the m a = 10 −27 eV mass bin and Ω a < 0.0058 in the m a = 10 −26 eV mass bin, with both at a 95% confidence level. This is the first time that constraints on ultralight axions have been obtained using the growth of structure measured by galaxy cluster number counts. These results pave the way for large surveys, which can be utilized to obtain tight constraints on the mass and relic density of ultralight axions with better theoretical modeling of the abundance of halos.

cosmological parameters↗

DOE OSTI2025

Deuterium and tritium anomalous transport in the generalized Hasegawa–Wakatani resistive drift wave turbulence model with finite ion Larmor radius

Anomalous transport of mixed deuterium–tritium plasma in the edge of magnetic fusion reactors is investigated using numerical solutions of resistive drift wave turbulence model equations, including finite Larmor radius effects, that are derived within the generalized Hasegawa–Wakatani framework. The anomalous cross field diffusivities of deuterium and tritium are compared in turbulence regimes with different values of the electron adiabaticity parameter controlling the existence of zonal flow. The dependence of the tritium-to-deuterium diffusivity ratio on the deuterium and tritium densities and the logarithmic density gradients is analyzed, and a scaling relation is obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Computationally guided experimental validation of divacancy defect formation in 4H-SiC

Recent research into solid-state qubits for quantum information science has focused on optically addressable spin defects such as the negatively charged nitrogen-vacancy center in diamond and the neutrally charged divacancy (VV) in 4H-SiC as scalable quantum sensors and networking qubits. Within this context, direct investigations of the structural origin and defect formation dynamics of a sub-set of the VV center in 4H-SiC remain lacking. Here, we take a systematic experimental approach guided by predictions from first-principles simulations to gain a thorough mechanistic understanding of the VV defect formation and control in 4H-SiC. We study the effect of annealing time and temperature on VV formation in high-purity semi-insulating 4H-SiC samples following electron irradiation. Three different temperatures (1123, 1273, and 1473 K) and annealing duration (from 0.5 to 72 h) are chosen to explore VV formation in different regions. We find that samples annealed at 1273 K give the highest VV-related photoluminescence (PL) intensities, in agreement with the prediction from first-principles calculations. Furthermore, the logarithmic dependence of VV-related PL intensities on the annealing duration at 1273 K indicates that 1273 K provides sufficient thermal energy for silicon vacancy migration but not for VV migration. Together, these results suggest that efficient VV formation occurs above the V Si migration temperature and below the VV migration threshold.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Similarity for downscaled kinetic simulations of electrostatic plasmas: Reconciling the large system size with small Debye length

A simple similarity has been proposed for kinetic (e.g., particle-in-cell) simulations of plasma transport that can effectively address the long-standing challenge of reconciling the tiny Debye length with the vast system size. This applies to both transport in unmagnetized plasma and parallel transport in magnetized plasmas, where the characteristics length scales are given by the Debye length, collisional mean free paths, and the system or gradient lengths. The controlled scaled variables are the configuration space, x/L, and an artificial Coulomb Logarithm, L ln Λ, for collisions, while the scaled time, t/L, and electric field, LE, are automatic outcomes. The similarity properties are examined, demonstrating that the macroscopic transport physics is preserved through a similarity transformation while keeping the microscopic physics at its original scale of Debye length. To showcase the utility of this approach, two examples of 1D plasma transport problems were simulated using the VPIC code: the plasma thermal quench in tokamaks [Li et al., Nuclear Fusion 63, 066030 (2023)] and the plasma sheath in the high-recycling regime [Li et al., Physics of Plasmas 30, 063505 (2023)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Intermediate time sub-diffusion and stress relaxation in ring polymer melts

The slow dynamics of non-concatenated ring melts remains a frontier problem in polymer science with implications for many soft material environments including cellular biophysics. Here, in this work, we report large-scale simulations of model ring melts that analyze the monomer and center-of-mass (CM) mean square displacements (MSD) and stress relaxation function on intermediate time and length scales. The degree of dynamical slowing down is characterized by the maximally sub-diffusive fractional time scaling exponents. The data span an exceptionally wide range of ring degrees of polymerization and stiffnesses and are not successfully organized based on the classic measure linear chain entanglement, N/N e . Rather, we find that the crossover degree of polymerization, N D , based on ring macromolecular caging that successfully allows master curves to be constructed for the long-time CM self-diffusion constant also collapses these temporal dynamic scaling exponents. Different properties display different exponents and exhibit one or two regimes of linear variation with the logarithm of N D / N . A distinct crossover of the CM-MSD and stress relaxation exponents emerges at sufficiently large N or stiffness that is not found for the monomer MSD, indicating a novel form of dynamic decoupling. This crossover aligns with the predicted critical degree of polymerization for transitioning from a weak to strong caging regime, indicative of activated transport. The latter may reflect the emergence of an intermolecular collective contribution to stress in analogy with dense soft colloidal matter. Suggestions are made for future theoretical work to address the rich patterns of behavior discovered.

Anomalous diffusion↗

DOE OSTI2026

Burn mode signatures enabled by high dynamic range fusion reaction history

The evolution of the fusion burn of a compressed inertial confinement fusion (ICF) implosion gives information about the evolution of the temperature, mass, and volume of the hot spot. Currently, the fusion reaction history has been measured with about a decade of dynamic range, giving information about just the peak of the fusion burn. There are proposals for extending the dynamic range to 1000×, measuring the rising edge of the burn earlier in time. Using fusion hot spot theory and a set of ICF simulations, we identify and categorize different stages of fusion burn and what signatures could be measured. For ice layered implosions, the details, conditions, and dynamics of the fusion burn propagation could be observed. For double shell and OMEGA scale implosions, the evolution of the final compression and rebounding shock before ignition could be observed. Higher dynamic range expands investigation into the logarithmic derivative, α, as a signature of various mechanisms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

The Role of Nuclear Data Sensitivities in Prompt α-Eigenvalue Predictions of Delayed Critical Benchmarks

Alpha (α) eigenvalues, which describe the logarithmic time derivative of the neutron population in a multiplying system, are integral to time-dependent behavior and diagnostic applications. However, uncertainties in the evaluated nuclear data can significantly impact the accuracy of transport simulations for such quantities. This work explores the use of machine learning models to predict two key outputs, α-eigenvalues and keff bias, using input features derived from α-eigenvalue sensitivities to nuclear data. The criticality safety benchmark models used in this study come from the International Handbook of Evaluated Criticality Safety Benchmark Experiments. Three models, random forest, XGBoost, and NGBoost, are trained on both energy-resolved and energy-summed α sensitivities. For the α-eigenvalue bias prediction, NGBoost achieved the highest R 2 (0.9476) using energy-resolved features, while XGBoost performed best using summed sensitivities. In contrast, when predicting the keff bias, all the models showed moderate predictive capability (best R 2 ≈ 0.72), as the mapping from the static α-sensitivities to the static keff bias was less direct. SHAP (SHapley Additive exPlanations) analysis was used to interpret the model predictions. Across both prediction tasks, the features associated with neutron capture [H-1 (n, γ)], uranium scattering reactions (such as 235 U elastic/inelastic), and actinide capture/fission reactions (such as 239 Pu and 234 U) were consistently identified as the most impactful. This highlights the key role of specific nuclear reactions and energy ranges in shaping both time-dependent and steady-state criticality behavior. These results demonstrated that α-sensitivities, despite being computed for time-dependent metrics, can provide valuable insights for predicting both α-eigenvalues and the keff bias. Moreover, machine learning models offer a promising pathway for uncovering important nuclear data dependencies and guiding future data evaluation efforts.

Nuclear data↗

DOE OSTI2025

Full-Shape analysis of the power spectrum and bispectrum of DESI DR1 LRG and QSO samples

We present the first joint analysis of the power spectrum and bispectrum using the Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI), focusing on Luminous Red Galaxies (LRGs) and quasars (QSOs) across a redshift range of 0.4 ≤ z ≤ 2.1. By combining the two- and three-point statistics, we are able to partially break the degeneracy between the logarithmic growth rate, f(z), and the amplitude of dark matter fluctuations, σ s8 (z), which cannot be measured separately in analyses that only involve the power spectrum. In comparison with the (fiducial) Planck ΛCDM cosmology we obtain f/f fid = {0.888 -0.089 +0.186 ,0.977 -0.220 +0.182 ,1.030 -0.085 +0.368 }, σ s8 /σ fid s8 = {1.224 -0.133 +0.091 ,1.071 -0.163 +0.278 ,1.00 0 -0.223 +0.088 } respectively for the three LRG redshift bins, corresponding to a cumulative 10.1% constraint on f, and of 8.4% on σ s8 , including the systematic error budget. Additionally, we obtain constraints for the ShapeFit compressed parameters describing the isotropic scaling parameter, α iso (z), the Alcock-Paczyński parameter, α AP (z), the combined growth of structure parameter fσ s8 (z), and the combined shape parameter m(z)+n(z). Their cumulative constraints from our joint power spectrum-bispectrum analysis are respectively σ αiso = 0.9% (9% improvement with respect to our power spectrum-only analysis); σ α AP = 2.3% (no improvement with respect to power spectrum-only analysis, which is expected given that the bispectrum monopole has no significant anisotropic signal); σ fσs8 = 5.1% (9% improvement); σ m+n = 2.3% (11% improvement). These results are fully consistent with the main DESI power spectrum analysis, demonstrating the robustness of the DESI cosmological constraints, and compatible with Planck ΛCDM cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Cosmological analysis of the DESI DR1 Lyα 1D power spectrum

We present the cosmological analysis of the one-dimensional Lyman-α flux power spectrum from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We capture the dependence of the signal on cosmology and intergalactic medium physics using an emulator trained on a cosmological suite of hydrodynamical simulations, and we correct its predictions for the impact of astrophysical contaminants and systematics, many of these not considered in previous analyses. We employ this framework to constrain the amplitude and logarithmic slope of the linear matter power spectrum at k ★ = 0.009 km -1 s and redshift z = 3, obtaining Δ 2 ★ = 0.379 ± 0.032 and n ★ = -2.309 ± 0.019 https://github.com/igmhub/cobaya_lya_p1d. The robustness of these constraints is validated through the analysis of mocks and a large number of alternative data analysis variations, with cosmological parameters kept blinded throughout the validation process. We then combine our results with constraints from DESI BAO and temperature, polarization, and lensing measurements from Planck, ACT, and SPT-3G to set constraints on ΛCDM extensions. While our measurements do not significantly tighten the limits on the sum of neutrino masses from the combination of these probes, they sharpen the constraints on the effective number of relativistic species, N eff = 3.02 ± 0.10, the running of the spectral index, α s = 0.0014 ± 0.0041, and the running of the running, β s = -0.0006 ± 0.0048, by a factor of 1.18, 1.27, and 1.90, respectively. We conclude by outlining the improvements needed to fully reach the level of confidence implied by these uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗