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DOE OSTI2020

Hydrodynamic and Radiographic Toolbox (HART)

With a multi-lab and university team, we propose to develop new methods for a Hydrodynamic and Radiographic Toolbox (HART) that will enable a fuller and more extensive use of experimental radiographic data towards better characterizing and reducing uncertainties in predictive modeling of weapons performance. We will achieve this by leveraging recent developments in areas of computational imaging, statistical and machine learning, and reduced order modeling of hydrodynamics. In terms of software practices, by partnering with XCP (RISTRA Project) we will conform to recent XCP standards that are inline with modern software practices and standards and ensure compatibility and ease of inter-operability with existing codes. Three new activities under this proposal include (a) the development and use of deep learning-based surrogates to accelerate reconstruction and variational inference of density fields from radiographs of hydrotests, (b) a model-data fusion strategy that couples deep learning-based density reconstructions with fast hydrodynamics simulators to better constrain the reconstruction, and (c) a method for treating asymmetries using techniques adopted from limited view tomography. All three new activities will be based on improved treatment of scatter, noise, beam spot movement, detector blur, and flat fielding in the forward model, and a use of sophisticated priors to aid in the re construction. The improvements to the forward model and improved algorithmic design of the reconstruction when complete will be contained in the iterative reconstruction code SHIVA—a code project that we have recently initiated. The many ways in which machine learning can be used in the reconstruction work will be contained in a code HERMES that has been initiated with DTRA support. For example, the significant levels of acceleration that will likely be achieved by the use of machine learning techniques will permit us (and are required) to quantify uncertainties in density retrievals. Next, the two-way coupling between density reconstruction and model-based simulation of the hydrodynamics will be contained in code EREBUS, and will permit a fuller realization of the potential of the data to constrain the hydrodynamic model and better address issues related to asymmetries in the problem. Finally, we anticipate that the better consistency with physics achieved in our reconstructions will allow them to be used by X-Division more so than today.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

A Review of Bayesian Networks for Spatial Data

We report Bayesian networks are a popular class of multivariate probabilistic models as they allow for the translation of prior beliefs about conditional dependencies between variables to be easily encoded into their model structure. Due to their widespread usage, they are often applied to spatial data for inferring properties of the systems under study and also generating predictions for how these systems may behave in the future. We review published research on methodologies for representing spatial data with Bayesian networks and also summarize the application areas for which Bayesian networks are employed in the modeling of spatial data. We find that a wide variety of perspectives are taken, including a GIS-centric focus on efficiently generating geospatial predictions, a statistical focus on rigorously constructing graphical models controlling for spatial correlation, as well as a range of problem-specific heuristics for mitigating the effects of spatial correlation and dependency arising in spatial data analysis. Special attention is also paid to potential future directions for integration of Bayesian networks with spatial processes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

On the impact of the galaxy window function on cosmological parameter estimation

One important source of systematics in galaxy redshift surveys comes from the estimation of the galaxy window function. Up until now, the impact of the uncertainty in estimating the galaxy window function on parameter inference has not been properly studied. In this paper, we show that the uncertainty and the bias in estimating the galaxy window function will be salient for ongoing and next-generation galaxy surveys using a simulation-based approach. With a specific case study of cross-correlating emission-line galaxies from the DESI Legacy Imaging Surveys and the Planck cosmic microwave background lensing map, we show that neural network-based regression approaches to modelling the window function are superior in comparison to linear regression-based models. Here, we additionally show that the definition of the galaxy overdensity estimator can impact the overall signal-to-noise of observed power spectra. Finally, we show that the additive biases coming from the window functions can significantly bias the modes of the inferred parameters and also degrade their precision. Thus, a careful understanding of the window functions will be essential to conduct cosmological experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Mitigation of spatial nonstationarity with vision transformers

Spatial nonstationarity, the location variance of features’ statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction trends, in mineral deposits grades vary due to sedimentation and concentration processes, in hydrology rainfall varies due to the atmosphere and topography interactions, and in metallurgy crystalline structures vary due to differential cooling. Conventional geostatistical modeling workflows rely on the assumption of stationarity to be able to model spatial features for geostatistical inference. Nevertheless, this is often not a realistic assumption when dealing with nonstationary spatial data and this has motivated a variety of nonstationary spatial modeling workflows such as trend and residual decomposition, cosimulation with secondary features, and spatial segmentation and independent modeling over stationary subdomains. The advent of deep learning technologies has enabled new workflows for modeling spatial relationships. However, there is a paucity of demonstrated best practice and general guidance on mitigation of spatial nonstationarity with deep learning in the geospatial context. We demonstrate the impact of two common types of geostatistical spatial nonstationarity on deep learning model prediction performance and propose the mitigation of such impacts using self-attention (vision transformer) models. We demonstrate the utility of vision transformers for the mitigation of nonstationarity with relative errors as low as 10%, exceeding the performance of alternative deep learning methods such as convolutional neural networks. We establish best practice by demonstrating the ability of self-attention networks for modeling large-scale spatial relationships in the presence of commonly observed geospatial nonstationarity.

58 GEOSCIENCES↗

DOE OSTI2026

Bayesian Inference of Hybrid Star Properties from Future High-precision Measurements of Their Radii

Future high-precision X-ray and gravitational-wave observations of neutron stars (NSs) are expected to constrain NS radii with uncertainties as small as σ ≃ 0.1 km. Such unprecedented precision offers a unique opportunity to extract new information about the nature and equation of state (EOS) of supradense matter in NS cores. Using mock radius data with uncertainties ranging from σ = 1.0 to 0.1 km, together with a flexible meta-model NS EOS that allows for a first-order hadron–quark phase transition, we perform a Bayesian statistical analysis to assess the impact of radius measurements on EOS constraints. We find that high-precision radius measurements, particularly for massive NSs, significantly tighten constraints on the hadron–quark transition density ρ t , the quark matter mass fraction in NS cores, and several parameters characterizing the EOS of supranuclear hadronic matter, although the degree of improvement depends on the assumed prior range of ρ t . In contrast, even with the highest precision considered, NS radii—including those of massive stars—remain largely insensitive to the stiffness of quark matter, independent of the measurement accuracy or the prior range adopted for ρ t .

Neutron stars↗

DOE OSTI2025

Measurement of the time-integrated 𝐶⁢𝑃 asymmetry in 𝐷 0 → 𝐾$^{0}_{S}$𝐾$^{0}_{S}$ decays using opposite-side flavor tagging at Belle and Belle II

We measure the time-integrated 𝐶⁢𝑃 asymmetry in 𝐷 0 → 𝐾$^{0}_{S}$𝐾$^{0}_{S}$ decays reconstructed in 𝑒 + ⁢𝑒 − → $c\bar{c}$ events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 and 428 fb −1 , respectively. To infer the flavor of the 𝐷 0 meson, we exploit the correlation between the flavor of the reconstructed decay and the electric charges of particles reconstructed in the rest of the 𝑒 + ⁢𝑒 − → $c\bar{c}$ event. This results in a sample which is independent from any other previously used at Belle or Belle II. The result, 𝐴 𝐶⁢𝑃 ⁡(𝐷 0 → 𝐾$^{0}_{S}$𝐾$^{0}_{S}$)=(1.3±2.0±0.2)%, where the first uncertainty is statistical and the second systematic, is consistent with previous determinations and with 𝐶⁢𝑃 symmetry.

CP violation↗

DOE OSTI2026

A Framework for Parametric and Predictive Uncertainty Quantification in the E3SM Land Model: Assessing Site and Observable Generalizability

Quantifying parametric uncertainty using observations from individual sites provides a critical foundation for Earth system modeling, serving as a necessary first step before scaling up to regional or global applications. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable generalizability using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the E3SM land model, we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian process emulators were employed to expedite GSA and model calibration. Four critical parameters that strongly influence selected land-atmosphere fluxes were identified by GSA. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same plant functional type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, thereby maximizing predictive capabilities with limited observations. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models and deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Uncertainties in Density and Simulation Parameters for Radiographic Reconstructions Using Machine Learning

We will develop new and improved methods that will enable a fuller and more extensive use of experimental data, such as from radiographic imaging, towards better characterizing and reducing uncertainties in predictive modeling of weapons performance. We will achieve this by leveraging recent developments in the areas of computational imaging, statistical and machine learning, and reduced order modeling. Key new aspects of our approach include (a) a coupling of deep learning based density reconstruction with fast hydrodynamics simulators that will permit the development of certain guarantees on extrapolatability and bounds on certain other hydrodynamics-related para- metric uncertainties and (b) a dual approach towards better characterizing uncertainties in density reconstruction using deep learning based surrogates to accelerate Bayesian reconstructions on the one hand and using variational inference and Bayesian machine learning on the other hand.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

AtomAI framework for deep learning analysis of image and spectroscopy data in electron and scanning probe microscopy

Over the past several decades, electron and scanning probe microscopes have become critical components of condensed matter physics, materials science and chemistry research. At the same time, the infrastructure for establishing a connection between microscopy observations and materials behaviour over a broader parameter space is lacking. In this work, we introduce AtomAI, an open-source software package bridging instrument-specific Python libraries, deep learning and simulation tools into a single ecosystem. AtomAI allows direct applications of deep neural networks for atomic and mesoscopic image segmentation converting image and spectroscopy data into class-based local descriptors for downstream tasks such as statistical and graph analysis. For atomically resolved imaging data, the output is types and positions of atomic species, with an option for subsequent refinement. AtomAI further allows the implementation of a broad range of image and spectrum analysis functions, including invariant variational autoencoders for disentangling structural factors of variation and im2spec type of encoder–decoder models for mapping structure–property relationships. Finally, our framework allows seamless connection to the first principles modelling with a Python interface on the inferred atomic positions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

The Mira–Titan Universe – IV. High-precision power spectrum emulation

Modern cosmological surveys are delivering data sets characterized by unprecedented quality and statistical completeness; this trend is expected to continue in the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the non-linear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira–Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. This gravity-only set of simulations covers the standard six cosmological parameters {ω m , ω b , σ 8 , $h, n_s, w_0$} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state {ω ν , $w_a$}. In this paper, we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1 Gpc) 3 volume and evolving 3200 3 particles. In this work, an additional set of 1776 lower resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly non-linear regimes (maximum wavenumber $\textit{k}$ = 5 Mpc –1 ). The emulator provides predictions at the 2–3 percent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A Computational Review of Privacy-Preserving Mechanisms for the Smart Grid

Smart grid technologies have rapidly become one of the largest and most comprehensive sources of data for the modern utility. For the most part, data streams are seen as an essential tool that enable utilities to carry their day-to-day business operations, but they also create the need for efficient and secure data management strategies. In the context of the smart grid, ensuring data privacy is becoming an increasing concern due to a combination of factors that range from shifts in operational paradigms and rapid technology evolution to changes in legislation. Furthermore, researchers have highlighted the risks associated with improperly protected energy records. For example, energy consumption data from homes could be used to infer the behaviors and habits of home occupants through activity recognition or user profiling (Fan, 2017), which may lead to unfair service pricing, targeted advertising, or other personal security violations. Similarly, Electric Vehicles’ (EVs) charging metadata could be used to reveal private information about the owner such as their payment methods, preferred charging stations, and other locational and timing information that could be used to reconstruct the vehicle owner’s behaviors. The privacy of user data, even when used for statistical analysis or machine learning training processes, also needs to be carefully considered, as an individual’s private traits may still be vulnerable if their inclusion/exclusion greatly impacts the result or could be linked to a public dataset through cross-reference. The breach of user privacy also has severe impacts for organizations that store, transmit, or work on the data in the form of diminishing the public’s trust in them while potentially incurring legal consequences (e.g., fines and suspensions under the European Union General Data Protection Regulation, Health Insurance Portability and Accountability Act, etc.). Because of these risks, several privacy-preserving mechanisms are available to help organizations comply with privacy legislations and prevent the unauthorized and malicious use of user data. In light of these concerns, this report focuses on performing a computational review of privacy-preserving mechanisms that have received a significant amount of interest in literature. It specifically focuses on 1) homomorphic encryption, 2) zero-knowledge proofs, 3) differential privacy, and 4) federated learning. It is worth noting that although many of the methods presented in this document rely on cryptographic primitives, their intent is not to provide perfect secrecy, but rather to enable users to maintain privacy, and thus they shall not be compared or equated to other constructs that are aimed to address cybersecurity constructs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Diverse ATPase Proteins in Mobilomes Constitute a Large Potential Sink for Prokaryotic Host ATP

Prokaryote mobilome genomes rely on host machineries for survival and replication. Given that mobile genetic elements (MGEs) derive their energy from host cells, we investigated the diversity of ATP-utilizing proteins in MGE genomes to determine whether they might be associated with proteins that could suppress related host proteins that consume energy. A comprehensive search of 353 huge phage genomes revealed that up to 9% of the proteins have ATPase domains. For example, ATPase proteins constitute ~3% of the genomes of Lak phages with ~550 kbp genomes that occur in the microbiomes of humans and other animals. Statistical analysis shows the number of ATPase proteins increases linearly with genome length, consistent with a large sink for host ATP during replication of megaphages. Using metagenomic data from diverse environments, we found 505 mobilome proteins with ATPase domains fused to diverse functional domains. Among these composite ATPase proteins, 61.6% have known functional domains that could contribute to host energy diversion during the mobilome infection cycle. As many have domains that are known to interact with nucleic acids and proteins, we infer that numerous ATPase proteins are used during replication and for protection from host immune systems. We found a set of uncharacterized ATPase proteins with nuclease and protease activities, displaying unique domain architectures that are energy intensive based on the presence of multiple ATPase domains. In many cases, these composite ATPase proteins genomically co-localize with small proteins in genomic contexts that are reminiscent of toxin-antitoxin systems and phage helicase-antibacterial helicase systems. Small proteins that function as inhibitors may be a common strategy for control of cellular processes, thus could inspire future biochemical experiments for the development of new nucleic acid and protein manipulation tools, with diverse biotechnological applications.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Are Terrestrial Biosphere Models Fit for Simulating the Global Land Carbon Sink?

The Global Carbon Project estimates that the terrestrial biosphere has absorbed about one-third of anthropogenic CO 2 emissions during the 1959–2019 period. This sink-estimate is produced by an ensemble of terrestrial biosphere models and is consistent with the land uptake inferred from the residual of emissions and ocean uptake. The purpose of our study is to understand how well terrestrial biosphere models reproduce the processes that drive the terrestrial carbon sink. One challenge is to decide what level of agreement between model output and observation-based reference data is adequate considering that reference data are prone to uncertainties. To define such a level of agreement, we compute benchmark scores that quantify the similarity between independently derived reference data sets using multiple statistical metrics. Models are considered to perform well if their model scores reach benchmark scores. Our results show that reference data can differ considerably, causing benchmark scores to be low. Model scores are often of similar magnitude as benchmark scores, implying that model performance is reasonable given how different reference data are. While model performance is encouraging, ample potential for improvements remains, including a reduction in a positive leaf area index bias, improved representations of processes that govern soil organic carbon in high latitudes, and an assessment of causes that drive the inter-model spread of gross primary productivity in boreal regions and humid tropics. The success of future model development will increasingly depend on our capacity to reduce and account for observational uncertainties.

58 GEOSCIENCES↗

DOE OSTI2024

A Causal Approach to Model Validation and Calibration

This poster presents a novel method for validation and verification that focuses on identifying causal relationships between data elements, moving beyond traditional statistical and machine learning approaches. These methods employ causal discovery techniques to reveal the underlying mechanisms of data generation. The research utilizes structural causal models and directed acyclic graphs to depict causal relationships. This approach assists in achieving alignment between simulation models and reality.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Extracting a mixing parameter from 2D radiographic imaging of variable-density turbulent flow

We extract a suitably averaged fluctuating density from the two-dimensional radiographic image of a flow. The X-ray attenuation is given by the Beer–Lambert law which exponentially damps the incident beam intensity by a factor proportional to the density, opacity and thickness of the target. By making reasonable assumptions for the mean density, opacity and effective thickness of the target flow, we estimate the density fluctuation contribution to the attenuation. The extracted density fluctuations averaged across the thickness of the flow in the direction of the beam may be used to form the density–specific-volume correlation $b$. In a statistical description of variable-density turbulence, $b$ quantifies the degree of mixedness. The ability to extract a measure of mixedness from experimental data would be a powerful tool that could be used in the validation of mix models. The scheme proposed is tested for DNS data computed for variable density buoyancy-driven mixing. We quantify the deficits in the extracted value of $b$ due to target thickness, Atwood number and modeled signal noise. This analysis justifies using the proposed scheme to infer the mix parameter from thin targets at moderate to low Atwood numbers. Furthermore, to illustrate how the scheme might be used in a practical problem, we demonstrate its application to a radiographic image of counter-shear flow obtained from experiments at the National Ignition Facility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Quantifying bias due to non-Gaussian foregrounds in an optimal reconstruction of CMB lensing and temperature power spectra

We estimate the magnitude of the bias due to non-Gaussian extragalactic foregrounds on the optimal reconstruction of the cosmic microwave background (CMB) lensing potential and temperature power spectra. The reconstruction is performed using a Bayesian inference method known as the marginal unbiased score expansion (MUSE). We apply MUSE to a minimum variance combination of multifrequency maps drawn from the Agora publicly available simulations of the lensed CMB and correlated extragalactic foreground emission. Taking noise levels appropriate to the SPT-3G D1 release, we find non-Gaussian foregrounds may bias the MUSE reconstruction of the lensing potential amplitude at the level of (0.7 ± 0.3)σ when using modes up to ℓ max = 3500. We do not detect a statistically significant bias, finding a value of (-0.4 ± 0.3)σ, when restricted to lower angular multipoles, ℓ max = 3000. This work is a first step toward understanding the impact of extragalactic foregrounds on optimal reconstructions of CMB temperature and lensing potential power spectra.

Statistical sampling techniques↗

DOE OSTI2025

The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models

We use new cosmic microwave background (CMB) primary temperature and polarization anisotropy measurements from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) to test foundational assumptions of the standard cosmological model, ΛCDM, and set constraints on extensions to it. We derive constraints from the ACT DR6 power spectra alone, as well as in combination with legacy data from the Planck mission. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1. To test the dependence of our results on non-ACT data, we also explore combinations replacing Planck with WMAP and DESI with BOSS, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index dn s /d ln k = 0.0062 ± 0.0052) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming (N eff = 2.86 ± 0.13, which combined with astrophysical measurements of primordial helium and deuterium abundances becomes N eff = 2.89 ± 0.11), for non-zero neutrino masses (∑m ν < 0.089 eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation (N idr < 0.134), or for early-universe variation of fundamental constants, including the fine-structure constant (α EM /α EM,0 = 1.0043 ± 0.0017) and the electron mass (m e /m e,0 = 1.0063 ± 0.0056). Our data are consistent with standard big bang nucleosynthesis (we find Y p = 0.2312 ± 0.0092), the COBE/FIRAS-inferred CMB temperature (we find T CMB = 2.698 ± 0.016 K), a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant (w = -0.986 ± 0.025), and the late-time growth rate predicted by general relativity (γ = 0.663 ± 0.052). We find no statistically significant preference for a departure from the baseline ΛCDM model. In fits to models invoking early dark energy, primordial magnetic fields, or an arbitrary modified recombination history, we find H 0 = 69.9 +0.8 -1.5 , 69.1 ± 0.5, or 69.6 ± 1.0 km/s/Mpc, respectively; using BOSS instead of DESI BAO data reduces the central values of these constraints by 1–1.5 km/s/Mpc while only slightly increasing the error bars. In general, models introduced to increase the Hubble constant or to decrease the amplitude of density fluctuations inferred from the primary CMB are not favored over ΛCDM by our data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗