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DOE OSTI2025

Tailoring composition and deformation modes at the microstructural level for next generation low-cost high-strength austenitic stainless steels

The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.

08 HYDROGEN↗

NASA NTRS1988

Patch structured surface grid with dynamic curvature clustering

The numerical technique developed by Eiseman (1985) to generate surface grids with lines clustered in areas of greater curvature is described and demonstrated. This approach combines the direct active use of surface curvature with a mean-value relaxation scheme and multigrid methods; it permits an arbitrary number of patches to be organized in a single integer array based on a patch number, an edge number, and a boundary-condition index. Grids for typical CFD applications are presented and briefly characterized.

Wang, YI↗

NASA NTRS2022

Effects of Debulking on the Fiber Microstructure and Void Distribution in Carbon Fiber Reinforced Plastics

Carbon Fiber Reinforced Plastics (CFRPs) are widely used due to their high stiffness to weight ratios. A common process manufacturers use to increase the strength to weight ratio is debulking. Debulking is the process of compacting a dry fibrous reinforcement prior to resin infusion. This process is meant to decrease the average inter-fiber distance, effectively increasing the fiber volume fraction of the sample. While this process is widely understood macroscopically its effects on fibrous microstructures have not yet been well characterized. The aim of this work is to compare the microstructures of three CFRP laminates, varying only the debulking step in the manufacturing process. High resolution serial sections of all three laminates were taken for analysis. Using these scans, the fiber positions were reconstructed. Statistical descriptors such as local fiber and void volume fractions, fiber orientation, and void distribution and morphology were then generated for each sample. Fiber clusters present within the material were identified and analyzed for each level of debulking applied. Using these descriptors, the effects of debulking on the morphology and organization of the composite microstructure was evaluated.

carbon fiber↗

DOE OSTI2024

Streamlined spatial and environmental expression signatures characterize the minimalist duckweed Wolffia australiana

Single-cell genomics permits a new resolution in the examination of molecular and cellular dynamics, allowing global, parallel assessments of cell types and cellular behaviors through development and in response to environmental circumstances, such as interaction with water and the light–dark cycle of the Earth. Here, we leverage the smallest, and possibly most structurally reduced, plant, the semiaquaticWolffia australiana, to understand dynamics of cell expression in these contexts at the whole-plant level. We examined single-cell-resolution RNA-sequencing data and foundWolffiacells divide into four principal clusters representing the above- and below-water-situated parenchyma and epidermis. Although these tissues share transcriptomic similarity with model plants, they display distinct adaptations thatWolffiahas made for the aquatic environment. Within this broad classification, discrete subspecializations are evident, with select cells showing unique transcriptomic signatures associated with developmental maturation and specialized physiologies. Assessing this simplified biological system temporally at two key time-of-day (TOD) transitions, we identify additional TOD-responsive genes previously overlooked in whole-plant transcriptomic approaches and demonstrate that the core circadian clock machinery and its downstream responses can vary in cell-specific manners, even in this simplified system. Distinctions between cell types and their responses to submergence and/or TOD are driven by expression changes of unexpectedly few genes, characterizingWolffiaas a highly streamlined organism with the majority of genes dedicated to fundamental cellular processes.Wolffiaprovides a unique opportunity to apply reductionist biology to elucidate signaling functions at the organismal level, for which this work provides a powerful resource.

Biochemistry & Molecular Biology↗

DOE OSTI2020

Observations of grain-boundary phase transformations in an elemental metal

The theory of grain boundary (the interface between crystallites, GB) structure has a long history 1 and the concept of GBs undergoing phase transformations was proposed 50 years ago 2,3 . The underlying assumption was that multiple stable and metastable states exist for different GB orientations 4,5,6 . The terminology ‘complexion’ was recently proposed to distinguish between interfacial states that differ in any equilibrium thermodynamic property 7 . Different types of complexion and transitions between complexions have been characterized, mostly in binary or multicomponent systems 8,9,10,11,12,13,14,15,16,17,18,19 . Simulations have provided insight into the phase behaviour of interfaces and shown that GB transitions can occur in many material systems 20,21,22,23,24 . However, the direct experimental observation and transformation kinetics of GBs in an elemental metal have remained elusive. In this work we demonstrate atomic-scale GB phase coexistence and transformations at symmetric and asymmetric $[11\bar{1}]$ tilt GBs in elemental copper. Atomic-resolution imaging reveals the coexistence of two different structures at Σ19b GBs (where Σ19 is the density of coincident sites and b is a GB variant), in agreement with evolutionary GB structure search and clustering analysis 21,25,26 . We also use finite-temperature molecular dynamics simulations to explore the coexistence and transformation kinetics of these GB phases. Our results demonstrate how GB phases can be kinetically trapped, enabling atomic-scale room-temperature observations. Our work paves the way for atomic-scale in situ studies of metallic GB phase transformations, which were previously detected only indirectly 9,15,27,28,29 , through their influence on abnormal grain growth, non-Arrhenius-type diffusion or liquid metal embrittlement.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Membrane lipids drive formation of KRAS4b-RAF1 RBDCRD nanoclusters on the membrane

The oncogene RAS, extensively studied for decades, presents persistent gaps in understanding, hindering the development of effective therapeutic strategies due to a lack of precise details on how RAS initiates MAPK signaling with RAF effector proteins at the plasma membrane. Recent advances in X-ray crystallography, cryo-EM, and super-resolution fluorescence microscopy offer structural and spatial insights, yet the molecular mechanisms involving protein-protein and protein-lipid interactions in RAS-mediated signaling require further characterization. This study utilizes single-molecule experimental techniques, nuclear magnetic resonance spectroscopy, and the computational Machine-Learned Modeling Infrastructure (MuMMI) to examine KRAS4b and RAF1 on a biologically relevant lipid bilayer. MuMMI captures long-timescale events while preserving detailed atomic descriptions, providing testable models for experimental validation. Both in vitro and computational studies reveal that RBDCRD binding alters KRAS lateral diffusion on the lipid bilayer, increasing cluster size and decreasing diffusion. RAS and membrane binding cause hydrophobic residues in the CRD region to penetrate the bilayer, stabilizing complexes through β-strand elongation. These cooperative interactions among lipids, KRAS4b, and RAF1 are proposed as essential for forming nanoclusters, potentially a critical step in MAP kinase signal activation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Uniform modelling of the stellar density of thirteen tidal streams within the Galactic halo

ABSTRACT We present the results of fitting a flexible stellar stream density model to a collection of thirteen streams around the Milky Way, using photometric data from DES, DECaLS, and Pan-STARRS. We construct density maps for each stream and characterize their tracks on the sky, width, and distance modulus curves along the length of each stream. We use these measurements to compute lengths and total luminosities of streams and identify substructures. Several streams show prominent substructures, such as stream broadening, gaps, large deviations of stream tracks, and sharp changes in stream densities. Examining the group of streams as a population, as expected we find that streams with globular cluster progenitors are typically narrower than those with dwarf galaxy progenitors, with streams around 100 pc wide showing overlap between the two populations. We also note the average luminosity of globular cluster streams is significantly lower than the typical luminosity of intact globular clusters. The likely explanation is that observed globular cluster streams preferentially come from lower luminosity and lower density clusters. The stream measurements done in a uniform manner presented here will be helpful for more detailed stream studies such as identifying candidate stream members for spectroscopic follow up and stellar stream dynamical modelling.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Mildly Hierarchical Triple Dynamics and Applications to the Outer Solar System

Three-body interactions are ubiquitous in astrophysics. For instance, Kozai–Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly hierarchical triples also play an important role, but they are less explored. In this work, we consider the secular dynamics of a test particle in a mildly hierarchical configuration. We find the limit within which the secular approximation is reliable when the outer perturber is in a circular orbit. In addition, we present resonances and chaotic regions using surface-of-section plots, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer Solar System. We focus on the distribution of extreme trans-Neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet 9), and find that in addition to a low-inclination Planet 9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Combined Machine Learning and Molecular Dynamics Reveal Two States of Hydration of a Single Functional Group of Cationic Polymeric Brushes

The state of hydration of a macromolecular system regulates a plethora of different properties of such a system. In this article, we develop a novel machine learning (ML) approach, based on the unsupervised clustering algorithm, for probing the hydration behavior of the {N(CH 3 ) 3 } + functional group of the PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] polyelectrolyte (PE) brush system. The PE brushes and the brush-supported water molecules and counterions (chloride ions) are first described using all-atom molecular dynamics (MD) simulations. The simulation data is subsequently used in our ML framework to identify that (1) the {N(CH 3 ) 3 } + functional groups of the PMETAC brushes have two distinct hydration states with one state (state 1) being characterized by less structured water molecules and the other state (state 2) being characterized by more structured water molecules and (2) an enhancement in the brush grafting density leads to the progressive dissapparenace of state 2. An increase in the grafting density increases the number of chloride counterions in a given volume around the {N(CH 3 ) 3 } + functional group and increases the number of shared water molecules between the {N(CH 3 ) 3 } + and Cl - . The chloride counterions are associated with a hydration layer with much less structured water molecules. Therefore, with an increase in the grafting density, an increase in the percentage of shared water molecules leads to the prevalence of the hydration state [of the {N(CH 3 ) 3 } + moiety] with less structured water molecules. Finally, we explain how the present findings are commensurate with two key previous related results, namely a significantly large chloride ion mobility inside the PMETAC brush layer and the {N(CH 3 ) 3 } + -Cl - average distance remaining independent of the PMETAC brush grafting density. Furthermore, we anticipate that the combined ML-MD-simulation approach proposed in this study can be adapted to probe other soft matter systems to reveal new insights of the underlying mechanisms of emergent phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Range and strength of mechanical interactions of force dipoles in elastic fiber networks

Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal medium – a disordered, viscoelastic network of biopolymers. The resulting cell size scale force chains can in principle mediate mechanical interactions between distant actomyosin units, leading to self-organized structural order in the cell cytoskeleton. Inspired by such force transmission through elastic structures in the cytoskeleton, we consider a percolated fiber lattice network, where fibers are represented as linear elastic elements that can both bend and stretch, and the contractile activity of myosin motors is represented by force dipoles. Then, by using a variety of metrics, we show how two such contractile force dipoles interact with each other through their mutual mechanical deformations of the elastic fiber network. As a prelude to two-dipole interactions, we quantify how forces propagate through the network from a single anisotropic force dipole by analyzing clusters of nodes connected by highly strained bonds, as well as through the decay rate of strain energy with distance from a force dipole. We show that predominant fiber bending screens out force propagation, resulting in reduced and strongly network configuration-dependent dipole interactions. On the other hand, stretching-dominated networks support longer-ranged inter-dipole interactions that recapitulate the predictions of linear elasticity theory. By characterizing the differences between tensile and compressive force propagation in the fiber network, we show how inter-dipole interaction depends on the dipoles’ mutual separation and orientation. The resulting elastic interaction energy may mediate a force between multiple distant dipoles, leading to their self-organization into ordered configurations. In conclusion, this provides a potential pathway for active mechanical force-driven structural order in elastic biopolymer networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Deep-learning-enabled Bayesian inference of fuel magnetization in magnetized liner inertial fusion

Fuel magnetization in magneto-inertial fusion (MIF) experiments improves charged burn product confinement, reducing requirements on fuel areal density and pressure to achieve self-heating. By elongating the path length of 1.01 MeV tritons produced in a pure deuterium fusion plasma, magnetization enhances the probability for deuterium–tritium reactions producing 11.8-17.1 MeV neutrons. Nuclear diagnostics thus enable a sensitive probe of magnetization. Characterization of magnetization, including uncertainty quantification, is crucial for understanding the physics governing target performance in MIF platforms, such as magnetized liner inertial fusion (MagLIF) experiments conducted at Sandia National Laboratories, Z-facility. We demonstrate a deep-learned surrogate of a physics-based model of nuclear measurements. A single model evaluation is reduced from O ( 10 – 100 ) (10–100) CPU hours on a high-performance computing cluster down to O ( 10 – 100 ) (10) ms on a laptop. This enables a Bayesian inference of magnetization, rigorously accounting for uncertainties from surrogate modeling and noisy nuclear measurements. The approach is validated by testing on synthetic data and comparing with a previous study. We analyze a series of MagLIF experiments systematically varying preheat, resulting in the first ever systematic experimental study of magnetic confinement properties of the fuel plasma as a function of fundamental inputs on any neutron-producing MIF platform. We demonstrate that magnetization decreases from B R ∼ 0.2 ~0.5 to B R ∼ 0.2 ~0.2 MG cm as laser preheat energy deposited increases from E preheat ∼ 460 ~460 J to E preheat ∼ 460 ~1.4 kJ. This trend is consistent with 2D LASNEX simulations showing Nernst advection of the magnetic field out of the hot fuel and diffusion into the target liner.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Compositionally-Driven Formation Mechanism of Hierarchical Morphologies in Co-Deposited Immiscible Alloy Thin Films

Co-deposited, immiscible alloy systems form hierarchical microstructures under specific deposition conditions that accentuate the difference in constituent element mobility. The mechanism leading to the formation of these unique hierarchical morphologies during the deposition process is difficult to identify, since the characterization of these microstructures is typically carried out post-deposition. We employ phase-field modeling to study the evolution of microstructures during deposition combined with microscopy characterization of experimentally deposited thin films to reveal the origin of the formation mechanism of hierarchical morphologies in co-deposited, immiscible alloy thin films. Our results trace this back to the significant influence of a local compositional driving force that occurs near the surface of the growing thin film. We show that local variations in the concentration of the vapor phase near the surface, resulting in nuclei (i.e., a cluster of atoms) on the film’s surface with an inhomogeneous composition, can trigger the simultaneous evolution of multiple concentration modulations across multiple length scales, leading to hierarchical morphologies. We show that locally, the concentration must be above a certain threshold value in order to generate distinct hierarchical morphologies in a single domain.

36 MATERIALS SCIENCE↗

NASA NTRS1976

In situ investigation of the mobility of small gold clusters on cleaved MgO surfaces

The mobility of small clusters of gold (about 10 A in diameter) on electron-beam-cleaved MgO surfaces was studied by in situ transmission electron microscopy under controlled vacuum and temperature conditions. During the first 10 min following a deposition at room temperature, over 10 per cent of the crystallites moved over short distances (about 20 A) discontinuously, with a velocity greater than 150 A/sec. Eighty per cent of the mobility events were characterized by the avoidance of proximity of other crystallites, and this was tentatively explained as the result of repulsive elastic forces between the interacting crystallites.

Metois, J. J.↗

NASA NTRS1992

Where have all the sources gone?

In the continuing quest for an understanding of the cosmic x-ray background, the most difficult technical barrier remains the mismatch between the wavelength band in which the discrete source populations are best characterized (0.1 to 3.5 keV), and the band in which the spectrum of the background is well determined and the bulk of the energy density resides (3.5 to 50 keV). A progress report in an attempt to resolve this conundrum using the Einstein Imaging Proportional Counter (IPC) database and analysis system is presented. The IPC data base is described and how it can be used to search both for missing clusters of galaxies and highly obscured active galactic nuclei is addressed. All 4083 imaging proportional counter observations were examined after flat fielding and editing to optimize sensitivity for diffuse emission on various size scales ranging up to 10 feet. A '2 sigma source' catalog which, when filtered by matching with source catalogs from other wavelength regimes, is shown to reveal new source classes which may be significant contributors to the cosmic x-ray background is being constructed. Optimization techniques are described and the source catalogs which result are presented. Limits on the contributions both classes of sources make to resolving the discrepancy with the higher energy observations are set.

Helfand, D. J.↗

NASA NTRS1993

Two-dimensional spatiotemporal coding of linear acceleration in vestibular nuclei neurons

Response properties of vertical (VC) and horizontal (HC) canal/otolith-convergent vestibular nuclei neurons were studied in decerebrate rats during stimulation with sinusoidal linear accelerations (0.2-1.4 Hz) along different directions in the head horizontal plane. A novel characteristic of the majority of tested neurons was the nonzero response often elicited during stimulation along the "null" direction (i.e., the direction perpendicular to the maximum sensitivity vector, Smax). The tuning ratio (Smin gain/Smax gain), a measure of the two-dimensional spatial sensitivity, depended on stimulus frequency. For most vestibular nuclei neurons, the tuning ratio was small at the lowest stimulus frequencies and progressively increased with frequency. Specifically, HC neurons were characterized by a flat Smax gain and an approximately 10-fold increase of Smin gain per frequency decade. Thus, these neurons encode linear acceleration when stimulated along their maximum sensitivity direction, and the rate of change of linear acceleration (jerk) when stimulated along their minimum sensitivity direction. While the Smax vectors were distributed throughout the horizontal plane, the Smin vectors were concentrated mainly ipsilaterally with respect to head acceleration and clustered around the naso-occipital head axis. The properties of VC neurons were distinctly different from those of HC cells. The majority of VC cells showed decreasing Smax gains and small, relatively flat, Smin gains as a function of frequency. The Smax vectors were distributed ipsilaterally relative to the induced (apparent) head tilt. In type I anterior or posterior VC neurons, Smax vectors were clustered around the projection of the respective ipsilateral canal plane onto the horizontal head plane. These distinct spatial and temporal properties of HC and VC neurons during linear acceleration are compatible with the spatiotemporal organization of the horizontal and the vertical/torsional ocular responses, respectively, elicited in the rat during linear translation in the horizontal head plane. In addition, the data suggest a spatially and temporally specific and selective otolith/canal convergence. We propose that the central otolith system is organized in canal coordinates such that there is a close alignment between the plane of angular acceleration (canal) sensitivity and the plane of linear acceleration (otolith) sensitivity in otolith/canal-convergent vestibular nuclei neurons.

NASA Discipline Neuroscience↗

NASA NTRS2018

Nature of and Lessons Learned from Lunar Ice Cube and the First Deep Space Cubesat 'Cluster'

Cubesats operating in deep space face challenges Earth-orbiting cubesats do not. 15 deep space cubesat 'prototypes' will be launched over the next two years including the two MarCO cubesats, the 2018 demonstration of dual communication system at Mars, and the 13 diverse cubesats being deployed from the SLS EM1 mission within the next two years. Three of the EM1 cubesat missions, including the first deep space cubesat 'cluster', will be lunar orbiters with remote sensing instruments for lunar surface/regolith measurements. These include: Lunar Ice Cube, with its 1-4 micron broadband IR spectrometer, BIRCHES, to determine volatile distribution as a function of time of day; Lunar Flashlight, to confirm the presence of surface ice at the lunar poles, utilizing an active source (laser), and looking for absorption features in the returning signal; and LunaH-Map to characterize ice at or below the surface at the poles with a compact neutron spectrometer. In addition, the BIRCHES instrument on Lunar Ice Cube will provide the first demonstration of a microcryocooler (AIM/IRIS) in deep space. Although not originally required to do so, all will be delivering science data to the Planetary Data System, the first formal archiving effort for cubesats. 4 of the 20 recently NASA-sponsored (PSDS3) study groups for deep space cubesat/smallsat mission concepts were lunar mission concepts, most involving 12U cubesats. NASA SIMPLEX 2/SALMON 3 AO will create ongoing opportunities for low-cost missions as 'rides' on government space program or private sector vehicles as these become available.

Ice Cube↗

NASA NTRS2018

Nature of and Lessons Learned from Lunar Ice Cube and the First Deep Space Cubesat 'Cluster'

Bujold, Emily↗

DOE OSTI2020

Linear point and sound horizon as purely geometric standard rulers

The baryon acoustic oscillations feature (BAO) imprinted in the clustering correlation function is known to furnish us cosmic distance determinations that are independent of the cosmological-background model and the primordial perturbation parameters. These measurements can be accomplished rigorously by means of the purely geometric BAO methods. To date two different purely geometric BAO approaches have been proposed. The first exploits the linear-point standard ruler. The second, called correlation-function model-fitting, exploits the sound-horizon standard ruler. A key difference between them is that, when estimated from clustering data, the linear point makes use of a cosmological-model-independent procedure to extract the ratio of the ruler to the cosmic distance, while the correlation-function model-fitting relies on a phenomenological cosmological model for the correlation function. Nevertheless the two rulers need to be precisely defined independently of any specific observable (e.g., the BAO). We define the linear point and sound horizon and we fully characterize and compare the two rulers’ cosmological-parameter dependence. We find that they are both geometrical (i.e., independent of the primordial cosmological parameters) within the required accuracy, and that they have the same parameter dependence for a wide range of parameter values. We estimate the rulers’ best-fit values and errors, given the cosmological constraints obtained by the Planck Satellite team from their measurements of the cosmic microwave background temperature and polarization anisotropies. We do this for three different cosmological models encompassed by the purely geometric BAO methods. In each case we find that the relative errors of the two rulers coincide and they are insensitive to the assumed cosmological model. Interestingly both the linear point and the sound horizon shift by 0.5σ when we do not fix the spatial geometry to be flat in Λ CDM. Finally, this points toward a sensitivity of the rulers to different cosmological models when they are estimated from the cosmic microwave background.

79 ASTRONOMY AND ASTROPHYSICS↗