Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “distance measure”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Modelling the impact of host galaxy dust on type Ia supernova distance measurements

Type Ia Supernovae (SNe Ia) are a critical tool in measuring the accelerating expansion of the universe. Recent efforts to improve these standard candles have focused on incorporating the effects of dust on distance measurements with SNe Ia. In this paper, we use the state-of-the-art Dark Energy Survey 5 year sample to evaluate two different families of dust models: empirical extinction models derived from SNe Ia data and physical attenuation models from the spectra of galaxies. In this work, we use realistic simulations of SNe Ia to forward-model different models of dust and compare summary statistics in order to test different assumptions and impacts on SNe Ia data. Among the SNe Ia-derived models, we find that a logistic function of the total-to-selective extinction R V best recreates the correlations between supernova distance measurements and host galaxy properties, though an additional 0.02 mag of grey scatter is needed to fully explain the scatter in SNIa brightness in all cases. These empirically derived extinction distributions are highly incompatible with the physical attenuation models from galactic spectral measurements. From these results, we conclude that SNe Ia must either preferentially select extreme ends of galactic dust distributions, or that the characterization of dust along the SNe Ia line-of-sight is incompatible with that of galactic dust distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Higher d Eisenstein series and a duality-invariant distance measure

The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series E s ($τ$, $\overline{τ}$) and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

On the use of NMR distance measurements for assessing surface site homogeneity

The past few decades have seen tremendous growth in the area of single-site heterogeneous catalysis, which aims to combine the best aspects of homogeneous and heterogeneous catalysis, namely molecular-level site control and ease of separation/recycling. Despite this, we still do not have a means of assessing site homogeneity and whether the produced catalyst is indeed a “single-site”. Recent developments have enabled the use of NMR-based distance measurements to determine the conformations and configurations of surface sites, leading to the question whether such measurements can be used to distinguish materials containing either single or multiple surface sites with otherwise indistinguishable NMR properties. Here, we describe a Monte Carlo-based multi-structure search algorithm and its application to the determination of multi-site structures from supported metal complexes. The sensitivity of REDOR data to the existence of multiple sites is assessed using synthetic data and prior literature examples are revisited to determine whether the single-site approximation was indeed appropriate. We lastly apply this new methodology to differentiate the configurations of zirconocene complexes grafted onto alumina supports that were thermally treated at different temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Comparing the DES-SN5YR and Pantheon+ SN cosmology analyses: investigation based on ‘evolving dark energy or supernovae systematics’?

Recent cosmological analyses measuring distances of type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO) have all given similar hints at time-evolving dark energy. To examine whether underestimated SN Ia systematics might be driving these results, Efstathiou (2025) compared overlapping SN events between Pantheon+ and DES-SN5YR (20 per cent SNe are in common), and reported evidence for an $\sim$0.04 mag offset between the low- and high-redshift distance measurements of this subsample of events. If this offset is arbitrarily subtracted from the entire DES-SN5YR sample, the preference for evolving dark energy is reduced. In this paper, we show that this offset is mostly due to different corrections for Malmquist bias between the two samples; therefore, an object-to-object comparison can be misleading. Malmquist bias corrections differ between the two analyses for several reasons. First, DES-SN5YR used an improved model of SN Ia luminosity scatter compared to Pantheon+ but the associated scatter-model uncertainties are included in the error budget. Secondly, improvements in host mass estimates in DES-SN5YR also affected SN standardized magnitudes and their bias corrections. Thirdly, and most importantly, the selection functions of the two compilations are significantly different, hence the inferred Malmquist bias corrections. Even if the original scatter model and host properties from Pantheon+ are used instead, the evidence for evolving dark energy from CMB, DESI BAO Year 1 and DES-SN5YR is only reduced from 3.9$\sigma$ to 3.3$\sigma$, consistent with the error budget. Finally, in this investigation, we identify an underestimated systematic uncertainty related to host galaxy property uncertainties, which could increase the final DES-SN5YR error budget by 3 per cent. In conclusion, we confirm the validity of the published DES-SN5YR results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Conformal geometry from entanglement

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (\mathfrak{c}_{\textrm{tot}}, \eta) ( 𝔠 tot , η ) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity \mathfrak{c}_{\textrm{tot}} 𝔠 tot is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) \mathfrak{c}_{\textrm{tot}} 𝔠 tot is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) \eta η is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of \mathfrak{c}_{\textrm{tot}} 𝔠 tot is equivalent to a vector fixed-point equation involving \eta η , making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions.

Kim, Isaac H.↗
DOE OSTI2025

Characterizing IHE Response to Multiple Shock Loading

The response of high explosives to shock loading is traditionally measured with a steady loading pressure. In many accident scenarios involving fragment impact, however, a loading duration that is shorter than the build up to detonation may occur. Fragments passing through multiple materials before reaching a high explosive charge may produce loading that is comprised of more than one shock wave. Additionally, the build up to detonation in high explosive corner turning loads the explosive a short duration pressure pulse, since rarefactions can often rapidly overtake the reactive wave. For these reasons, we have studied the response of the insensitive high explosive (IHE) materials PBX 9502 and LX-17 to complex loadings of varied intensity and duration. We refer to a single loading of limited duration as a “thin pulse”, whereas more complex scenarios were studied with an impactor that produces a double shock in the explosive. The following report presents experimental data and analyses of thin pulse shock initiation and double shock experiments designed to guide development of models of Insensitive High Explosives (IHEs) under controlled one-dimensional conditions relevant to accident scenarios and corner turning. Thin pulse shock initiation data on PBX 9502 and LX-17 were obtained under varied pulse duration, pressed density, and temperature conditions in order to probe various parameters essential for the development of a physics-based Cheetah reactive flow hotspot model. In situ pressure gauges provide insight into the degree of reaction in the explosive that are not obtainable with optical PDV measurements or distance measurements such as run to detonation. Double shock data was obtained to inform a Composition Aware Cheetah model which can be applied to any TATB-based IHEs. This model supports efforts to find a new IHE formulation and potentially incorporate new binders into IHE formulations. Simulations of each experiment are included to demonstrate the utility of these focused experiments to developing models of HE behavior. One-dimensional gas gun experiments are essential for characterizing shocked HE behavior and informing HE models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

ELVES-Field: Isolated Dwarf Galaxy Quenched Fractions Rise below M ∗ ≈ 10 7 M ⊙

We use a new sample of low-mass (M * < 10 9 M ⊙ ) isolated galaxies from the Exploration of Local VolumE Survey-Field (ELVES-Field) to examine the star formation properties and sizes of field dwarf galaxies in the Local Volume (LV; D < 10 Mpc). This volume-limited sample was selected from nearly 3000 deg 2 of imaging, relying on surface brightness fluctuations to determine distances to the majority of the systems and is complete to M * ≈ 10 6 M ⊙ . Across the surveyed area, we catalog over 2300 candidate LV dwarfs, of which we confirm 95 as genuine LV members and reject over 1600 as background contaminants, with the remaining 600 candidates still requiring a distance measurement. Of the confirmed LV dwarfs, 46 are either new discoveries or confirmed via a distance measurement for the first time here. We explore different environmental criteria to select isolated dwarfs but primarily focus on dwarfs that are >2 × R vir in projection from any known group with M ⋆ > 10 9 M ⊙ . We find that, at higher dwarf masses (M ⋆ ≳ 10 7 M ⊙ ), essentially all field dwarfs are star forming as has been found before. In contrast, at M ⋆ ≲ 10 7 M ⊙ , ∼30% of field dwarfs appear to be quenched. Finally, we find that isolated dwarfs are noticeably smaller (∼20%) than satellite dwarfs of the same stellar mass, regardless of quenched status.

Carlsten, Scott G. [Princeton Univ., NJ (United St↗
DOE OSTI2022

The Exploration of Local VolumE Satellites (ELVES) Survey: A Nearly Volume-limited Sample of Nearby Dwarf Satellite Systems

We present the final sample of the Exploration of Local VolumE Satellites (ELVES) survey, a survey of the dwarf satellites of a nearly volume-limited sample of Milky Way (MW)-like hosts in the Local Volume. Hosts are selected simply via a cut in luminosity (${M}_{{K}_{s}}\lt -22.1$ mag) and distance (D < 12 Mpc). We cataloged the satellites of 25 of the 31 such hosts, with another five taken from the literature. All hosts are surveyed out to at least 150 projected kpc ( ~ R vir /2), with the majority surveyed to 300 kpc ( ~ R vir ). Satellites are detected using a consistent semiautomated algorithm specialized for low surface brightness dwarfs. As shown through extensive tests with injected galaxies, the catalogs are complete to M V ~ -9 mag and μ 0,V ~ 26.5 mag arcsec -2 . Candidates are confirmed to be real satellites through distance measurements including redshift, tip of the red giant branch, and surface brightness fluctuations. Across all 30 surveyed hosts, there are 338 confirmed satellites with M V < -9 mag, with a further 106 candidates awaiting distance measurement. For the vast majority of these, we provide consistent multiband Sérsic photometry. We show that satellite abundance correlates with host mass, with the MW being quite typical among comparable systems, and that satellite quenched fraction rises steeply with decreasing satellite mass, mirroring the quenched fraction for the MW and M31. The ELVES survey represents a massive increase in the statistics of surveyed systems with known completeness, and the provided catalogs are a unique data set to explore various aspects of small-scale structure and dwarf galaxy evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Automated tape-target centering based on template matching for construction measurement tasks using robotic total station

Robotic total stations have transformed surveying and construction mapping through precise, efficient, and automated measurements. These instruments integrate a theodolite, which measures horizontal and vertical angles, with an electronic distance measurement (EDM) unit to determine distances, allowing accurate 3D measurement of observable points. Traditionally, users manually aimed the total station at a target. Recent advancements in robotic motor control and integration of cameras now enable automatic rotation and aiming, typically requiring only a single operator to position the target. Automated aiming is commonly performed using retroreflector prisms, which reflect light back to the source with minimal scattering, enabling high-precision measurements over long distances. However, retroreflectors, especially those designed for 360 degree, can be expensive and impractical for certain applications. This paper presents an algorithm for automating the center detection of low-cost disposable tape targets using the total station's onboard camera and a template matching algorithm. The algorithm identifies the target's center pixel in the image, and the instrument is commanded to aim at that location. We evaluated the performance of this template-matching-based centering method under various distances, angles, lighting conditions, and field environments, comparing its results to both manual aiming and conventional automated aiming of tape targets. Manual aiming was used as the baseline operational reference in the absence of an independent ground-truth measurement. The proposed approach achieves target centering results comparable to the manual baseline. This method provides a cost-effective alternative for high-precision applications where retroreflector targets are constrained by budget or logistics.

Harrington, Joshua [ORNL]↗
DOE OSTI2022

Sub-percentage measure of distances to redshift of 0.1 by a new cosmic ruler

ABSTRACT Distance-redshift diagrams probe expansion history of the Universe. We show that the stellar mass-binding energy (massE) relation of galaxies proposed in our previous study offers a new distance ruler at cosmic scales. By using elliptical galaxies in the main galaxy sample of the Sloan Digital Sky Survey Data Release 7, we construct a distance-redshift diagram over the redshift range from 0.05 to 0.2 with the massE ruler. The best-fit dark energy density is 0.675 ± 0.079 for flat Λ-cold dark matter (ΛCDM) model, consistent with those by other probes. At the median redshift of 0.11, the median distance is estimated to have a fractional error of 0.34 per cent, much lower than those by supernova (SN) Ia and baryonic acoustic oscillation (BAO) and even exceeding their future capability at this redshift. The above low-$\mathit{ z}$ measurement is useful for probing dark energy that dominates at the late Universe. For a flat dark energy equation of state model (flat wCDM), the massE alone constrains w to an error that is only a factor of 2.2, 1.7, and 1.3 times larger than those by BAO, SN Ia, and cosmic microwave background (CMB), respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Dependence of the Type Ia Supernova Host Bias on Observation or Fitting Technique

More luminous Type Ia supernovae prefer less massive hosts and regions of higher star formation. This correlation is inverted during width–color–luminosity light-curve standardization resulting in step-like biases of distance measurements with respect to host properties. Using the PMAS/PPak Integral-field Supernovahosts COmpilation (PISCO) supernova host sample and Sloan Digital Sky Survey, Galaxy Evolution Explorer, and Two Micron All Sky Survey photometry, we compare host stellar mass and specific star-formation rate (sSFR) from different observation methods, including local versus global, and fitting techniques to measure their impact on the host step biases. Mass-step measurements for all our mass samples are consistent within a 1σ significance from –0.03 ± 0.02 mag to –0.04 ± 0.02 mag. Including or excluding UV information had no effect on measured mass-step size or location. sSFR step sizes are more significant than mass-step measurements and varied from 0.05 ± 0.03 mag (Hα) and 0.06 ± 0.02 mag (UV) for a 51 host sample. The sSFR step location is influenced by the mass sample used to normalize star formation and by sSFR tracer choice. The step size is reduced to 0.04 ± 0.03 mag when using all available 73 hosts with Hα measurements. This 73 PISCO host subsample overall lacked a clear step signal, but here we are searching for whether different choices of mass or sSFR estimation can create a step signal. We find no evidence that different observation or fitting techniques choices can create a distance measurement step in either mass or sSFR.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Integrated Spatial, Spectral, & Temporal Optical Reflectance System for Precision Occupancy & Location Sensing to Improve Building Energy Efficiency

Buildings consume approximately 35% of the electricity used in the U.S. and building owners can significantly reduce this energy use by providing services like heating, electrical power and lighting only when people are present. The ARPAe funded program titled “INTEGRATED SPATIAL, SPECTRAL, & TEMPORAL OPTICAL REFLECTANCE SYSTEM FOR PRECISION OCCUPANCY & LOCATION SENSING TO IMPROVE BUILDING ENERGY EFFICIENCY” demonstrates how a low cost sensor technology developed for measuring distances can be used to count and locate occupants with a high degree of precision with a very low error rates. This platform tells a building control system where occupants are located (but not who they are) so that energy consuming services can be provided only when the services are needed by building occupants. The original proof of concept involved using low cost, commercially available time-of-flight (TOF) sensors that measure distance, but the performance of these existing sensors was lacking, as they could not operate properly in the presence of sunlight, which blinded the simple TOF sensors and limited their utility in buildings. This project proposed a powerful new class of TOF sensors that used state-of-the-art integrated circuit (IC) fabrication processes that combined advanced photonics with conventional silicon chip circuitry for improved sensor performance. An equally important part of this project was to find ways to maximize occupant count and location accuracy while using the fewest number of sensors possible, in order to keep costs low. By using building blueprints to create digital twins of commercial building spaces, the team developed new algorithms to maximize occupant count and tracking accuracy by properly locating the minimum number of sensors at just the right spots in the building. This capability not only minimizes system costs but also simplified sensor installation and system commissioning. Our simulations of our sensor networks for a range of commercial floorplan designs demonstrated that our installed cost target of $0.08/sqft was attainable, though not fully demonstrated during the project. Finally, we noted that the TOF sensor concept could provide a valuable role in health and eldercare by tracking patients without the need for worn sensors and would be useful for fall detection and other patient safety metrics, including tracking healthcare/patient interactions. We feel that, when fully developed, this new class of sophisticated TOF sensors and support software will be a powerful new approach to improving building energy efficiency based on occupant centric control platforms and will also open new levels of patient safety in healthcare operations. To realize this potential, the team formed the Troy Sensor Company LLC to oversee licensing of the programs patents and continue to seek commercialization of this program’s activity sensing technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Measurement of the Hubble constant with high-energy neutrinos

Measuring distances in the Universe is one of the hardest problems in physics and astronomy. Almost every distance probe relies on photons, whose propagation across cosmic distances introduces extinction, absorption, scattering, and radiative-transfer effects. Neutrinos suffer none of these and propagate unattenuated through dust, intergalactic medium, and dense source environments alike. We introduce a new distance-ladder method for measuring the Hubble constant $H_0$ using high-energy astrophysical neutrinos from point sources as standardizable candles, and report its first observational realization. Using 12 X-ray-selected Seyfert galaxies for which IceCube reports significant per-source neutrino excesses in its 14-year public point-source release, we exploit the disk-corona correlation $L_ν= κ\, L_X^β$ between neutrino and X-ray luminosities to construct a neutrino distance ladder anchored by non-redshift distances to NGC 1068 (Cepheid + TRGB). We find $H_0 = 49^{+40}_{-30}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and $β= 0.67^{+0.16}_{-0.25}$ (68% credible intervals), with the corona slope disfavoring the calorimetric limit $β= 1$ at ${\sim}2σ$. The result is consistent with existing $H_0$ determinations from Planck and SH0ES within 1$σ$. While the uncertainty on $H_0$ is large, the measurement is free of electromagnetic propagation systematics and demonstrates the viability of neutrinos as a novel cosmographical probe.

Herrera, Gonzalo [MIT, MKI; Harvard U.] (ORCID:000↗
DOE OSTI2022

Phosphorothioate-Based Site-Specific Labeling of Large RNAs for Structural and Dynamic Studies

Pulsed electron-electron double resonance (PELDOR) spectroscopy, X-ray scattering interferometry (XSI), and single-molecule Forster resonance energy transfer (smFRET) are molecular rulers that provide inter- or intramolecular pair-wise distance distributions in the nanometer range, thus being ideally suitable for structural and dynamic studies of biomolecules including RNAs. The prerequisite for such applications requires site-specific labeling of biomolecules with spin labels, gold nanoparticles, and fluorescent tags, respectively. Recently, site-specific labeling of large RNAs has been achieved by a combination of transcription of an expanded genetic alphabet containing A-T/G-C base pairs and NaM-TPT3 unnatural base pair (UBP) with posttranscriptional modifications at UBP bases by click chemistry or amine-NHS ester reactions. However, due to the bulky sizes of functional groups or labeling probes used, such strategies might cause structural perturbation and decrease the accuracy of distance measurements. Here, we synthesize an a-thiophosphorylated variant of rTPT3TP (rTPT3aS), which allows for post-transcriptional site-specific labeling of large RNAs at the internal a-phosphate backbone via maleimide-modified probes. Subsequent PELDOR, XSI, and smFRET measurements result in narrower distance distributions than labeling at the TPT3 base. The presented strategy provides a new route to empower the molecular rulers for structural and dynamic studies of large RNA and its complex.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Graph Metric Learning Quantifies Morphological Differences between Two Genotypes of Shoot Apical Meristem Cells in Arabidopsis

We present a method for learning “spectrally descriptive” edge weights for graphs. We generalize a previously known distance measure on graphs (Graph Diffusion Distance), thereby allowing it to be tuned to minimize an arbitrary loss function. Because all steps involved in calculating this modified GDD are differentiable, we demonstrate that it is possible for a small neural network model to learn edge weights which minimize loss. We apply this method to discriminate between graphs constructed from shoot apical meristem images of two genotypes of Arabidopsis thaliana specimens: wild-type and trm678 triple mutants with cell division phenotype. Training edge weights and kernel parameters with contrastive loss produces a learned distance metric with large margins between these graph categories. We demonstrate this by showing improved performance of a simple k-nearest-neighbors classifier on the learned distance matrix. We also demonstrate a further application of this method to biological image analysis. Once trained, we use our model to compute the distance between the biological graphs and a set of graphs output by a cell division simulator. Comparing simulated cell division graphs to biological ones allows us to identify simulation parameter regimes which characterize mutant vs. wild-type Arabidopsis cells. We find that trm678 mutant cells are characterized by increased randomness of division planes and decreased ability to avoid previous vertices between cell walls.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

DESI EDR: Calibrating the Tully–Fisher Relationship with the DESI Peculiar Velocity Survey

We calibrate the Tully–Fisher relation (TFR) with data from the DESI Peculiar Velocity (PV) Survey taken during the Survey Validation (SV) period of the DESI galaxy redshift survey. Placing spectroscopic fibers on the centers and major axes of spatially extended spiral galaxies identified in the 2020 Siena Galaxy Atlas using the DESI Legacy Surveys, we measure the rotational velocities at 0.33R 26 for 1155 (1128 + 27 dwarf) spiral galaxies observed during SV. Using 39 spiral galaxies observed in the Coma cluster, we find a slope for the TFR of −8.32 ± 0.15 AB mag in the r band, with a scatter about the TFR of 1.12 ± 0.03 AB mag. We calibrate the zero-point of the TFR using galaxies with independent distances measured using type Ia supernovae (SNe Ia) via the cosmological distance ladder. From the SN Ia distances, we measure a zero-point of $-19.21^{+0.30}_{-0.31}$ AB mag in the r band. We produce a public catalog of the distances to these 1128 spiral galaxies observed during DESI SV as part of the DESI PV Survey with our calibrated TFR. This is, to our knowledge, the first catalog of TFR distances produced with velocities measured at a single point in the disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The Dark Energy Survey Supernova Program: an updated measurement of the Hubble constant using the inverse distance ladder

We measure the current expansion rate of the Universe, Hubble’s constant $H_0$, by calibrating the absolute magnitudes of supernovae to distances measured by baryon acoustic oscillations (BAO). This ‘inverse distance ladder’ technique provides an alternative to calibrating supernovae using nearby absolute distance measurements, replacing the calibration with a high-redshift anchor. We use the recent release of 1829 supernovae from the Dark Energy Survey spanning $0.01\lt z\lt 1.13$ anchored to the recent baryon acoustic oscillation measurements from Dark Energy Spectroscopic Instrument (DESI) spanning $0.30 \lt z_{\mathrm{eff}}\lt 2.33$. To trace cosmology to $z=0$, we use the third-, fourth-, and fifth-order cosmographic models, which, by design, are agnostic about the energy content and expansion history of the universe. With the inclusion of the higher redshift DESI-BAO data, the third-order model is a poor fit to both data sets, with the fourth-order model being preferred by the Akaike Information Criterion. Using the fourth-order cosmographic model, we find $H_0=67.19^{+0.66}_{-0.64}\mathrm{~km} \mathrm{~s}^{-1} \mathrm{~Mpc}^{-1}$, in agreement with the value found by Planck without the need to assume Flat-$\Lambda$CDM. However, the best-fitting expansion history differs from that of Planck, providing continued motivation to investigate these tensions.

79 ASTRONOMY AND ASTROPHYSICS↗