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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Asteroids for μ Hz gravitational-wave detection

A major challenge for gravitational-wave (GW) detection in the μHz band is engineering a test mass (TM) with sufficiently low acceleration noise. We propose a GW detection concept using asteroids located in the inner Solar System as TMs. Our main purpose is to evaluate the acceleration noise of asteroids in the μHz band. We show that a wide variety of environmental perturbations are small enough to enable an appropriate class of ~10 km-diameter asteroids to be employed as TMs. This would allow a sensitive GW detector in the band (few) × 10 -7 Hz ≲ fGW ≲ (few) × 10 -5 Hz, reaching strain hc ~ 10 -19 around f GW ~10 μHz, sufficient to detect a wide variety of sources. To exploit these asteroid TMs, human-engineered base stations could be deployed on multiple asteroids, each equipped with an electromagnetic transmitter/receiver to permit measurement of variations in the distance between them. We discuss a potential conceptual design with two base stations, each with a space-qualified optical atomic clock measuring the round-trip electromagnetic pulse travel time via laser ranging. Trade space exists to optimize multiple aspects of this mission: for example, using a radio-ranging or interferometric link system instead of laser ranging. This motivates future dedicated technical design study. This mission concept holds exceptional promise for accessing this GW frequency band.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

AuriDESI: mock catalogues for the DESI Milky Way Survey

The Dark Energy Spectroscopic Instrument Milky Way Survey (DESI MWS) will explore the assembly history of the Milky Way by characterizing remnants of ancient dwarf galaxy accretion events and improving constraints on the distribution of dark matter in the outer halo. We present mock catalogues that reproduce the selection criteria of MWS and the format of the final MWS data set. These catalogues can be used to test methods for quantifying the properties of stellar halo substructure and reconstructing the Milky Way’s accretion history with the MWS data, including the effects of halo-to-halo variance. The mock catalogues are based on a phase-space kernel expansion technique applied to star particles in the Auriga suite of six high-resolution lambda-cold dark matter magnetohydrodynamic zoom-in simulations. They include photometric properties (and associated errors) used in DESI target selection and the outputs of the MWS spectral analysis pipeline (radial velocity, metallicity, surface gravity, and temperature). They also include information from the underlying simulation, such as the total gravitational potential and information on the progenitors of accreted halo stars. We discuss how the subset of halo stars observable by MWS in these simulations corresponds to their true content and properties. These mock Milky Ways have rich accretion histories, resulting in a large number of substructures that span the whole stellar halo out to large distances and have substantial overlap in the space of orbital energy and angular momentum.

dynamics↗
DOE OSTI2023

On de Sitter spacetime and string theory

We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, [Formula: see text]-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

Astronomy & Astrophysics↗
DOE OSTI2022

Neural network acceleration of large-scale structure theory calculations

Here, we make use of neural networks to accelerate the calculation of power spectra required for the analysis of galaxy clustering and weak gravitational lensing data. For modern perturbation theory codes, evaluation time for a single cosmology and redshift can take on the order of two seconds. In combination with the comparable time required to compute linear predictions using a Boltzmann solver, these calculations are the bottleneck for many contemporary large-scale structure analyses. Here, we construct neural network-based surrogate models for Lagrangian perturbation theory (LPT) predictions of matter power spectra, real and redshift space galaxy power spectra, and galaxy-matter cross power spectra that attain ~ 0.1% (at one sigma) accuracy over a broad range of scales in a ωCDM parameter space. The neural network surrogates can be evaluated in approximately one millisecond, a factor of 1000 times faster than the full Boltzmann code and LPT computations. In a simulated full-shape redshift space galaxy power spectrum analysis, we demonstrate that the posteriors obtained using our surrogates are accurate compared to those obtained using the full LPT model. We make our surrogate models public at https://github.com/sfschen/EmulateLSS, so that others may take advantage of the speed gains they provide to enable rapid iteration on analysis settings, something that is essential in complex contemporary large-scale structure analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Astrometric gravitational-wave detection via stellar interferometry

Here, we evaluate the potential for gravitational-wave (GW) detection in the frequency band from 10 nHz to 1 μ Hz using extremely high-precision astrometry of a small number of stars. In particular, we argue that nonmagnetic, photometrically stable, hot white dwarfs (WD) located at ~kpc distances may be optimal targets for this approach. Previous studies of astrometric GW detection have focused on the potential for less precise surveys of large numbers of stars; our work provides an alternative optimization approach to this problem. Interesting GW sources in this band are expected at characteristic strains around h c ~10 -17 × (μHz/ $f$ GW ). The astrometric angular precision required to see these sources is Δθ~h c after integrating for a time T~1/$f$GW. We show that jitter in the photometric center of WD of this type due to starspots is bounded to be small enough to permit this high-precision, small-N approach. We discuss possible noise arising from stellar reflex motion induced by orbiting objects and show how it can be mitigated. The only plausible technology able to achieve the requisite astrometric precision is a space-based stellar interferometer. Such a future mission with few-meter-scale collecting dishes and baselines of $\mathscr{O}$(100 km ) is sufficient to achieve the target precision. This collector size is broadly in line with the collectors proposed for some formation-flown, space-based astrometer or optical synthetic-aperture imaging-array concepts proposed for other science reasons. The proposed baseline is however somewhat larger than the km-scale baselines discussed for those concepts, but we see no fundamental technical obstacle to utilizing such baselines. A mission of this type thus also holds the promise of being one of the few ways to access interesting GW sources in this band.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

EMPDF : inferring the Milky Way mass with data-driven distribution function in phase space

We introduce the emPDF (empirical distribution function), a novel dynamical modelling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fitting potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining enclosed masses of M (,r) = 26±8, 46±8, 90±13⁠, and 149±40 x 10 10 M ⊙ at r = 30, 50, 100⁠, and 200 kpc, respectively. These are consistent with the updated constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. emPDF is currently implemented for tracers with complete 6D kinematics within spherical potentials, but it can potentially be extended to address more general problems.

Astrophysics of Galaxies (astro-ph.GA)↗
DOE OSTI2022

Marginal unbiased score expansion and application to CMB lensing

Here, we present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces, yielding Gaussianized asymptotically unbiased and near-optimal constraints on global parameters of interest. It is computationally much cheaper than exact alternatives like Hamiltonian Monte Carlo (HMC), excelling on funnel problems which challenge HMC, and does not require any problem-specific user supervision like other approximate methods such as variational inference or many simulation-based inference methods. MUSE makes possible the first joint Bayesian estimation of the delensed Cosmic Microwave Background (CMB) power spectrum and gravitational lensing potential power spectrum, demonstrated here on a simulated data set as large as the upcoming South Pole Telescope 3G 1500 deg 2 survey, corresponding to a latent dimensionality of ~6 million and of order 100 global bandpower parameters. On a subset of the problem where an exact but more expensive HMC solution is feasible, we verify that MUSE yields nearly optimal results. We also demonstrate that existing spectrum-based forecasting tools which ignore pixel-masking underestimate predicted error bars by only ~10%. This method is a promising path forward for fast lensing and delensing analyses which will be necessary for future CMB experiments such as SPT-3G, Simons Observatory, or CMB-S4, and can complement or supersede existing HMC approaches. The success of MUSE on this challenging problem strengthens its case as a generic procedure for a broad class of high-dimensional inference problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Demonstration and Automation of Reflected Target Optical Measurement for Heliostats

Accurate optical surfaces are a primary driver of concentrated solar power plant performance. Errors in pointing and tracking mirrors, the canting of individual mirror facets, and the surface slope of the mirror itself can be caused by errors during assembly, transportation, wind loading, gravity, and many other sources. The tools that exist to measure these error sources today largely rely on fringe deflectometry (SOFAST, QDec, others), or photogrammetry with targets attached to the mirror surface. Since 2022, NREL has been developing a measurement method called the Reflected Target Non-intrusive Assessment (ReTNA) system. This system differs from most established methods in that we perform deflectometry with a pattern of coded targets, identified in space with photogrammetry. Reflected target systems have several advantages over traditional fringe deflectometry systems. Firstly, they can be operated in bright or ambient lighting, a challenge for fringe systems that use a projector and screen. Reflected target systems also can use a much lighter and less expensive target than projector-based systems. Lastly, 2D slope measurement can be solved from a single image, which leads to several advantages for accommodating faster measurements and smaller sized targets. These advantages make ReTNA particularly well-suited for applications where there are space or lighting constraints, like performing heliostat quality assurance on an assembly line. It's also useful when a lightweight, flexible system is needed, like for heliostat developers to quickly measure a new heliostat design at different orientations, to observe gravitational effects on the mirror surface shape. In the last year, significant improvements were made to this tool to make it more useful for these applications. These improvements were focused around validation of the ReTNA measurement system, and automation of the setup and measurement process. First, we present an improved ReTNA layout, for use on the heliostat assembly line. Next, we detail the various changes to the ReTNA software and computer vision methods to automate data collection in this new setup, and lessons learned from this process. The goal with this new setup is to perform a full heliostat surface characterization without removing the mirror from the assembly line. Lastly, we share results from several ReTNA validation studies undertaken over the last year. These include repeated ReTNA measurement on demonstration mirror facets, comparisons with other optical measurement tools, and some studies aimed at quantifying the uncertainty of ReTNA measurement under various constraints (mirror-target spacing, camera resolution, etc.). These results are compared with 2024 HelioCon performance targets, and our planned next steps for the ReTNA measurement system are presented.

CSP↗
DOE OSTI2025

Inferring Neutron Star Merger Ejecta Morphology with Kilonovae

In this study we incorporate a new grid of kilonova simulations produced by the Monte Carlo radiative transfer code SuperNu in an inference pipeline for astrophysical transients and evaluate their performance. These simulations contain four different two-component ejecta morphology classes. We analyze follow-up observational strategies by Vera Rubin Observatory in optical and James Webb Space Telescope (JWST) in mid-infrared (MIR). Our analysis suggests that, within these strategies, it is possible to discriminate between the four different morphologies only when late-time JWST observations in MIR are available. We conclude that follow-ups by the new Vera Rubin Observatory alone are not sufficient to determine ejecta morphology. Additionally, we make comparisons between surrogate models based on radiative transfer simulation grids by SuperNu and POSSIS, by analyzing the historic kilonova AT2017gfo that accompanied the gravitational wave event GW170817. We show that both SuperNu and POSSIS models provide similar fits to photometric observations but their qualitative interpretations differ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Galactic ArchaeoLogIcaL ExcavatiOns (GALILEO) II. t-SNE portrait of local fossil relics and structures

Based on high-quality Apache Point Observatory Galactic Evolution Experiment (APOGEE) DR17 and Gaia DR3 data for 1742 red giants stars within 5 kpc of the Sun and not rotating with the Galactic disk (V φ < 100 km s -1 ), we used the nonlinear technique of unsupervised analysis t-Distributed Stochastic Neighbor Embedding (t-SNE) to detect coherent structures in the space of ten chemical-abundance ratios: [Fe/H], [O/Fe], [Mg/Fe], [Si/Fe], [Ca/Fe], [C/Fe], [N/Fe], [Al/Fe], [Mn/Fe], and [Ni/Fe]. Additionally, we obtained orbital parameters for each star using the nonaxisymmetric gravitational potential GravPot16. Seven structures are detected, including Splash, Gaia-Sausage-Enceladus (GSE), the high-α heated-disk population, N-C-O peculiar stars, and inner disk-like stars, plus two other groups that did not match anything previously reported in the literature, here named Galileo 5 and Galileo 6 (G5 and G6). These two groups overlap with Splash in [Fe/H], with G5 having a lower metallicity than G6, and they are both between GSE and Splash in the [Mg/Mn] versus [Al/Fe] plane, with G5 being in the α-rich in situ locus and G6 on the border of the α-poor in situ one. Nonetheless, their low [Ni/Fe] hints at a possible ex situ origin. Their orbital energy distributions are between Splash and GSE, with G5 being slightly more energetic than G6. We verified the robustness of all the obtained groups by exploring a large range of t-SNE parameters, applying it to various subsets of data, and also measuring the effect of abundance errors through Monte Carlo tests.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The Multiple Paths to Merger of Unequal-mass Black Hole Binaries in the Disks of Active Galactic Nuclei

The accretion disks that power active galactic nuclei (AGN) are thought to house populations of stars and compact objects; after forming binaries these compact objects may merge, begetting gravitational waves (GWs) such as those detected by LIGO and VIRGO. We present a comprehensive study of the early evolution of binaries within AGN disks as their orbits are influenced by the surrounding gas, focusing on eccentric and unequal-mass binaries. Nearly equal-mass binaries behave similarly to their equal-mass counterparts: Prograde binaries inspiral, albeit somewhat slowly, and have their eccentricities damped; retrograde binaries inspiral ∼2–3 times faster than their prograde counterparts, and those with near-equal masses are driven quickly toward near-unity eccentricities. However, the primaries in retrograde binaries with mass ratios of m 2 /m 1 ≲ 0.4 experience significantly weaker headwinds and retain substantial accretion disks that help damp binary eccentricities, slowing binary inspirals. Additionally, we find that while accretion drives prograde binaries toward equal masses thanks to the exchange of material between the primary and secondary accretion disks, retrograde binaries are driven slowly toward more extreme mass ratios. Prograde binaries, and generally those with low mass ratios, likely accrete for multiple e-folding timescales before merger. On the other hand, high-mass-ratio retrograde binaries may merge before accreting substantially, potentially approaching merger with detectable eccentricity. Future ground-based GW observatories, with their broader frequency coverage, should be particularly useful for studying these populations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Improved time-delay lens modelling and H 0 inference with transient sources

ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.

Ding, Xuheng↗
DOE OSTI2023

Detecting Long-period Variability in the SDSS Stripe 82 Standards Catalog

We report the results of a search for long-period (100 < P < 600 days) periodic variability in the SDSS Stripe 82 standards catalog. The SDSS coverage of Stripe 82 enables such a search because there are on average 20 observations per band in ugriz bands for about one million sources, collected over about 6 yr, with a faint limit of r ~ 22 mag and precisely calibrated 1%–2% photometry. We calculated the periods of variable source candidates in this sample using the Lomb–Scargle periodogram and considered the three highest periodogram peaks in each of the gri filters as relevant. Only those sources with gri periods consistent within 0.1% were later studied. We use the Kuiper statistic to ensure uniform distribution of data points in phased light curves. We present five sources with the spectra consistent with quasar spectra and plausible periodic variability. This SDSS-based search bodes well for future sensitive large-area surveys, such as the Rubin Observatory Legacy Survey of Space and Time, which, due to its larger sky coverage (about a factor of 60) and improved sensitivity (~2 mag), will be more powerful for finding such sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Constraints on f ( R ) and normal-branch Dvali-Gabadadze-Porrati modified gravity model parameters with cluster abundances and galaxy clustering

In this report we present forecasted cosmological constraints from combined measurements of galaxy cluster abundances from the Simons Observatory and galaxy clustering from a DESI-like experiment on two well-studied modified gravity models, the chameleon-screened Hu-Sawicki f(R) model and the nDGP braneworld Vainshtein model. A Fisher analysis is conducted using σ 8 constraints derived from thermal Sunyaev-Zel’dovich (tSZ) selected galaxy clusters as well as linear and quasilinear redshift-space 2-point galaxy correlation functions. We find that the cluster abundances drive the constraints on the nDGP model while f(R) constraints are led by galaxy clustering. The two tracers of the cosmological gravitational field are found to be complementary, and their combination significantly improves constraints on the f(R) in particular in comparison to each individual tracer alone. For a model of f(R) with a general relativity (GR) fiducial case (f R0 = 0), we find a 2-σ upper limit of f R0 ≤ 5.68 x10 -7 . For the well-studied log-based fiducial parameter value in f(R), log 10 (f R0 ) = -5, paired with the parameter value n = 1, we find combined 1-σ constraints of σ(log 10 (f R0 )) = 0.12 and σ(n) = 0.36. For the nDGP model with fiducial n nDGP = 1 we find σ( n nDGP ) = 0.087. Our results present the exciting potential to utilize upcoming galaxy and CMB survey data available in the near future to discern and/or constrain cosmic deviations from GR.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

BICEP/Keck. XVI. Characterizing Dust Polarization through Correlations with Neutral Hydrogen

We characterize Galactic dust filaments by correlating BICEP/Keck and Planck data with polarization templates based on neutral hydrogen (H i) observations. Dust polarization is important for both our understanding of astrophysical processes in the interstellar medium (ISM) and the search for primordial gravitational waves in the cosmic microwave background (CMB). In the diffuse ISM, H i is strongly correlated with the dust and partly organized into filaments that are aligned with the local magnetic field. We analyze the deep BICEP/Keck data at 95, 150, and 220 GHz, over the low-column-density region of sky where BICEP/Keck has set the best limits on primordial gravitational waves. We separate the H i emission into distinct velocity components and detect dust polarization correlated with the local Galactic H i but not with the H i associated with Magellanic Stream i. We present a robust, multifrequency detection of polarized dust emission correlated with the filamentary H i morphology template down to 95 GHz. For assessing its utility for foreground cleaning, we report that the Hi morphology template correlates in B modes at a ~10%–65% level over the multipole range 20 < ℓ < 200 with the BICEP/Keck maps, which contain contributions from dust, CMB, and noise components. We measure the spectral index of the filamentary dust component spectral energy distribution to be β = 1.54 ± 0.13. We find no evidence for decorrelation in this region between the filaments and the rest of the dust field or from the inclusion of dust associated with the intermediate velocity H i. Finally, we explore the morphological parameter space in the H i-based filamentary model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A differentiable perturbation-based weak lensing shear estimator

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-per cent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (fpfs), using jax, which is publicly available as part of a new suite of analytic shear algorithms called anacal. This code can analytically calibrate the shear response of any non-linear observable constructed with the fpfs shapelets and detection modes utilizing autodifferentiation (ad), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the ad capability of jax, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new anacal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the 10 yr LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10 –3 (99.7 per cent confidence interval), and the effective galaxy number density is improved by 5 per cent. We also discuss some planned future additions to the anacal software suite to extend its applicability beyond the fpfs measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Entire four-graviton EFT from the duality between color and kinematics

The Bern-Carrasco-Johansson (BCJ) double-copy construction reveals a fundamental structural connection between gauge and gravity theories. At its core, the BCJ double copy is directly due to a duality between the algebraic relations of a color root and those of a kinematic root. We generalize this principle beyond the conventional Lie algebra structure of tree-level Yang-Mills theory. By demanding color-kinematics duality for the complete basis of four-point color structures—including those involving the symmetric 𝑑 𝑎⁢𝑏⁢𝑐 constants—we define the universal double copy. We systematically classify the bases of all such parity-even generalized gauge-theory numerators and, independently, the space of all parity-even four-graviton higher-derivative operators. We demonstrate that our universal double-copy construction precisely spans the entire tower of parity-even four-graviton amplitudes in any dimension, except for the Lovelock 𝑅 3 contribution in 𝐷 > 6 which we can express in terms of a particularly simple universal triple-copy involving gauge theories coupled to scalars. Explicit machine-readable expressions for the complete basis of gauge-theory numerators and fundamental gravitational building blocks are provided in the Supplemental Material. This establishes that all possible four-point gravitational interactions can be factorized into products of gauge-theory building blocks governed by this universal notion of color-kinematics duality.

Carrasco, John Joseph M. [Northwestern Univ., Evan↗