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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 19 records

Proliferated Resilient Economical Half-Meter Aperture Space Telescopes (PREEMPT)

The PREEMPT LDRD was motivated by a major national need for better space-based imaging systems that are both high performing and affordable for the US Government. Current optical payloads for intelligence, surveillance and reconnaissance (ISR) and space domain awareness (SDA) missions can cost hundreds of millions of dollars and take years to develop, which makes it difficult to build the large constellations required for persistent, world-wide coverage. To address this, the team aimed to advance a different kind of large-aperture (>25 cm) telescope, called a monolithic telescope, in which key optical surfaces are built into a single piece of fused silica. This design greatly reduces payload and spacecraft complexity, the need for precision focus actuators, improves mechanical and thermal robustness, and lowers cost when compared with traditional Cassegrain telescopes that rely on many precisely aligned components. The project focused on five primary thrusts. The first thrust was to advance the concept of a V10, 25 cm, monolithic telescope forward from optical design to flight-ready stage. This was accomplished in partnership with Optimax, who delivered the first test unit in the early stages of the LDRD. The team developed several technologies necessary for this optic to be integrated into a flight demonstration. These include carbon fiber housings, highly detailed structural and thermal models and stress-reducing elastic averaging Hirth groove designs. These technologies resulted in a successful maturation of the optic, which is now slated to fly in late 2026/early 2027 for a demonstration mission. The second thrust was to advance the manufacturability of these optics. In collaboration with NIF’s optical manufacturing shop, we reduced polishing time from 480 hours to 65 hours through the implementation of optimized processes and new tools. The NIF team utilized a conceptual V8 (18 cm) optic to demonstrate this optimization, though it can be applied to the rest of the monolithic optic portfolio. Third, the team developed the first conceptual V20 (50 cm) payload, which is slated to be the next generation of LLNL optical payload systems. A set of structural, dynamic and thermal simulations were performed to identify potential challenges in the future development of this payload. Early-stage simulations suggest the payload is feasible, though thermal management will be the key focus area to maintain optimal performance. Fourth, a non-linear model of Viton was developed, to further enhance the reliability of our structural and dynamic models for future payloads. Viton acts as the primary interface material between the optic and its housing. Lastly, the team focused on successfully displaying the feasibility of using additively manufactured metal composites for optical space payloads. The team successfully demonstrated layer by layer deposition of Al-SiC composites, which have highly tunable structural and coefficient of thermal expansion (CTE) properties. These are crucial for optical payloads because CTE mismatch is one of the causes for degraded optical performance for telescopes in orbit. Overall, the work showed that monolithic telescopes could become a practical, lower-cost path to high-resolution space imaging for both national security and scientific missions.

42 ENGINEERING↗

Heat exposure and maternal stress: evidence from the GRAPHS pregnancy cohort in Ghana

Heat exposure has been linked to psychosocial stress, an established antecedent of perinatal depression; however, evidence on heat-related stress during pregnancy in sub-Saharan Africa remains limited. We analyzed psychosocial stress scores and covariate data from the Ghana Randomized Air Pollution and Health Study, linking daily maximum and minimum shaded wet bulb globe temperature (WBGT) metrics to participants’ stress scores derived from the Crisis in Family Systems-Revised Life Events Questionnaire. We evaluated associations using ordinal logistic regression of pregnancy-average and trimester-average exposures and distributed lag non-linear models (DLNMs) to assess time-varying associations across gestation. Higher average maximum WBGT exposure across pregnancy was associated with increased odds of higher psychosocial stress; each 1 °C increase in maximum WBGT was associated with 64% higher odds of belonging to a higher stress category (OR = 1.64; 95% CI = 1.17–2.31; p = 0.0040). In trimester-average models, higher first-trimester maximum WBGT was also associated with higher stress (OR = 1.44; 95% CI = 1.15–1.81; p = 0.0014). DLNMs suggested that relatively cooler daily maximum WBGT values (25th percentile) were associated with decreased odds of stress in early pregnancy, whereas extreme daily maximum WBGT values (99th percentile) showed a pattern consistent with increased odds of stress in mid-to-late gestation. These findings highlight gestational windows in which heat exposure may influence stress, emphasizing the need for further research into underlying mechanisms and effective interventions to protect maternal mental health in heat-vulnerable settings.

White, Lewis [Columbia University] (ORCID:00090005↗

Rapid Coal-Ash Characterization using Geophysical Methods & Machine Learning

Coal combustion products (CCP) are challenging to delineate in heterogeneous field settings. Conventional methods (test pits, coring, and laboratory analyses) are labor-intensive, slow, invasive, and provide sparse spatial coverage. This study evaluates whether rapid non-invasive geophysical screening methods—induced polarization (IP), magnetic susceptibility, and nuclear magnetic resonance (NMR) —combined with surface colorimetry (RGB_24), can discriminate CCP-soil mixtures and provide reliable estimates of CCP content. Laboratory measurements were collected on five CCP-soil mixtures (series) and modeled using (i) a linear baseline, (ii) a calibrated non-linear (power-mean) model, and (iii) a machine-learning (ML) Random Forest approach, with validation via leave-one-series-out and site-specific tests. Across the five series, individual signals—particularly IP and magnetic susceptibility—were strongly predictive of ash content but were consistently outperformed by combined models. The pooled calibrated non-linear and ML models captured the observed non-linearity and achieved high accuracy and precision, improving on linear fits. Colorimetry showed the weakest direct relationship with ash content for the tested samples but improved performance when included in multi-signal models. At pre-selected 3.5% decision threshold, calibrated and ML approaches yielded near-perfect classification (Matthews correlation coefficient ˜ 1), suggesting strong practical operability for field screening. Additionally, field-analog tests highlighted the role of endmembers—accuracy declined without access to end-member measurements but was largely recovered by collecting a minimal labeled pair for local recalibration. With end members, accuracy remained high. Globally trained models performed well on three operational unknowns; however, series-specific refits provided the most accurate predictions. Overall, these results highlight the potential of combining rapid geophysics and minimal local calibration for improved coal-ash delineation.

Peshtani, Klaudio↗

A fast and robust computational modeling approach for density and shape predictions in powder metallurgy hot isostatic pressing

Powder metallurgy hot isostatic pressing (PM-HIP) is an advanced manufacturing process that produces near-net-shape parts with high material utilization and uniform microstructures. PM-HIP is frequently used for producing small-scale parts with complicated geometries and is potentially economical for producing large-scale parts. However, excessive post-HIP shape distortions can reduce its effectiveness and economic advantage, especially for larger parts. A PM-HIP computational model can predict and help mitigate these distortions. However, due to complex deformation mechanisms and thermo-mechanical coupling present in PM-HIP processes, these non-linear computational models sometimes become numerically unstable. The numerical instabilities in these models can lead to very slow convergence or no convergence at all, which often translates to slow and unreliable models. These limitations are more pronounced in large models with complicated geometries. Hence, in this work, an alternative modeling approach is presented that improves numerical stability and computational performance. The presented approach achieves these improvements through approximating the fully coupled thermo-mechanical PM-HIP model as a decoupled model and adding inertial damping to the model’s mechanical part. In conclusion, a comparison with the fully coupled model indicated a slight dip in prediction accuracy (<5% error) but significant improvements in numerical stability (>20 times larger time step size) and computational performance (5-10 times speed-up with less computational resource usage) when using the presented approach.

Hot isostatic pressing↗

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Emulating galaxy and peculiar velocity clustering on non-linear scales

We explore the potential of cross-correlating galaxies and peculiar velocities on non-linear scales to enhance cosmological constraints. Leveraging the ABACUSSUMMIT simulation suite and the halo occupation distribution (HOD) formalism, we trained emulator models to describe the non-linear clustering of galaxies and velocities in redshift space. Our analysis demonstrates that combining galaxy and peculiar velocity clustering provides tighter constraints on both HOD and cosmological parameters, particularly on σ8 and w0. We further applied our models to realistic mock catalogues, reproducing the expected density and peculiar velocity errors of type-Ia supernovae, Tully-Fisher and fundamental plane measurements for the combined ZTF and DESI measurements. While systematic biases arise in the HOD parameters, the cosmological constraints remain unbiased, yielding a 3.8% precision measurement on fσ 8 compared to 4.7% when using galaxy clustering alone. We demonstrate that while combining tracers with realistic velocity measurements still yields an improvement, the gains are diminished, highlighting the need for further efforts to reduce velocity measurement uncertainties and correct observational systematics on small scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Ambient and Initial Temperature Effects on Energy Consumption Rate Modeled in FASTSim

Ambient and initial temperatures significantly impact the energy consumption rate (ECR) of battery electric vehicles (BEVs) due to auxiliary loads and the temperature dependence of battery efficiency. This study introduces a streamlined, physics-based thermal modeling approach within the FASTSim tool that bridges the gap between oversimplified constant-load models and computationally expensive high-fidelity simulations. By employing a lumped thermal mass framework, the model captures fundamental energy balances and critical non-linear energy penalties while maintaining the computational efficiency required for expansive sensitivity studies. The simulations evaluated a compact BEV hatchback with a resistive heater over city (UDDS) and highway (HWFET) test cycles. Compared to a 22 degrees Celsius initial and ambient temperature baseline, a -7 degrees Celsius initial/ambient temperature resulted in a 221% increase in the ECR for the city cycle and a 100% increase for the highway cycle. Conversely, a 45 degrees Celsius initial / 40 degrees Celsius ambient temperature resulted in a 40% increase for UDDS and an 18% increase for HWFET. These results demonstrate that while cold conditions impose the most severe energy penalties due to resistive heating, the impact is consistently more pronounced in city driving where auxiliary loads represent a larger proportion of total energy. This lightweight yet robust framework enables researchers to rapidly quantify BEV thermal sensitivity across diverse climates without the need for high-overhead simulation environments.

33 ADVANCED PROPULSION SYSTEMS↗

The Energy Exascale Earth System Model Version 3: 2. Overview of the Coupled System

The Energy Exascale Earth System Model version 3 (E3SMv3) represents the latest advancement in Earth system modeling developed by the U.S. Department of Energy (DOE). Building upon previous versions, E3SMv3 introduces significant updates across its coupled components to enhance capability and improve fidelity. The atmosphere component incorporates advancements in chemistry, aerosol-cloud interactions, convection, and microphysics. The ocean features a new time-stepping scheme and a higher-resolution unstructured mesh with sub-ice-shelf cavities, while the sea ice model integrates advanced snow and ice physics for more realistic cryospheric simulations. The land model introduces prognostic vegetation dynamics and a new sub-grid topographic treatment of solar radiation. A new tri-grid configuration harmonizes the horizontal grids of the land and river components for improved process coupling. It is enabled by a new non-linear remapping between the atmosphere and land. E3SMv3 underwent extensive testing through a comprehensive simulation campaign, including pre-industrial control, idealized CO 2 experiments, and historical simulations spanning 1850–2024. The model demonstrates significant improvements in simulating the evolution of the historical surface temperature, particularly addressing the “pothole cooling” bias in earlier versions. Reduced aerosol-related forcing contributes to more realistic radiative forcing and better alignment with the observational record. Ocean heat content (OHC) and sea ice trends are also improved as a result.

54 ENVIRONMENTAL SCIENCES↗

Oil price states and drivers: An analysis of the second-month spot-futures price differential

Oil remains a dominant component of global energy use, and its price, characterized by frequent changes and an ever-present potential for large swings, continues to be a focus of industry participants, policymakers and analysts attention. Here, this study examines the behavior of future spot oil prices using a continuous-time hidden Markov model (HMM) and daily price data spanning years 2007 to 2024. We identify six states in the second-month WTI spot-futures price differential and assess the roles of eleven futures price, quantity, financial market, and geopolitical/volatility variables in each state. The model yields several insights into the workings of the oil market and the relative roles of these drivers. We find support for several theoretical and empirical findings in the oil market literature, including the role of inventory, volatility/risk, and market responses to contango/backwardation in futures markets. A novel finding is that “normal contango” conditions represent a significant portion of next-day states in our in-sample data. Under the most volatile normal contango state, many of the oil market drivers differ markedly in coefficient signs and magnitudes from those in other states. The resulting model also performed well out-of-sample and would, in addition to understanding the impact of market drivers, be useful for short-term forecasting. Overall, the findings highlight the highly non-linear, regime-dependent interactions of the oil price and its drivers, emphasizing the importance of detailed information to market stakeholders.

Oladosu, Gbadebo A. [Oak Ridge National Laboratory↗

Advances in 3D transient plasma dynamics and control through MHD and hybrid fluid-kinetic simulations with JOREK

Transient phenomena and their control are of high relevance in magnetic confinement fusion plasmas to guarantee a stable and safe plasma operation. Interpretative simulations can maximize the insights gained from experiments on present machines and predictive simulations can help in the preparation of design, mitigation techniques and operational scenarios for future devices. In this article, we provide an overview of recent advances and novel scientific results obtained with the 3D non-linear hybrid fluid-kinetic code JOREK, covering physics of plasma transients from the core to the scrape-off layer (SOL) both for tokamak and stellarator devices. Substantial progress was made in the physics understanding, model validation with experiments and experiment interpretation, thus, giving confidence for predictions to devices like DTT, ITER and DEMO. The topics addressed comprise a wide range: the edge physics of new operation scenarios and edge localized mode suppression; major disruptions with a focus on runaway electrons and vertical displacement events as well as disruption mitigation by shattered pellet injection; the physics mechanisms and operational limits of the flux pumping regime for sawtooth control; MHD limits of stellarators and work towards incorporating advanced edge/SOL/exhaust dynamics; continuing improvements of the code for more efficient hybrid simulations on conventional and accelerated high performance computing architectures.

disruptions↗

Large Load Impacts to Distribution System Hosting Capacity

This work examined the impact of large loads on utility distribution system models using the Sandia-developed open-source software DREAMS. It was shown that hosting capacity varies with location and changes after any asset is added to, or removed from, a system. Despite the tested models having similar rated voltages and other characteristics, their thermal and voltage constrained hosting capacity varied over 2 MW. The addition of a 3-phase balanced constant power large load with power factor of 1.0 exhibited non-linear reductions to all voltage constrained hosting capacities. The reductions to thermal constrained hosting capacity from a load with similar characteristics was more linear, related to the size of the added load, and did not impact all model buses. Co-located capacitors were shown to accommodate demand that was beyond the baseline voltage constrained hosting capacity limits, however, the costs and benefits from this approach were found to not be 1:1 and required additional available thermal capacity.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The effect of relative humidity and temperature on the response of stomatal conductance to vapor pressure deficit in tropical trees

Understanding how leaf gas exchange responds to changes in vapor pressure deficit (VPD) is key to predicting tropical forest resilience to climate change. Stomata regulate leaf water and CO2 diffusion, and respond to changes in temperature and relative humidity (RH), two drivers of VPD. At high temperatures, the cuticular pathway may also become significant and participate in the overall leaf conductance. Here, we measured gas exchange under light and dark conditions to investigate the stomatal and cuticular responses to temperature and RH on detached branches in five tropical tree species. Leaf conductance in the dark, when stomata are essentially closed, was not markedly impacted by temperature and RH, suggesting a minimal response of the cuticular pathway to these conditions. We compared six steady-state conductance models incorporating different effects of photosynthesis and evaporative demand on stomatal control. All models performed well (residual standard deviation, σ, < 0.025 mol m-2 s-1), but the best-fitting model (σ = 0.017 mol m-2 s-1) used a nonlinear relationship between photosynthesis and stomatal conductance and incorporated RH rather than vapor pressure difference. All models overestimated the steady-state conductance at high RH. Furthermore, leaf conductance immediately increased after a decrease in RH (wrong-way response), but not after an increase in leaf temperature. This suggests that the mechanisms underlying stomatal response to VPD need further investigation. The non-linear coupling between photosynthetic rate and stomatal conductance indicates a sharper physiological response than previously acknowledged.

Lamour, Julien↗

Evolution of the Antarctic Ice Sheet from 2000–2300 and beyond: model sensitivity and uncertainty analysis using MPAS-Albany Land Ice

We present a description of the Antarctic Ice Sheet model configuration submitted to the ISMIP6-Antarctica-2300 experiment using the MPAS-Albany Land Ice model, along with three new sets of simulations: (1) a set of extended simulations to 2500 for three forced experiments and to 2775 for the control experiment; (2) a sensitivity analysis of our model configuration to parameters controlling basal sliding and sub-shelf melt, and to model structural choices including the choice of the energy and stress balances; and (3) a 72-member ensemble run on graphics processing units (GPUs) and analysis of variance to determine the primary sources of uncertainty in our ice-sheet model projections. Our extended simulations predict rapid retreat beginning after 2300 for SSP1-2.6 forcing and after 2500 for present-day (control) forcing, primarily in the Amundsen Sea Embayment. We find that varying the sub-shelf melt parameter between the 5th to 95th percentile values for a mean-Antarctic calibration target results in an up to ∼ ± 40 % change in sea-level contribution relative to our baseline simulations that used the median value. Using a linear basal sliding law reduces sea-level contribution by 51 %–73 % relative to our baseline nonlinear sliding law with an exponent of 1/5. When using basal sliding law exponents of 1/3 and 1/10, the overall difference from our baseline simulations at 2300 is on the order of 10 %. The Amundsen Sea Embayment region displays a strongly non-linear dependence of mass loss on the sliding law exponent, with no discernible relationship between the sliding law exponent and the mass loss by 2300, while the sectors feeding the Ross and Filchner-Ronne ice shelves exhibit more mass loss with a more-plastic sliding law. Our model fidelity sensitivity experiments reveal a 9 %–31 % increase in sea-level contribution when using a depth-integrated stress balance approximation relative to our three-dimensional solver, while using a fixed-in-time temperature field increases sea-level contribution by 14 %–88 % relative to two thermomechanically coupled configurations. Our 72-member ensemble and analysis of variance show that the uncertainty in long-term projections is dominated by the choice of Earth system model forcing and the presence or absence of hydrofracture forcing, rather than uncertainty in sliding and sub-shelf melt parameters.

58 GEOSCIENCES↗

Robust optimization of flexible diafiltration systems for critical mineral separations

This paper provides major contributions in expanding the literature for membrane process design with critical mineral recovery applications and showcasing the importance of robust design techniques for reducing risks of underperformance in such systems. Here, a membrane process flowsheet featuring PrOMMiS membrane models for recovering lithium/cobalt from spent batteries is showcased, uncertainty in membrane sieving and localized fouling are considered, and robust designs are obtained using the PyROS toolset. This paper is intended for a general audience of researchers working in critical minerals, membranes, and optimization related areas.

36 MATERIALS SCIENCE↗

Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton–nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small-x gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky–Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small-x gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton–proton and proton–gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Joint Optimization of Multimodal Transit Frequency and Shared Autonomous Vehicle Fleet Size with Hybrid Metaheuristic and Nonlinear Programming

Shared autonomous vehicles (SAVs) bring competition to traditional transit services but redesigning multimodal transit network can utilize SAVs as feeders to enhance service efficiency and coverage. This paper presents an optimization framework for the joint multimodal transit frequency and SAV fleet size problem, a variant of the transit network frequency setting problem. The objective is to maximize total transit ridership (including SAV-fed trips and subtracting boarding rejections) across multiple time periods under budget constraints, considering endogenous mode choice (transit, point-to-point SAVs, driving) and route selection, while allowing for strategic route removal by setting frequencies to zero. Due to the problem’s non-linear, non-convex nature and the computational challenges of large-scale networks, we develop a hybrid solution approach that combines a metaheuristic approach (particle swarm optimization) with nonlinear programming for local solution refinement. To ensure computational tractability, the framework integrates analytical approximation models for SAV waiting times based on fleet utilization, multimodal network assignment for route choice, and multinomial logit mode choice behavior, bypassing the need for computationally intensive simulations within the main optimization loop. Applied to the Chicago metropolitan area’s multimodal network, our method illustrates a 33.3% increase in transit ridership through optimized transit route frequencies and SAV integration, particularly enhancing off-peak service accessibility and strategically reallocating resources.

Ng, Max↗

Dark Energy Survey Year 3 results: optimized $w$CDM simulation-based inference with weak lensing map-level hybrid statistics

We present cosmological constraints from the Dark Energy Survey Year 3 (DES Y3) weak lensing data using hierarchical hybrid statistics within a Bayesian simulation-based inference framework that is based on the Gower Street simulations. To maximize the precision of the inference, we have developed a new, information-theory based, data compression of the weak lensing maps to just seven highly informative summary statistics. The hybrid scheme exploits the high information content of the power spectrum, compressing both the power spectrum and neural-based summaries that are designed to extract further information. Our simulation-based approach enables principled forward modelling of all major sources of systematic uncertainty and survey properties into realistic mock observations, including the survey mask, photometric redshift uncertainties, intrinsic galaxy alignments, multiplicative shear calibration bias, source galaxy clustering, non-Gaussian shape noise, and non-linear structure formation. The summary statistics are then used in a Bayesian simulation-based inference pipeline. The inference is validated through coverage tests and checks for robustness against baryonic feedback. Assuming a $w$CDM cosmology, our analysis yields $S_8 = 0.808 \pm 0.017$, $Ω_{\rm m} = 0.325 \pm 0.024$, and $w < -0.766$ (marginalized posterior 68 per cent credible intervals). This rigorous combination of information theory, physics- and neural network-based extreme data compression, and principled Bayesian analysis improves the figure of merit for $(Ω_{\rm m}, S_8, w)$ by 60 per cent over the previous state-of-the-art, and by almost a factor of 3 over two-point analyses of the same data. They are the most precise joint constraints on $(Ω_{\rm m}, S_8, w)$ from weak gravitational lensing data alone of any survey to date. We intend to apply this analysis to the more recent DES Y6 data.

Williamson, J. [University Coll. London]↗

Gravitational Waves as a Source of Large-Scale White Noise: New Constraints

A stochastic gravitational wave (GW) background sources a shear in the flow of cosmic fluid which, through non-linear mode coupling, generates large-scale white noise (LSWN) in the kurvature density field. Building on the LSWN framework of our previous work, we derive the amplitude of this GW-induced LSWN and translate the observational non-detection of LSWN into bounds on the production redshift and density of gravity waves. In particular, a minimal constraint on gravity waves with $z=0$ density parameter $Ω_\mathrm{GW0}^*$ in frequency band $f_*$ generated at redshift $z_*$ must satisfy ${z_*}^2\,Ω_\mathrm{GW0}^*<5\times10^7\,(f_*/\mathrm{nHz})^{3/2}$. This, for example, precludes the gravity waves recently detected by pulsar timing arrays \cite{NANOGrav:2023hvm} from being present before $z_*\sim10^8$, long after the quark hadron phase transition. While orders of magnitude stronger than other constraints on gravity waves, this is a minimal LSWN constraint as realistic modeling of early universe gravity wave production, including the granularity of the gravity-wave sources and the LSWN produced by the associated acoustic waves would probably tighten this constraint by orders of magnitude.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗