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NASA NTRS2022

Variability of the Reconnection Guide Field in Solar Flares

Solar ﬂares may be the best-known examples of the explosive conversion of magnetic energy into bulk motion, plasma heating, and particle acceleration via magnetic re-connection. The energy source for all ﬂares is the highly sheared magnetic ﬁeld of a ﬁlament channel above a polarity inversion line (PIL). During the ﬂare, this shear ﬁeld becomes the so-called reconnection guide ﬁeld (i.e., the non-reconnecting component), which has been shown to play a major role in determining key properties of the recon-nection including the eﬃciency of particle acceleration. We present new high-resolution, three-dimensional, magnetohydrodynamics simulations that reveal the detailed evolution of the magnetic shear/guide ﬁeld throughout an eruptive ﬂare. The magnetic shear evolves in three distinct phases: shear ﬁrst builds up in a narrow region about the PIL, then expands outward to form a thin vertical current sheet, and ﬁnally is transferred by ﬂare reconnection into an arcade of sheared ﬂare loops and an erupting ﬂux rope. We demonstrate how the guide ﬁeld may be inferred from observations of the sheared ﬂare loops. Our results indicate that initially the guide ﬁeld is larger by about a factor of 5 than the reconnecting component, but it weakens by more than an order of magnitude over the course of the ﬂare. Instantaneously, the guide ﬁeld also varies spatially over a similar range along the three-dimensional current sheet. We discuss the implications of the remarkable variability of the guide ﬁeld for the timing and localization of eﬃcient particle acceleration in ﬂares.

Solar magnetic reconnection↗

DOE OSTI2026

Process-driven roadmap for depositing super duplex stainless steel via wire Arc additive manufacturing

Here, this study systematically investigates the effects of shielding gas, bead spacing, weld mode, and travel speed on the phase balance, porosity, and hardness of wire arc additively manufactured (WAAM) super duplex stainless steel (ER2594). Robotic WAAM was employed to fabricate multilayer walls under systematically varied process conditions, followed by phase transformation simulations, X-ray computed tomography (XCT), electron backscatter diffraction (EBSD), and microhardness evaluation. Thermodynamic simulations predicted rapid cooling of AM process can suppress the potential formation of deleterious precipitates which was later validated via cross-sectional microstructure analyses of printed samples. XCT revealed porosity levels below 0.2% for all deposits, with reduced travel speed significantly lowering defect volume. Microstructural analyses revealed the evolution of various austenite precipitates, including grain boundary austenite (GBA), Widmanstätten austenite (WA), and intergranular austenite (IGA), sequentially upon cooling of the ferrite phase. Among all process parameters, weld transfer mode exhibited the strongest influence on phase balance; pulsed mode promoted higher ferrite retention (~ 36%) compared to RapidX mode. No consistent relationship between stabilized phase fraction and captured microhardness was observed. This work provides critical insights for optimizing WAAM parameters to control phase balance and mechanical performance, which is essential for producing high-integrity super duplex stainless-steel components for nuclear and marine applications.

Grain orientation↗

DOE OSTI2022

Layered Nano-Mosaic of Niobium Disulfide Heterostructures by Direct Sulfidation of Niobium Carbide MXenes for Hydrogen Evolution

MXene-transition metal dichalcogenide (TMD) heterostructures are synthesized through a one-step heat treatment of Nb 2 C and Nb 4 C 3 . These MXenes are used without delamination or any pre-treatment. Heat treatments accomplish the sacrificial transformation of these MXenes into TMD (NbS 2 ) at 700 and 900 °C under H 2 S. This work investigates, for the first time, the role of starting MXene phase in the derivative morphology. It is shown that while treatment of Nb 2 C at 700 °C leads to the formation of pillar-like structures on the parent MXene, Nb 4 C 3 produces nano-mosaic layered NbS 2 . At 900 °C, both MXene phases, of the same transition metal, fully convert into nanomosaic layered NbS 2 preserving the parent MXene’s layered morphology. When tested as electrodes for hydrogen evolution reaction, Nb 4 C 3 -derived hybrids show better performance than Nb 2 C derivatives. The Nb 4 C 3 -derived heterostructure exhibits a low overpotential of 198 mV at 10 mA cm -2 and a Tafel slope of 122 mV dec -1 , with good cycling stability in an acidic electrolyte

36 MATERIALS SCIENCE↗

DOE OSTI2022

Simulating microgalvanic corrosion in alloys using the PRISMS phase-field framework

In this prospective paper, we first review the existing simulation tools to simulate microgalvanic corrosion during free immersion. Then, we describe a recently developed application that employs PRISMS-PF, an open-source, high-performance phase-field modeling framework. The model employed in the application accounts for the electrochemical reaction at the metal/electrolyte interface and ionic migration in the electrolyte to determine the evolution of the corrosion front. We present the implementation details for the application and discuss its features such as super-linear parallel scaling performance for a sufficiently large system. Finally, we demonstrate the capability of the application by simulating corrosion of the matrix phase of an alloy near a secondary phase particle in two and three dimensions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Electrochemical Control of the Ultrafast Lattice Response of a Layered Semimetal

The unique layer-stacking in two-dimensional (2D) van der Waals materials facilitates the formation of nearly degenerate phases of matter and opens novel routes for the design of low-power, reconfigurable functional materials. Electrochemical ion intercalation between stacked layers offers a promising approach to stabilize bulk metastable phases and to explore the effects of extreme carrier doping and strain. However, in situ characterization methods to study the structural evolution and dynamical functional properties of these intercalated materials remains limited. Here a novel experimental platform is presented capable of simultaneously performing electrochemical lithium-ion intercalation and multimodal ultrafast characterization of the lattice using both electron diffraction and nonlinear optical techniques. Using the layered semimetal WTe 2 as a model system, the interlayer shear phonon mode that modulates stacking between 2Dlayers is probed, showing that small amounts of lithiation enhance the amplitude and lifetime of the phonon, contrary to expectations. This results from the dynamically fluctuating and anharmonic structure between nearly degenerate phases at room temperature, which can be stabilized by electronic carriers accompanying the inserted lithium ions. At high lithiation, the T d ’ structure emerges and quenches the phonon response. This work defines new approaches for using electrochemistry to engineer the dynamic structure of 2D materials.

36 MATERIALS SCIENCE↗

NASA NTRS2012

Automation and Process Improvement Enables a Small Team to Operate a Low Thrust Mission in Orbit Around the Asteroid Vesta

NASA's Dawn mission to the asteroid Vesta and dwarf planet Ceres launched September 27, 2007 and arrived at Vesta in July of 2011. This mission uses ion propulsion to achieve the necessary delta-V to reach and maneuver at Vesta and Ceres. This paper will show how the evolution of ground system automation and process improvement allowed a relatively small engineering team to transition from cruise operations to asteroid operations while maintaining robust processes. The cruise to Vesta phase lasted almost 4 years and consisted of activities that were built with software tools, but each tool was open loop and required engineers to review the output to ensure consistency. Additionally, this same time period was characterized by the evolution from manually retrieved and reviewed data products to automatically generated data products and data value checking. Furthermore, the team originally took about three to four weeks to design and build about four weeks of spacecraft activities, with spacecraft contacts only once a week. Operations around the asteroid Vesta increased the tempo dramatically by transitioning from one contact a week to three or four contacts a week, to fourteen contacts a week (every 12 hours). This was accompanied by a similar increase in activity complexity as well as very fast turn around activity design and build cycles. The design process became more automated and the tools became closed loop, allowing the team to build more activities without sacrificing rigor. Additionally, these activities were dependent on the results of flight system performance, so more automation was added to analyze the flight data and provide results in a timely fashion to feed the design cycle. All of this automation and process improvement enabled up the engineers to focus on other aspects of spacecraft operations, including spacecraft health monitoring and anomaly resolution.

ground system automation↗

DOE OSTI2024

One-Step Synthesis and Operando Electrochemical Impedance Spectroscopic Characterization of Heterostructured MoP–Mo 2 N Electrocatalysts for Stable Hydrogen Evolution Reaction

Here this study presents a novel synthesis of self-standing MoP and Mo 2 N heterostructured electrocatalysts with enhanced stability and catalytic performance. Facilitated by the controlled phase and interfacial microstructure, the seamless structures of these catalysts minimize internal resistivity and prevent local corrosion, contributing to increased stability. The chemical synthesis proceeds with etching step to activate the surface, followed by phosphor-nitriding in a chemical vapor deposition chamber to produce MoP-Mo 2 N@Mo heterostructured electrocatalysts. X-ray diffraction analyses confirm the presence of MoP, Mo 2 N, and Mo phases in the electrocatalyst. Morphology studies using scanning electron microscopy characterizes the hierarchical growth of structures, indicating successful formation of the heterostructure. X-ray photoelectron spectroscopy (XPS) analyses of the as-synthesized and post-catalytic activity samples reveal the chemical shift in terms of binding energy (BE) of Mo 3d XPS peak, especially after catalytic activity. The XPS BE shifts attributed to changes in oxidation state, electron transfer, and surface reconstruction during catalysis. Electrochemical evaluation of the catalysts demonstrates the superior performance of the MoP-Mo 2 N@Mo heterostructured catalyst in hydrogen evolution reactions (HER), with lower overpotentials and enhanced Tafel slopes. Stability tests reveal changes in double layer capacitance over time, suggesting surface reconstruction and increased active surface area during catalysis. Operando electrochemical impedance spectroscopy (EIS) further elucidates the dynamic changes in resistance and charge transfer during HER. Overall, comprehensive understanding of the synthesis, characterization, and electrochemical behavior of the developed MoP-Mo 2 N@Mo heterostructured electrocatalyst as presented in this paper highlights their potential utilization in sustainable energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Design of a Subscale, Inert Gas Test for Plume-Surface Interactions in a Reduced Pressure Environment

Rocket plume-surface interaction is a multi-phase, complex discipline characterized by plume flow physics, erosion physics, and ejecta dynamics. To provide critical data for the validation of predictive modeling capabilities, an inert-gas, subscale ground test has been designed, with one test phase focused on cratering and ejecta and another test phase focused on plume structure and behavior. Using a supersonic, heated N2 jet impinging onto six different mechanical regolith simulants, visual data on the temporal evolution of cratering and ejecta are collected in a vacuum chamber at ambient pressures ranging from 600 Pa down to approximately 7 Pa. Using the same N2 jet impinging onto an instrumented plate, NO planar laser-induced fluorescence data are obtained at lower ambient pressures for the validation of both continuum and rarefied gas-phase physics. This paper discusses the design of this test and data products, with emphasis on the cratering and ejecta experiments, along with the physical scaling, challenges, and relevance of these data to the maturation of the plume-surface interaction discipline.

Ashley M Korzun↗

DOE OSTI2024

Oxygen redox activities governing high-voltage charging reversibility of Ni-rich layered cathodes

A schematic illustration indicative of the improved structural reversibility through stabilizing oxidized oxygen by Al doping. The chemical reactions and phase transitions at high voltages are generally considered to determine the electrochemical properties of high-voltage layered cathodes such as Ni-rich rhombohedral oxides. Even if significantly higher SOCs (states-of-charge) are utilized above the capability of transition metal redox (primarily Ni and Co), the effect of oxygen redox on Ni-rich rhombohedral oxides still looks mysterious thereby necessitating research that can clarify the relationship between redox reactions and phase transitions. Here, we performed a comprehensive and comparative study of the cationic and anionic redox reactions, as well as the structural evolution of a series of commercial Ni-rich layered oxides with and without Al doping. We combined the results from X-ray spectroscopy, operando electrochemical mass spectrometry, and neutron diffraction with electrochemical properties and thereby revealed the different oxygen redox activities associated with structural and electrochemical degradations. We reveal that Al doping suppresses the irreversible oxygen release but enhances the lattice oxygen oxidization. With this modulated oxygen redox activity, the Ni-rich layered oxides’ notorious H2–H3 structural phase transition becomes highly reversible. Our findings disentangle the different oxygen redox activities during high-voltage cycling and clarify the role of dopants in the Ni-rich layered oxides in terms of structural and electrochemical stability, shedding light on the future direction of optimizing layered cathode materials for safer high energy-density secondary batteries.

Lee, Gi-Hyeok↗

NASA NTRS2014

On Helium-Dominated Stellar Evolution: The Mysterious Role of the O(He)-Type Stars

Context. About a quarter of all post-asymptotic giant branch (AGB) stars are hydrogen-deficient. Stellar evolutionary models explain the carbon-dominated H-deficient stars by a (very) late thermal pulse scenario where the hydrogen-rich envelope is mixed with the helium-rich intershell layer. Depending on the particular time at which the final flash occurs, the entire hydrogen envelope may be burned. In contrast, helium-dominated post-AGB stars and their evolution are not yet understood. Aims. A small group of very hot, helium-dominated stars is formed by O(He)-type stars. A precise analysis of their photospheric abundances will establish constraints to their evolution. Methods. We performed a detailed spectral analysis of ultraviolet and optical spectra of four O(He) stars by means of state-of-the-art non-LTE model-atmosphere techniques. Results. We determined effective temperatures, surface gravities, and the abundances of H, He, C, N, O, F, Ne, Si, P, S, Ar, and Fe. By deriving upper limits for the mass-loss rates of the O(He) stars, we found that they do not exhibit enhanced mass-loss. The comparison with evolutionary models shows that the status of the O(He) stars remains uncertain. Their abundances match predictions of a double helium white dwarf (WD) merger scenario, suggesting that they might be the progeny of the compact and of the luminous helium-rich sdO-type stars. The existence of planetary nebulae that do not show helium enrichment around every other O(He) star precludes a merger origin for these stars. These stars must have formed in a different way, for instance via enhanced mass-loss during their post-AGB evolution or a merger within a common-envelope (CE) of a CO-WD and a red giant or AGB star. Conclusions. A helium-dominated stellar evolutionary sequence exists that may be fed by different types of mergers or CE scenarios. It appears likely that all these pass through the O(He) phase just before they become WDs.

evolution↗

DOE OSTI2025

Bidirectional Ultrafast Control of Charge Density Waves via Phase Competition

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Here, leveraging time-resolved x-ray diffraction, we demonstrate ultrafast control of a CDW in EuTe 4 upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photoexcitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in EuTe 4 , but also highlight the versatility of optical control over order parameters enabled by phase competition.

charge density waves↗

NASA NTRSDate not supplied

Three-dimensional in Situ Observations of Polycrystalline Microstructure Evolution During Directional Solidification of Transparent Alloys Aboard the ISS and Quantitative Comparison with Numerical Modeling

Cellular/dendritic microstructures formed during solidification have a crucial influence on the mechanical properties of a wide range of structural alloys. By minimizing the amount of gravity-induced convection in the liquid, directional solidification experiments using transparent organic alloys conducted in the DECLIC-DSI onboard the International Space Station have provided unique 3D in situ observations of the spatiotemporal evolution of the solid-liquid interface during the formation of cellular and dendritic microstructures under purely diffusive growth conditions in polycrystalline samples containing several grains with a small misorientation with respect to the temperature gradient. Those observations have made it possible to perform benchmark quantitative comparisons with the predictions of state-of-the-art phase-field simulations of microstructure formation in 3D on experimentally relevant length and time scales. This talk will report quantitative comparisons between microgravity experiments and phase-field simulations in succinonitrile-camphor alloys of two different compositions that shed new light on the role of subgrain boundaries in the spatiotemporal evolution of the primary cellular spacing and the selection of dendritic array structures.

Kaihua Ji↗

NASA NTRS1995

Cooling of solar flares plasmas. 1: Theoretical considerations

Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phase where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an 'evaporation' of chromospheric material, the cooling time scales L(exp 5/6)/p(exp 1/6), where the coronal phase (defined as the time maximum temperature). When the conductive cooling is static, the cooling time scales as L(exp 3/4)n(exp 1/4). In deriving these results, use was made of an important scaling law (T proportional to n(exp 2)) during the radiative cooling phase that was forst noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, & Vaiana (1978). for different radiative loss functions, other scaling result, with T and n scaling almost linearly when the radiative loss falls off as T(exp -2). It is shown that these scaling laws are part of a class of analytic solutions developed by Antiocos (1980).

Cargill, Peter J.↗

DOE OSTI2026

Electronic coherence evolution at the nearly commensurate-incommensurate CDW boundary of 1⁢T−TaS 2

Transition-metal dichalcogenides host a variety of charge-density-wave phases that couple lattice, charge, and correlation effects. In 1⁢𝑇−TaS 2 , the commensurate and nearly commensurate states are well characterized, yet the transition near 350 K into the incommensurate phase has lacked direct momentum-resolved insight. In this work, we use temperature-dependent angle-resolved photoemission spectroscopy to track the electronic structure across this transition. We observe a suppression of quasiparticle spectral weight at the Brillouin-zone center, coincident with the transport anomaly, but without clear evidence of a full band-gap opening. The transition appears to involve momentum-dependent redistribution of spectral weight, consistent with a loss of coherence that reshapes the Fermi surface while leaving conduction dispersions largely intact. These results suggest that the nearly commensurate–incommensurate transition may not align with a conventional metal-insulator transition picture, but rather as an electronic reconstruction driven by loss of coherence. Our work provides new microscopic insight into the resistivity anomaly near room temperature and may guide design principles for collective electronic switching in transition-metal dichalcogenides.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Aerosol Optical Tweezers Elucidate the Chemistry, Acidity, Phase Separations, and Morphology of Atmospheric Microdroplets

Aerosol particles represent unique chemical environments because of their high surface area-to-volume ratio that promotes the effects of interfacial chemistry in confined environments. Properties such as viscosity, diffusivity, water content, pH, and morphology—following liquid–liquid phase separation—can strongly alter how a particle interacts with condensable vapors and reactive trace gases, thus modifying its continual evolution and environmental effects. Our understanding of this chemical evolution of atmospheric particulate matter and its environmental impacts is largely limited by our ability to directly observe how these critical particle properties respond to the addition or reactive uptake of new chemical components. Aerosol optical tweezers (AOT) stably trap particles in focused laser beams, providing positional control and the retrieval of many of these critical properties required to understand and predict the chemistry of aerosolized microdroplets. The analytical power of the AOT stems from the retrieval of the cavity-enhanced Raman spectrum induced by the trapping laser. Analysis of the whispering gallery modes (WGMs) that resonate as a standing wave around the droplet’s interface, provide high accuracy measurements of the droplet’s size, refractive index (and thus a measurement of composition), and can distinguish between core–shell, partially engulfed, and homogeneous morphologies. In this study, we have advanced the ability to determine the properties of the core and shell phases in biphasic droplets, including obtaining high-accuracy pH measurements. These capabilities were applied to perform AOT physical chemistry experiments on authentic secondary organic aerosol (SOA) produced directly in the AOT chamber by ozonolysis of terpene vapors. The propensity of the SOA to phase separate as a shell from a wide range of nonpolar to polar core phases was observed, along with the discovery of a stable emulsified state of SOA particles in an aqueous salt droplet. Micron-thick SOA shells did not impede the gain or loss of water or squalane from the core to the surrounding air, indicating no significant diffusional limitations to condensational growth or partitioning even under dry conditions. These experiments formed the foundation of a new framework that predicts how the phase-separated morphology of complex aerosols containing organic carbon evolves during continual atmospheric oxidation processes. Increases in oxidation state will quickly drive conversion from a partially engulfed to core–shell morphology that has dramatically different chemical reactivity since the core phase is completely concealed by the shell. The recent advances in the experimental capabilities of the AOT technique such as presented here enable novel experimental methodologies that provide insights into the chemistry and multidimensional properties of aerosol microdroplets, and how these coevolve and respond to continual chemical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

The impact of mineral reactive surface area variation on simulated mineral reactions and reaction rates

Reactive transport modeling is an essential tool to simulate complex geochemical reactions in porous media that can impact formation properties including porosity and permeability. However, simulating these reactions is challenging due to uncertainties in model parameters, particularly mineral surface areas. Imaging has emerged as a powerful means of estimating model parameters including porosity and mineral abundance, accessibility and accessible surface area. However, these parameters, particularly mineral accessible surface area, vary with image resolution. This work aims to enhance understanding of the impact of image resolution and other means of estimating mineral reactive surface area on simulated mineral reactions and reaction rates. Mineral surface areas calculated from images with resolutions of 0.34 μm and 5.71 μm were used to simulate mineral reactions in the context of geologic CO 2 sequestration in the Paluxy formation at the continuum scale. Additional simulations were carried out using BET surface areas collected from the literature and geometric surface areas. Simulations were run for 7300 days and mineral volume fractions and effluent ion concentrations tracked and compared. Variations in mineral surface areas measured from images are within 1 order of magnitude and yield similar simulation results, indicating the impact of image resolution on simulated reactions and reaction rates is minimum for the resolutions and sample considered. In comparison, surface areas obtained from BET and geometric approaches are 1–4 orders of magnitude higher than image-obtained surface areas and result in greater simulated reaction rates and extents. Minerals with high reaction rates (calcite and siderite) are most impacted by surface area values at short times where simulated mineral volume fractions at longer times agree relatively well, even for simulations with several orders of magnitude variation in surface area. Phases with lower reaction rates, such as K-feldspar and muscovite, are predominantly impacted over longer times where variations in surface areas impact reaction extents and porosity evolution. Overall, variations in surface areas due to image resolution are small and result in little variation in simulated reactions and reaction rates while there are significant variations in simulation results when other surface area estimates are used. These variations, however, depend on the reactivity of the mineral phase where surface areas of fast-reacting phases largely impact simulations at short (hours to days) timescales and surface areas of slower-reactive phases impact longer term simulations (years).

58 GEOSCIENCES↗

DOE OSTI2023

A Limit to Accelerated Free-Sintering: Nano-Phase Separation Interferes With Organic Debinding

Nano-phase separating Ni–12 at. pct Ag powders are processed via high-energy ball milling and brought into a supersaturated state with a reduction of the grain size to the nanocrystalline scale, a combination that is designed to encourage rapid densification by phase separation upon heating. This unstable powder is then characterized by dilatometry, in-situ x-ray diffraction, thermogravimetry and microstructure analysis for sintering cycles up to 940 °C. However, these powder compacts exhibit excessive pore evolution and significant macroscopic swelling caused by removal of the organic process additives. This competition of organic removal with densification is known in nanocrystalline metals, but the present study adds an additional dimension of phase separation, which shifts the dominant swelling mechanism as the formation of the second phase traps the volatilizing organics and hinders the debinding process. The creep swelling and overall loss in relative density is then dominated by the creep deformation of the second Ag phase. The interference between organic removal and low-temperature onset of consolidation represents a new challenge to efforts aimed at rapid free sintering and should guide the design of rapidly sintering alloys; specifically, the present work emphasizes the need to select alloys that have their sintering-accelerating phase separation temperature above the range where gases are evolved.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Reconstructing quintessence

We present an Effective Field Theory based reconstruction of quintessence models of dark energy directly from cosmological data. We show that current cosmological data possess enough constraining power to test several quintessence model properties for redshifts z ϵ [0, 1.5] with no assumptions about the behavior of the scalar field potential. We use measurements of the cosmic microwave background, supernovae distances, and the clustering and lensing of galaxies to constrain the evolution of the dark energy equation of state, Swampland Conjectures, the shape of the scalar field reconstructed potential, and the structure of its phase space. The standard cosmological model still remains favored by data and, within quintessence models, deviations from its expansion history are bounded to be below the 10% level at 95% confidence at any redshift below z = 1.5.

79 ASTRONOMY AND ASTROPHYSICS↗