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At least 325 records · Page 18

Get Non-Real: Randomized Sketching for High-Dimensional Non-Real Valued Data (Final Report)

In our final report for DE-C0022186, we describe the work we did on this grant towards the goals we proposed. Our first goal was characterizing fundamental limits for sketching of discrete high-dimensional matrices with low-dimensional structures. Our second main goal was designing algorithms for data reconstruction from sketches. We focus on approaches that are either specifically designed for non-real-valued data (binary, finite field) or that will translate more readily to that setting.

97 MATHEMATICS AND COMPUTING↗

Getting Electric Vehicle Ready in Indian Country

As electric vehicles (EV) become more common, Tribes can guide how charging infrastructure is planned, approved, and built on Tribal lands. Tribes can prepare for future infrastructure projects by updating codes, zoning, parking rules, and permitting process, as well as improving electrical infrastructure and broadband access.

33 ADVANCED PROPULSION SYSTEMS↗

Getting Warmer: IceCube Nears Freeze Out

IceCube has recently detected a diffuse population of high-energy neutrinos arising from the Milky Way. We use this high-significance detection to place new limits on dark matter (DM) annihilation to neutrinos with two complementary approaches. The first method uses the background-subtracted Galactic longitude distribution of shower events to place a conservative bound on the DM annihilation cross section that does not rely on any assumed Galactic cosmic ray emission model; the resulting limits on the velocity-averaged annihilation cross section improve upon existing bounds by factors of a few. The second method uses the template-dependent neutrino energy spectra from the Inner Galaxy, inferred under different Galactic cosmic ray emission models. This complementary approach shows that the inferred Galactic neutrino intensities are already sensitive to DM contributions near the thermal-relic benchmark for a range of TeV-scale DM masses, though this comparison is more model-dependent. Our results demonstrate that measurements of diffuse Galactic neutrino emission can be used as a powerful probe of DM annihilation into neutrinos. Future observations with IceCube-Gen2 and KM3NeT will substantially extend this sensitivity, potentially allowing a decisive test of the thermal freeze-out mechanism with Galactic neutrino observations.

Mukhopadhyay, Mainak [Fermilab; Chicago U., KICP; ↗

Regal Beloit Final Technical Report

The original project proposal submitted from NovaTorque Inc (NovaTorque) in 2016 was to improve the existing motor with 95% efficiency by reducing the losses by 21% to achieve 96%. A few months after the proposal was submitted, NovaTorque lost funding and went out of business. The assets of NovaTorque were then acquired by Regal Beloit Corporation (“Regal Beloit” or “Regal”). When the NovaTorque proposal was selected, the project was transferred to Regal Beloit. Once we had production samples from the new Regal production line, they were tested at the Regal Beloit test lab in Wausau, WI. The original NovaTorque motor had an efficiency of 95%, but when the technology was transferred to Regal Beloit, there were multiple manufacturing improvements made, even though the basic electromagnetic design did not change. The test results in Wausau showed that the motors made at the Regal Beloit plant had an efficiency of 96%. Since the goal of the project was to reduce the losses by 21%, a new efficiency target of 96.8% became the project objective. In the first budget period, motors were tested to get the baseline performance. We then used FEA modeling with ANSYS Maxwell to model the existing motor to get correlation between the FEA simulations and the actual test results. Once the model was validated, we evaluated some changes that could be made to the stator to reduce the losses and improve efficiency without changing the rotor or stator housing, keeping the modifications easy to implement. The changes were primarily in the area of making the stator axially shorter and adding Soft Magnetic Composite (SMC) tooth tips. In the second budget period, we proceeded to design and build the new stator that was identified above and identified additional improvements in the process that included a stator machining modification and the use of rectangular wire. When we actually built the motor, the choice of rectangular wire turned out to be a problem. The wire was made by squishing round wire to get the rectangular shape, which caused work hardening, making the wire too stiff to make the desired coils. We shifted to annealed square wire which was better, but we still could not maintain the proper coil envelope. The result was that we had reduced cross section area for stator laminations. We also had to have a radial offset resulting in a radial misalignment between the stator and rotor because of the oversized coils. After the motor was completed, it was shipped to Texas A&M University for testing. With the loss of flux from these issues, the measured motor efficiency was only 96.3%. The primary focus of this motor was to make sure our FEA simulation model predicted the measured losses and overall efficiency, this we moved on to the FEA simulation. The FEA simulations of the motor “as built” with misalignments had good correlation with the test results, so the next step was to use that model to optimize the design of the motor for a final build. This time we considered changes to the stator and rotor and also minor changes to the housing diameter. In the third budget period, we did the detailed design and construction of the final prototypes. The final prototypes had a slight increase in the stator diameter to fit in a standard Regal Beloit housing. We shortened the stator and use more layers of wire in the coils. We also increased the cone angle of the rotor and stator from the original 110 degrees to 130 degrees to get some additional efficiency and optimized the stator cross section. The predicted efficiency from the FEA simulations was 96.9%. When completed, the motors were tested. We were a little short of reaching our target efficiency goal of 96.8%. We were only able to get to 96.7% efficiency. While it may be possible with additional iterations in designs and future builds to gain that additional 0.1%, we believe that we are close to the best we can achieve from a practical viewpoint, and additional iterations would be more work than the potential gains would be worth. No other motor in this class can even reach the 96% that we started with.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Application of a Machine Learning Algorithm in Generating an Evapotranspiration Data Product From Coupled Thermal Infrared and Microwave Satellite Observations

Land surface evapotranspiration (ET) is one of the main energy sources for atmospheric dynamics and a critical component of the local, regional, and global water cycles. Consequently, accurate measurement or estimation of ET is one of the most active topics in hydro-climatology research. With massive and spatially distributed observational data sets of land surface properties and environmental conditions being collected from the ground, airborne or space-borne platforms daily over the past few decades, many research teams have started to use big data science to advance the ET estimation methods. The Geostationary satellite Evapotranspiration and Drought (GET-D) product system was developed at the National Oceanic and Atmospheric Administration (NOAA) in 2016 to generate daily ET and drought maps operationally. The primary inputs of the current GET-D system are the thermal infrared (TIR) observations from NOAA GOES satellite series. Because of the cloud contamination to the TIR observations, the spatial coverage of the daily GET-D ET product has been severely impacted. Based on the most recent advances, we have tested a machine learning algorithm to estimate all-weather land surface temperature (LST) from TIR and microwave (MW) combined satellite observations. With the regression tree machine learning approach, we can combine the high accuracy and high spatial resolution of GOES TIR data with the better spatial coverage of passive microwave observations and LST simulations from a land surface model (LSM). The regression tree model combines the three LST data sources for both clear and cloudy days, which enables the GET-D system to derive an all-weather ET product. This paper reports how the all-weather LST and ET are generated in the upgraded GET-D system and provides an evaluation of these LST and ET estimates with ground measurements. The results demonstrate that the regression tree machine learning method is feasible and effective for generating daily ET under all weather conditions with satisfactory accuracy from the big volume of satellite observations.

54 ENVIRONMENTAL SCIENCES↗

When There are Different Types of Smoke in the Sky It Changes How the Sun Light Goes Through the Sky

When the sky gets smoke in it, it can be more or less bright (white) than before. This is because the small smoke bits can change whether sun light gets through the sky to the ground, can change how much white sky water there is, and can change how the sky air moves around. If the smoke is blacker, it can make the sky warmer and if the smoke is whiter, it can make the sky (and the ground) cooler because the sun light doesn't get through. So we wanted to know whether the smoke is blacker or whiter over the big water far away from here, near where there are a lot of fires on the land.We went to the big water place and watched the sky, the air, the sky smoke, and the white sky water. We did this by flying in the sky with our computers. We watched the smoke in a lot of different ways: we can look at the smoke from near the water and see what sun light gets through the sky, or from above and see how the sun light comes back up to space, or go right in the smoke with our flying computer eyes. Then we looked at whether the different ways of seeing showed that the same smoke was different (blacker or whiter) or the same. A lot of time they said it was the same, at least in some ways, but sometimes the smoke looked different and it changed a lot in different places over the big water.We hope other people can put these answers into their computer studies, or into their computers that fly REALLY high, and then we can better understand how the sky gets warmer or cooler from smoke.

Pistone, Kristina↗

Advanced Transmission Technologies (ATTs) Supplier Cohort Workshops Cohort Summary [Slides]

This Summary slide deck summarizes the key outcomes of the Advanced Transmission Technologies (ATTs) supplier cohort, part of Idaho National Laboratory’s (INL) Technical Assistance for Digital Assurance (TADA) program. The program aimed to strengthen grid resilience through cybersecurity controls, supply-chain security, and Cyber-Informed Engineering (CIE) for advanced transmission technologies. The cohort brought together vendors representing the full range of Grid-Enhancing Technologies (GETs), including providers of Dynamic Line Ratings (DLR), Advanced Power Flow Control (APFC), Transmission Topology Optimization (TTO), and High-Performance Conductors (HPCs). Discussions focused on institutional, integration, and operational barriers limiting GET adoption; cybersecurity risks at EMS/SCADA, cloud, and network integration points; and supply-chain transparency issues such as semiconductor dependence and SBOM/HBOM expectations. Participants also addressed operator trust, human-in-the-loop requirements, and challenges with utility adoption, while exploring how CIE can support secure deployment of GETs. This deck represents a consolidated summary of challenges and risks identified by vendors, cross-cutting themes and technology-specific insights from three cohort workshops, and actionable mitigations to guide utilities, vendors, and the Department of Energy in advancing secure, trusted deployment of GETs.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Commuting again to work on-site? Lab’s first drivers faced their own challenges decades ago

After a long pause in commuting, more and more Lab staff are filling travel mugs, topping off their tanks, and heading up the hill for on-site work. As long as the Lab has existed, workers have snaked through tight mountain roads to get to their jobs. And, back in the early 1940s, drivers faced even more challenges. In the Lab’s earliest years, drivers likely worried about getting stuck in the mud, navigating intense switchbacks, or making sure important equipment, such as a disassembled power plant, didn’t fall off the back of the truck that was hauling it. Creative solutions could go a long way to get out of a jam. As many of us return onsite and get reacquainted with commuting, we look back at how transportation has changed since the Manhattan Project, the U.S. government’s top secret effort at Los Alamos to create the first atomic bombs to help end World War II. These stories and photos are part of the collections in the National Security Research Center, which is the Lab’s classified library and also houses unclassified artifacts from our past.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

NSI conference support

One of the many services NSI provides as an extension of customer/user support is to attend major scientific conferences. The conference effort provides NASA/OSSA scientists with many benefits: (1) scientist get to see NSI in action; they utilize the network to read email, and have recently begun to demonstrate their scientific research to their colleagues; (2) scientist get an opportunity to meet and interact with NSI Staff, which gives scientists a chance to get status on their requirements, ask about network status, get acquainted with our procedures, and learn about services; and (3) scientists are exposed to networking in a larger sense; particularly by knowing about other NASA groups who provide valuable scientific resources over the Internet.

Aaron, Susan↗

Willpower

I am struck by how often failure is blamed on a lack of discipline. You often hear losing coaches cite this as the reason for a big loss. I don't recall the last time I heard one say that his team lost a game because of his players' lack of skill. I think a breakdown in discipline is also one of the key reasons why program and project management teams fail to meet expectations. The first program I ever managed had a clear set of priorities. I understood the mandate, and so did everyone else on the team. We set an ambitious schedule and started to work fervently. Not too long into the program the customer wanted to know what performance he was going to get. I replied by categorizing the performance parameters into three bins: 1. Performance you will get. 2. Performance you may get. 3. Performance that there's no way you will get. Did that cause an uproar. The customer demanded everything in the second bin be moved to the first, and most everything in the third bin moved to the second. My immediate impulse was to agree, but I managed to overcome that. In my heart, I knew that we would never meet the already ambitious schedule if we had to deliver more performance. No was my answer. The program turned out to be a huge success, but the result would have been largely different had senior management or I failed to maintain discipline.

Little, Terry↗

Coming of Age

One of the great perks I looked forward to when I turned sixteen was being able to give up my paper route and get a regular job. Paper routes are okay, but for a young, timid kid who was afraid to ask for money, it often proved to be a non-profit operation. At age sixteen, I could get a social security number, which meant that I could go get myself a real job. In my early days of running a division and having my own employees, I m sad to say that I emulated that behavior more than once. At the time, I rationalized it. Now, I know how wrong I was, and how I may have ruined the morale of employees who only wanted to do good work. I recognize that almost every time I didn't get what I wanted from an employee, it was because they didn't understand what I really expected from them, they didn't understand how to provide it, or there were constraints placed on them that stopped them from doing a good job. I'am sure OJ. is long dead and gone. He wasn't young when I worked for him. I think he would have been amazed to learn what a long-lasting effect his behavior that week in 1963 had on me.

Morgan, Ray↗

An Apparatus for Monitoring the Health of Electrical Cables

As with most elements of infrastructure, electrical wiring is innocuous; usually hidden away and unnoticed until it fails. Failure of infrastructure, however, sometimes leads to serious health and safety hazards. Electrical wiring fails when the polymeric (usually rubber) insulation material that sheathes the conductor gets embrittled with age from exposure to pressure, temperature or radiation cycling or when the insulation gets removed by the chafing of wires against each other. Miles of such wiring can be found in typical aircraft, with significant lengths of the wiring immersed in aviation fuel - a recipe for an explosion if a spark were to occur. Diagnosing the health of wiring is thus an important aspect of monitoring the health of aging aircraft. Stress wave propagation through wiring affords a quick and non-invasive method for health monitoring. The extent to which a stress wave propagating through the cable core gets attenuated depends on the condition of the surrounding insulation. When the insulation is in good condition - supple and pliable, there is more damping or attenuation of the waveform. As the insulation gets embrittled and cracked, the attenuation is likely to reduce and the waveform of the propagating stress wave is likely to change. The monitoring of these changes provides a potential tool to evaluate wiring or cabling in service that is not accessible for visual inspection. This experiment has been designed for use in an introductory mechanical or materials engineering instrumentation lab. Initial setup (after procuring all the materials) should take the lab instructor about 4 hours. A single measurement can be initiated and saved to disk in less than 3 minutes, allowing for all the students in a typical lab section to take their own data rather than share a single set of data for the entire class.

Pai, Devdas M.↗

Dawn: Cooperation, not Control

On September 27, 2007, a Delta II rocket carrying the Dawn spacecraft lifted off from Kennedy Space Center. Part of NASAs Discovery program, the $370 million Dawn mission began its three-billion-mile voyage to the asteroid belt to study the asteroid Vesta and Ceres, a dwarf planet. The spacecraft is scheduled to reach Vesta in 2011. After spending nine months measuring the composition, shape, and topography of that body, it will travel a billion miles to carry out a similar analysis of Ceres in 2015. The Important Lessons: The demands of Dawn and other challenging missions have taught some important lessons for successful program and project management. These are the main ones: a) Program management, particularly of uncoupled and loosely coupled projects, should be more about enabling than controlling. You're working with motivated, high-performing teams and institutions with a track record of quality and success. Emphasize commander's intent over rudder control; let them know where you want to go and when you want to be there, then let them figure out how to get there. b) Open and honest discussion of issues is essential. People fill the void of the unknown with their worst fears. Get folks around the table and have open, honest, and frank dialogue. I've seldom seen this fail to get to the root of issues. c) You have to earn your seat at the table, proving that you are competent, trustworthy, and dedicated to the success of the mission. d) Know when to fold 'em. Your pride can get rolled up in making a milestone or launch date, but you have to make a judgment based on the realities of the situation and not wear down the team trying to meet an increasingly impossible deadline. e) The NASA governance model that gives a voice to the concerns of engineers and safety experts works-trust it and use it.

May, Todd↗

Johnson Space Center's Free Range Bicycle Program.- Fall 2015 Intern Report

NASA's Johnson Space Center is a big place, encompassing 1,620 acres and more than a hundred buildings. Furthermore, there are reportedly 15 thousand employees, all of which have somewhere to be. To facilitate the movement of all these people JSC has historically relied on human power. Pedaling their way towards deep space, bicycles have been the go to method. Currently there are about 200 Free Range Bicycles at JSC. Free Range Bicycles belong to nobody, except NASA, and are available for anybody to use. They are not to be locked or hidden (although frequently are) and the intention is that there will always be a bike to hop on to get where you're going (although it may not be the bike you rode in on). Although not without its own shortcomings, the Free Range Bicycle Program has continued to provide low cost, simple transportation for NASA's JSC. In addition to the approximately 200 Free Range Bicycles, various larger divisions (like engineering) will often buy a few dozen bikes for their team members to use or individuals will bring their own personal bike to either commute or use on site. When these bicycles fall into disrepair or are abandoned (from retirees etc) they become a problem at JSC. They are an eye sore, create a safety hazard and make it harder to find a working bike in a time of need. The Free Range Program hopes to address this first problem by "tagging out" abandoned or out of service bicycles. A bright orange "DO NOT OPERATE" tag is placed on the bike and given a serial number for tracking purposes. See picture to the right. If the bike has an active owner with intentions to repair the bike the bottom of the tag has instructions for how to claim the abandoned bicycle. After being tagged the owner of the bicycle has 30 days to claim the bicycle and either haul it off site or get it repaired (and labeled) in accordance with Johnson's Bicycle Policy. If the abandoned bicycle is not claimed within 30 days it becomes the property of the Government. The bicycle is then (in short) repaired, labeled, documented and converted to a free range bicycle. Bikes beyond repair are cannibalized of useable parts and then scrapped. That was nearly the first thing I did when arriving at work. After getting settled in and coordinating the purchase of 50 new bicycles (elaboration below); I started combing the Center. Bikes are hidden and tucked away in the oddest of places and it was my priority to root all of them out. I tagged 70 bikes on the center, setting a record. I tagged so many bikes I ran out tags and had to make more. Long ago it was discovered that the same harsh elements that wreak havoc on the bikes, destroy the tags before the 30 day timeframe. The tags are labeled with instructions on how to claim the bike and numbered, then these paper labels are laminated with packing tape. It sounds like a simple process but nothing fits right, everything has to be trimmed, put on straight and is generally a pain in the neck. So I made an assembly process and knocked out a few hundred to save having to do it again for a while. I walked the center and tagged bikes at every building hiding in nearly every nook and cranny. Thus, in conclusion, I've done many things here at JSC on my first term and had a blast doing it. I've learned a lot from my multi-faceted roles and continual challenges. In short I've done my best to get folks at JSC on bikes and keep folks at JSC on bikes and tended a flock of free range bicycles. Everything from turning the rusty bolts and oiling chains to coordinating a $20,000 deal on 50 new free range bicycles. I am proud of the bicycle shop I have built and am infinitely grateful to the people who lead, help, guide and support me. I have fixed a great number of bicycles and cleaned the center of unsightly and unsafe piles of bicycles. I am immensely thankful for this opportunity to learn and serve and appreciate the privilege of coming back for a second term. A second term, in which I will continue to develop this awesome program.

Lee-Stockton, Willem↗

Review of a Draft - Avoiding the Impossible: Re-focusing a Non-Feasible Mission 2-Hrs into a 3-Day Engineering Session

Concurrent engineering offers a great many benefits to engineers and mission designers throughout the world of aerospace. The only downside of concurrent engineering, and this is somewhat unavoidable, is that you don’t know the results of a design session until the end when it is completed. Usually, this is not a problem – you wouldn’t start building a spacecraft before the design is finished. However, within mass and cost constrained systems, you may end up with a final design that although technically sound – is not feasible due to mass or cost limits. Employing in-session mass and cost models with flexible inputs that refine their estimates and variance as more detailed information comes in throughout a design session allows major design changes to be made when the probability of breaching a mass or cost cap exceeds a threshold level. This enables mission designers to re-focus the study, and avoid spending 3-days with 15 engineers designing a non-feasible mission. By understanding key correlations and nested relationships within mass or cost, and specifically mass or cost allocations per mission element by mission type, it’s possible to get flexible-input, statistically based mass and cost estimates very early in the design process. Baseline models are seeded using mission characteristics and general parameters (outer planetary orbiter-probe mission, $500M cost cap for example) to provide a rough estimate of the expected mass or cost. As information gets solidified during the session, it gets added to the model and the estimates are updated. Continuing the orbiter-probe mission example, modeling probe heat shield cost as a percent of total probe cost, and probe cost as a percent of total flight system cost, and total flight system cost as a percent of total mission cost allows a design team to roll-up solidified information to estimate the probability of fitting within a mass or cost constraint early in a concurrent design session. When only the heat shield cost is known, the variance of the final estimate is higher, whereas when the full probe gets defined, naturally, the variance of the estimate decreases. A methodology, model, verification and demo implementation for cost limit breach are presented.

Hihn, Jairus M.↗

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential

Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Probing the Effects of NO x and SO x Impurities on Oxy-Fuel Combustion in Supercritical CO 2 : Shock Tube Experiments and Chemical Kinetic Modeling

The direct-fired supercritical carbon dioxide cycles are one of the most promising power generation methods in terms of their efficiency and environmental friendliness. Two important challenges in implementing these cycles are the high pressure (300 bar) and high CO 2 dilution (>80%) in the combustor. The design and development of supercritical oxy-combustors for natural gas require accurate reaction kinetic models to predict the combustion outcomes. The presence of a small amount of impurities in natural gas and other feed streams to oxy-combustors makes these predictions even more complex. During oxy-combustion, trace amounts of nitrogen present in the oxidizer is converted to NO x and gets into the combustion chamber along with the recirculated CO 2 . Similarly, natural gas can contain a trace amount of ammonia and sulfurous impurities that get converted to NO x and SO x and get back into the combustion chamber with recirculated CO 2 . In this work, a reaction model is developed for predicting the effect of impurities such as NO x and SO x on supercritical methane combustion. The base mechanism used in this work is GRI Mech 3.0. H 2 S combustion chemistry is obtained from Bongartz et al. while NOx chemistry is from Konnov. The reaction model is then optimized for a pressure range of 30–300 bar using high-pressure shock tube data from the literature. It is then validated with data obtained from the literature for methane combustion, H 2 S oxidation, and NO x effects on ignition delay. The effect of impurities on CH 4 combustion up to 16 atm is validated using NO x -doped methane studies obtained from the literature. In order to validate the model for high-pressure conditions, experiments are conducted at the UCF shock tube facility using natural gas identical mixtures with N 2 O as an impurity at ~100 bar. Current results show that there is a significant change in ignition delay with the presence of impurities. A comparison is made with experimental data using the developed model and predictions are found to be in good agreement. The model developed was used to study the effect of impurities on CO formation from sCO 2 combustors. It was found that NO x helps in reducing CO formation while the presence of H 2 S results in the formation of more CO. The reaction mechanism developed herein can also be used as a base mechanism to develop reduced mechanisms for use in CFD simulations.

Energy & Fuels↗

The elastic vacuum

The quantum gravity vacuum must contain virtual fluctuations of black hole microstates. These extended-sized fluctuations get “crushed” when a closed trapped surface forms, and turn into on-shell “fuzzball” states that resolve the information puzzle. We argue that these same fluctuations can get “stretched” by the anti-trapped surfaces in an expanding cosmology, and that this stretching generates vacuum energy. The stretching happens when the Hubble deceleration reduces quickly, which happens whenever the pressure drops quickly. We thus get an inflation-scale vacuum energy when the heavy GUTS particles become nonrelativistic, and again a small vacuum energy when the radiation phase turns to dust. The expansion law in the radiation phase does not allow stretching, in agreement with the observed irrelevance of vacuum energy in that phase.

Astronomy & Astrophysics↗