Results for “Decay Correction” — Page 12

DOE OSTI2025

Diagnostic Systems in the Muon $g-2$ experiment at Fermilab

The muon anomalous magnetic moment, $a_\mu=\frac{g-2}{2}$, is a low-energy observable which can be both measured and computed to high precision, making it a sensitive test of the Standard Model and a probe for new physics. This anomaly was measured with a precision of $0.20$~parts per million (ppm) by the Fermilab's Muon g-2 (E989) experiment. The final goal of the E989 experiment is to reach a precision of $0.14$~ppm. The experiment is based on the measurement of the muon spin anomalous precession frequency, $\omega_a$, based on the arrival time distribution of high-energy decay positrons observed by 24 electromagnetic calorimeters, placed around the inner circumference of a $14$~m diameter storage ring, and on the precise knowledge of the storage ring magnetic field and of the beam time and space distribution. Achieving this level of precision requires strict control over systematics, which is ensured through several diagnostic devices. At the accelerator level, these devices monitor the quality of the injected beam (e.g., verifying that it has the correct momentum), while at the detector level, they track both the magnetic field and the gain of the calorimeters. In this work the devices and techniques used by the E989 experiment will be presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1985

An internally consistent gamma ray burst time history phenomenology

A phenomenology for gamma ray burst time histories is outlined. Order of their generally chaotic appearance is attempted, based on the speculation that any one burst event can be represented above 150 keV as a superposition of similarly shaped increases of varying intensity. The increases can generally overlap, however, confusing the picture, but a given event must at least exhibit its own limiting characteristic rise and decay times if the measurements are made with instruments having adequate temporal resolution. Most catalogued observations may be of doubtful or marginal utility to test this hypothesis, but some time histories from Helios-2, Pioneer Venus Orbiter and other instruments having one-to several-millisecond capabilities appear to provide consistency. Also, recent studies of temporally resolved Solar Maximum Mission burst energy spectra are entirely compatible with this picture. The phenomenology suggested here, if correct, may assist as an analytic tool for modelling of burst processes and possibly in the definition of burst source populations.

Cline, T. L.↗

NASA NTRS2006

Modification of Eccentric Gaze-Holding

Clear vision and accurate localization of objects in the environment are prerequisites for reliable performance of motor tasks. Space flight confronts the crewmember with a stimulus rearrangement that requires adaptation to function effectively with the new requirements of altered spatial orientation and motor coordination. Adaptation and motor learning driven by the effects of cerebellar disorders may share some of the same demands that face our astronauts. One measure of spatial localization shared by the astronauts and those suffering from cerebellar disorders that is easily quantified, and for which a neurobiological substrate has been identified, is the control of the angle of gaze (the "line of sight"). The disturbances of gaze control that have been documented to occur in astronauts and cosmonauts, both in-flight and postflight, can be directly related to changes in the extrinsic gravitational environment and intrinsic proprioceptive mechanisms thus, lending themselves to description by simple non-linear statistical models. Because of the necessity of developing robust normal response populations and normative populations against which abnormal responses can be evaluated, the basic models can be formulated using normal, non-astronaut test subjects and subsequently extended using centrifugation techniques to alter the gravitational and proprioceptive environment of these subjects. Further tests and extensions of the models can be made by studying abnormalities of gaze control in patients with cerebellar disease. A series of investigations were conducted in which a total of 62 subjects were tested to: (1) Define eccentric gaze-holding parameters in a normative population, and (2) explore the effects of linear acceleration on gaze-holding parameters. For these studies gaze-holding was evaluated with the subjects seated upright (the normative values), rolled 45 degrees to both the left and right, or pitched back 30 and 90 degrees. In a separate study the further effects of acceleration on gaze stability was examined during centrifugation (+2 G (sub x) and +2 G (sub z) using a total of 23 subjects. In all of our investigations eccentric gaze-holding was established by having the subjects acquire an eccentric target (+/-30 degrees horizontal, +/- 15 degrees vertical) that was flashed for 750 msec in an otherwise dark room. Subjects were instructed to hold gaze on the remembered position of the flashed target for 20 sec. Immediately following the 20 sec period, subjects were cued to return to the remembered center position and to hold gaze there for an additional 20 sec. Following this 20 sec period the center target was briefly flashed and the subject made any corrective eye movement back to the true center position. Conventionally, the ability to hold eccentric gaze is estimated by fitting the natural log of centripetal eye drifts by linear regression and calculating the time constant (G) of these slow phases of "gaze-evoked nystagmus". However, because our normative subjects sometimes showed essentially no drift (tau (sub c) = m), statistical estimation and inference on the effect of target direction was performed on values of the decay constant theta = 1/(tau (sub c)) which we found was well modeled by a gamma distribution. Subjects showed substantial variance of their eye drifts, which were centrifugal in approximately 20 % of cases, and > 40% for down gaze. Using the ensuing estimated gamma distributions, we were able to conclude that rightward and leftward gaze holding were not significantly different, but that upward gaze holding was significantly worse than downward (p<0.05). We also concluded that vertical gaze holding was significantly worse than horizontal (p<0.05). In the case of left and right roll, we found that both had a similar improvement to horizontal gaze holding (p<0.05), but didn't have a significant effect on vertical gaze holding. For pitch tilts, both tilt angles significantly decreased gaze-holding ility in all directions (p<0.05). Finally, we found that hyper-g centrifugation significantly decreased gaze holding ability in the vertical plane. The main findings of this study are as follows: (1) vertical gaze-holding is less stable than horizontal, (2) gaze-holding to upward targets is less stable than to downward targets, (3) tilt affects gaze holding, and (4) hyper-g affects gaze holding. This difference between horizontal and vertical gaze-holding may be ascribed to separate components of the velocity-to-position neural integrator for eye movements, and to differences in orbital mechanics. The differences between upward and downward gaze-holding may be ascribed to an inherent vertical imbalance in the vestibular system. Because whole body tilt and hyper-g affects gaze-holding, it is implied that the otolith organs have direct connections to the neural integrator and further studies of astronaut gaze-holding are warranted. Our statistical method for representing the range of normal eccentric gaze stability can be readily applied to normals who maybe exposed to environments which may modify the central integrator and require monitoring, and to evaluate patients with gaze-evoked nystagmus by comparing to the above established normative criteria.

Reschke, M. F.↗

NASA NTRS1990

Predicting thunderstorm evolution using ground-based lightning detection networks

Lightning measurements acquired principally by a ground-based network of magnetic direction finders are used to diagnose and predict the existence, temporal evolution, and decay of thunderstorms over a wide range of space and time scales extending over four orders of magnitude. The non-linear growth and decay of thunderstorms and their accompanying cloud-to-ground lightning activity is described by the three parameter logistic growth model. The growth rate is shown to be a function of the storm size and duration, and the limiting value of the total lightning activity is related to the available energy in the environment. A new technique is described for removing systematic bearing errors from direction finder data where radar echoes are used to constrain site error correction and optimization (best point estimate) algorithms. A nearest neighbor pattern recognition algorithm is employed to cluster the discrete lightning discharges into storm cells and the advantages and limitations of different clustering strategies for storm identification and tracking are examined.

Goodman, Steven J.↗

NASA NTRS1992

Compton telescope observations of gamma rays from SN 1987A

Results are reported of observations of a significant excess of gamma rays at energies of 1.0-2.5 MeV from the direction of SN 1987A, 418 days after detonation. Two features at 1.21 and 1.88 MeV are attributed to the 1.238 MeV and the combined 1.771, 2.015, and 2.035 MeV line emissions from the decay of Co-56 in the expanding ejecta with respective fluxes of (4.6 +/-1.4 +/-1.2) x 10 exp -4 and (3.5 +/-0.9 +/-0.9) x 10 exp -4 gamma/sq cm s, where the first error is statistical and the second systematic. The obtained energy resolution of 11 percent did not permit a definite separation of the 1.771-MeV line from the two other lines at 2.015 and 2.035 MeV that form the group at 1.88 MeV. The line fluxes were obtained after correcting for the north-south effect and the continuum.

Ait-Ouamer, Farid↗

NASA NTRS1979

A sensitivity analysis of volcanic aerosol dispersion in the stratosphere

A computer sensitivity analysis was performed to determine the uncertainties involved in the calculation of volcanic aerosol dispersion in the stratosphere using a 2 dimensional model. The Fuego volcanic event of 1974 was used. Aerosol dispersion processes that were included are: transport, sedimentation, gas phase sulfur chemistry, and aerosol growth. Calculated uncertainties are established from variations in the stratospheric aerosol layer decay times at 37 latitude for each dispersion process. Model profiles are also compared with lidar measurements. Results of the computer study are quite sensitive (factor of 2) to the assumed volcanic aerosol source function and the large variations in the parameterized transport between 15 and 20 km at subtropical latitudes. Sedimentation effects are uncertain by up to a factor of 1.5 because of the lack of aerosol size distribution data. The aerosol chemistry and growth, assuming that the stated mechanisms are correct, are essentially complete in several months after the eruption and cannot explain the differences between measured and modeled results.

Butler, C. F.↗

NASA NTRS1976

Deviation from a Maxwellian velocity distribution in regions of interstellar molecular hydrogen

The deviation from a Maxwellian velocity distribution caused by excitation of the J = 2 rotational level of parahydrogen (followed by radiative decay) in a molecular hydrogen gas is investigated. It is noted that inelastic collisions deplete the high-velocity tail of the distribution, while elastic collisions tend to refill it; the resulting steady-state distribution has a small depletion in the tail which slightly reduces the cooling rate of the gas. The elastic-collision transport is approximated by a continuous process, a simplified expression is obtained for the inelastic-collision operator, and the Boltzmann equation is then solved analytically. A correction to the inelastic-collision rate is evaluated, and it is found that the relative magnitude of the effect of tail depletion on the inelastic-collision rate is strongly temperature-dependent. The critical molecular density above which the J = 2 level deexcites by superelastic collisions is shown to be a weak function of temperature.

Gould, R. J.↗

DOE OSTI2026

A Gauss-Radau-Laguerre Discrete Variable Representation for Use in Continuum Electron Dynamics

In this work, we detail an implementation, suitable for calculations on highly correlated ionizing systems, of a modified finite element discrete variable representation (FE-DVR) appended with a Gauss-Radau-Laguerre element. The appended element includes exterior complex scaling (ECS) to impose outgoing wave boundary conditions on treatments of processes involving continuum electrons. In this “infinite range” ECS (irECS), the complications that introduce reflections from the end of the grid when the last ECS finite element has finite range are avoided by the use of the Laguerre-weighted exponentially decaying tails, while outgoing wave boundary conditions are still imposed via the ECS transformation. For highly correlated systems in the absence of strong external fields we find that accurate two-electron integrals are essential in this modified FE-DVR. To accurately compute the two-electron integrals over the entire ECS contour, we present a detailed examination of the implications from the boundary terms that arise in a solution of Poisson’s equation with the Radau-Laguerre basis. A boundary term correction is necessary, and when included, the Radau-Laguerre DVR can accurately describe highly correlated states such as the doubly excited states of helium over the entire ECS contour.

elements↗

NASA NTRS1983

Linearized transfer between inclined circular orbits using low-thrust blow down propulsion system

Noncoplanar transfers between neighboring circular orbits are presented for spacecraft using their own low-thrust blow down propulsion system. It is assumed that the out-of-plane angle between the decaying thrust vector and the current orbit plane remains constant for each extended burn. Switching conditions are derived for the cutoff and relight of the propulsion system in order to carry out a given transfer with inclination change. Furthermore the location where the thrust acceleration is initially applied with respect to the line of nodes of the two orbits is uniquely determined. Finally an analytic derivation of the linearized coplanar motion for stationkeeping and terminal rendezvous studies is also presented and a scheme for deriving the second order correction shown.

Kechichian, J. A.↗

NASA NTRS1984

The I-Pu-Xe age of the Moon

The Rb-Sr analyses of some lunar samples which indicate that the Moon is close to the age of primitive meteorites are only reliable to within about 100 m.y. A potentially more precise chronometer is the I-Pu-Xe system. I129 has a 17 m.y. halflife and decays to Xe129; Pu244, with an 82 m.y. halflife, produces Xe131 to Xe136 in fission. The I129/Pu244 ratio has a halflife of 21 m.y. Xenon retention for the Earth could have begun as late as the event that gave birth to the Moon. For the Moon, it is hard to imagine that xenon retention could have begun before re-accretion of the fissioned (and initially dispersed?) material, particularly if that material got hot enough to account for the depletion of the volatile elements. Thus, if fission model are correct, xenon retention in the Earth certainly began no later than in the Moon, and possibly began earlier. Therefore, the I-Pu-Xe system is only marginally consistent with a fission origin. If further study confirms that the I/U ratio of the Moon is .01 or less, or if gas-rich lunar highland breccias with higher ratios of I129 to Pu244 are found, it would be difficult to explain the results in an earth-fission model of lunar origin.

Swindle, T. D.↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

NASA NTRS1999

IMF Length Scales and Predictability: The Two Length Scale Medium

We present preliminary results from a systematic study using simultaneous data from three spacecraft, Wind, IMP 8 (Interplanetary Monitoring Platform) and Geotail to examine interplanetary length scales and their implications on predictability for magnetic field parcels in the typical solar wind. Time periods were selected when the plane formed by the three spacecraft included the GSE (Ground Support Equipment) x-direction so that if the parcel fronts were strictly planar, the two adjacent spacecraft pairs would determine the same phase front angles. After correcting for the motion of the Earth relative to the interplanetary medium and deviations in the solar wind flow from radial, we used differences in the measured front angle between the two spacecraft pairs to determine structure radius of curvature. Results indicate that the typical radius of curvature for these IMF parcels is of the order of 100 R (Sub E). This implies that there are two important IMF (Interplanetary Magnetic Field) scale lengths relevant to predictability: (1) the well-established scale length over which correlations observed by two spacecraft decay along a given IMF parcel, of the order of a few tens of Earth radii and (2) the scale length over which two spacecraft are unlikely to even observe the same parcel because of its curvature, of the order of a hundred Earth radii.

Collier, Michael R.↗

DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗

NASA NTRS2003

Energy Scales in X-Ray Microcalorimeters

Microcalorimeter pulse shape characteristics, such as pulse height, decay time and rise time, are dependent on the detector temperature and bias as well as the photon energy and flux. We examine the nature of the temperature dependency by illuminating the ASTRO-E2 X-ray Spectrometer (XRS) microcalorimeter array with X-rays generated by electron impact on a range of foil targets. The resulting pulses are collected for a range of detector temperatures. We observe and model the temperature dependence of the pulse shape characteristics by fitting the data with non-linear pulse models. Our aim is to determine a robust method for correcting the energy scale obtained in ground calibration for slight differences in the operating conditions while in orbit.

Tillotson, W. A.↗

DOE OSTI2024

Measurement of energy resolution with the NEXT-White silicon photomultipliers

The NEXT-White detector, a high-pressure gaseous xenon time projection chamber, demonstrated the excellence of this technology for future neutrinoless double beta decay searches using photomultiplier tubes (PMTs) to measure energy and silicon photomultipliers (SiPMs) to extract topology information. This analysis uses $^{83m}$Kr data from the NEXT-White detector to measure and understand the energy resolution that can be obtained with the SiPMs, rather than with PMTs. The energy resolution obtained of (10.9 ± 0.6)%, full-width half-maximum, is slightly larger than predicted based on the photon statistics resulting from very low light detection coverage of the SiPM plane in the NEXT-White detector. The difference in the predicted and measured resolution is attributed to poor corrections, which are expected to be improved with larger statistics. Furthermore, the noise of the SiPMs is shown to not be a dominant factor in the energy resolution and may be negligible when noise subtraction is applied appropriately, for high-energy events or larger SiPM coverage detectors. These results, which are extrapolated to estimate the response of large coverage SiPM planes, are promising for the development of future, SiPM-only, readout planes that can offer imaging and achieve similar energy resolution to that previously demonstrated with PMTs.[graphic not available: see fulltext]

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1979

Computational simulation of turbulent vortex merger and decay

The interaction and eventual merger of corotational vortices and the decay of a single vortex have been studied by employing zero-, one- and two-equation turbulent-flow models in order to gain a better understanding of the role of turbulence. An implicit finite-difference procedure is used to integrate the unsteady, two-dimensional equations in a cross-plane. The zero- and one-equation formulations utilize a mixing-length model, which incorporates the streamline curvature effect by prescribing a spatially-varying mixing-length. In the two-equation model, the turbulence kinetic energy equation and a modified rate of dissipation equation which includes a streamline curvature correction are solved. Computational results of different models applied to various flow-configurations are presented and compared with available experimental data whenever possible.

Raj, P.↗

DOE OSTI2024

Bare mass effects on the reheating process after inflation

We consider the effects of a bare mass term for the inflaton, when the inflationary potential takes the form V(Φ)=λΦ k about its minimum with k ≥ 4. We concentrate on k =4, but discuss general cases as well. Further, we assume $λΦ$$^{2}_{end}$ >> $m$$^{2}_{Φ}$, where Φ end is the inflaton field value when the inflationary expansion ends. We show that the presence of a mass term (which may be present due to radiative corrections or supersymmetry breaking) can significantly alter the reheating process, as the equation of state of the inflaton condensate changes from w Φ = $\frac{1}{3}$ to w Φ = 0 when λ⁢Φ 2 drops below $m$$^{2}_{Φ}$. We show that, for a mass mΦ ≳ 3⁢λ $\frac{1}{4}$ T RH , the mass term will dominate at reheating. The value of λ is relatively model independent as it is normalized by the cosmic microwave background perturbation spectrum. For T models of inflation, this leads to m Φ ≳ T RH /250. We compute the effects on the reheating temperature for cases where reheating is due to inflaton decay (to fermions, scalars, or vectors) or to inflaton scattering (to scalars or vectors). For scattering to scalars and in the absence of a decay, there is always a residual inflaton background that acts as cold dark matter. In this case, we derive a strong upper limit to the inflaton bare mass which for T models is m Φ < 350 MeV⁢(T RH /10 10 GeV) 3/5 . We also consider the effect of the bare mass term on the fragmentation of the inflaton condensate.

79 ASTRONOMY AND ASTROPHYSICS↗