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Inflatable Softgoods Testing Capability Development for Habitation

The Habitation Systems Development Office (HP40) at NASA Marshall Space Flight Center supports systems engineering, integration, and project management for next generation space habitats. The office is responsible for formulation activities for Lunar Surface Habitat and Mars Transit Habitat. HP40 also manages commercial partnerships for exploration habitat development. The Lunar Surface Habitat is intended to initially support a minimum of two crew on the lunar surface for an approximately 30-day mission, with the ability to accommodate four crew for short durations. The Mars Transit Habitat will transport four crew to and from Mars orbit on a potentially 1,200 day mission. Both concepts are envisioned to leverage inflatable softgoods as the primary structural material for the habitation portion of the architecture. Inflatable softgoods are a complex, multi-material system consisting of multiple layers which perform specific functions. A bladder layer (polymer) contains the habitat’s atmosphere. The bladder is indexed to a woven restraint layer, usually Kevlar or Vectran, which serves as the structural layer. The remaining outer layers are for micro-meteoroid orbital debris (MMOD) shielding, protection from atomic Oxygen (if the material system is to be deployed in low earth orbit), and thermal insulation. The primary advantage of inflatable softgoods is that they can offer a larger volume per unit mass relative to a rigid metal structure. Inflatable softgoods have a strong development heritage within NASA, beginning with work in the 1960s in partnership with Goodyear Aerospace and continuing with Johnson Space Center’s TransHab project in the 1990s . Some development efforts subsequently transitioned into the private sector to mature the material technology for flight applications, including human habitation. In August 2022, NASA published its guidelines for certification of crewed inflatable softgoods structures (JSC-67721). This document outlines a series of tests which will be needed to certify inflatable softgoods material systems for use in crewed mission applications. It includes burst testing at the subscale and full-scale to determine the ultimate burst pressure of the softgoods architecture. Creep (long term deformation of the material under stress) is a key failure mode which must be characterized. Creep testing at the component and module levels is also recommended to generate time to failure curves and verify that the inflatable system has a predicted operational life which exceeds mission parameters. ET (Test Engineering) at MSFC and HP40 have worked together to establish softgoods testing capabilities for the center. This includes the ability to conduct module level burst tests and creep tests. The poster will highlight these capabilities and provide examples of testing which has been performed to date by ET. NASA MSFC anticipates that these test capabilities will continue to offer critical support for companies pursuing inflatable softgoods for exploration applications (lunar surface habitation, Mars transit) as well as commercial low earth orbit platforms.

habitation↗

Low-Earth Flight Test of an Inflatable Decelerator (LOFTID) Aeroshell Flight Performance

On November 10, 2022, NASA launched the Low-earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) vehicle as a secondary payload mounted inside the launch vehicle adaptor on an Atlas V 401 out of the Vandenburg Space Force Base (VSFB). The primary payload, Joint Polar Satellite System-2 (JPSS-2), was delivered successfully to a sun synchronous trajectory shortly after launch, at which point the Centaur upper stage performed a burn to de-orbit the system. Once on the desired trajectory to enter the atmosphere the top of the payload adaptor was ejected to expose the LOFTID vehicle, then the LOFTID aeroshell, a Hypersonic Inflatable Aerodynamic Decelerator (HIAD), was deployed and inflated without issue. The Centaur pointed the LOFTID to the desired attitude to enter the atmosphere, spun the assembly to three rpm, separated the reentry vehicle, and finally performed a collision avoidance maneuver to prevent the Centaur from re-contacting the LOFTID after atmospheric entry. The LOFTID vehicle maintained the design attitude and spin rate from separation to atmospheric entry, roughly 30 minutes, demonstrating the aeroshell did not experience any energy damping from inflatable structure flexibility. The LOFTID vehicle entered the atmosphere over Alaska at >8km/sec and decelerated as designed demonstrating stable flight from hypersonic entry through subsonic parachute deployment. On-board visible light cameras captured the reactions of the heatshield through all phases of flight and co-located infrared light cameras captured the temperature distribution of the aft side of the heat shield anchored to a distribution of thermocouples on the inflatable structure (IS) in the field of view. Thermocouples were also embedded in the forward side of the aeroshell both in the Flexible Thermal Protection System (FTPS) as well as the IS. This presentation will discuss aeroshell response to the atmospheric entry. The visible light cameras captured mechanical response of the IS to the loads applied in the different phases of entry. Events seen on the visible light cameras correlate with the response of the load cell pins on webbing elements that attach the aeroshell to the centerbody structure. Thermocouple data captured verifies the aerothermal response of the aeroshell was in-kind with pre-flight analysis predictions although some-what lower in most locations. This data will allow the improvement of the aeroshell modeling tools predictive capability. Post-flight inspection of the aeroshell after splash down and ocean recovery shows that all the aeroshell materials and manufacturing techniques developed over the past 15 years of HIAD technology development performed as de-signed at large scale, a scale which cannot be replicated in ground test facilities. The HIAD supported the LOFTID vehicle high in the water after touching down under parachute and maintained buoyancy and integrity for the hour it took to position the recovery vessel near the LOFTID after splash down. There was no indication the HIAD would have experienced an issue maintaining buoyancy for many more hours after water impact as the component maintained adequate inflation pressure more than 12 hours after water extraction with no additional inflation gas in tanks, as the inflation gas remaining in the tank was vented prior to impact. The LOFTID aeroshell was an unqualified success and has opened up opportunities for commercial application.

LOFTID Aeroshell Flight Performance↗

Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) Mission Overview, Science Return, and Future Applications of This Technology

The Low-Earth Orbit (LEO) Flight Test of an Inflatable Decelerator (LOFTID) mission was the culmination of two decades of research and development for Hyper-sonic Inflatable Aerodynamic Decelerator (HIAD) technology. LOFTID was a project overseen by the Technology Demonstration Mission (TDM) program within NASA’s Space Technology Mission Directorate. The success of the LOFTID mission could enable new NASA missions to Mars, Venus, and most solar-system destinations with atmospheres, as well as cost-effective payload returns to Earth, including in-space manufactured materials and launch vehicle asset recovery. LOFTID, with its unique inflatable heat shield, was the first-of-a-kind orbital reentry flight, and the largest blunt body atmospheric entry of any kind. On November 10, 2022, just over 10 years since the previous flight test of the smaller sub-orbital Inflatable Reentry Vehicle Experiment-3 (IRVE-3) [1], NASA Langley Research Center, with partner United Launch Alliance (ULA), successfully launched and achieved reentry and recovery of the LOFTID Reentry Vehicle (RV), further demonstrating the viability of the HIAD technology for large-diameter, inflatable heat shields to safely and accurately deliver large payloads through an atmosphere via a controlled descent and landing. Launching as a secondary payload with the Joint Polar Satellite System 2 (JPSS-2) from Vandenberg Space Force Base, California, stowed inside an ex-tended payload adapter of the Atlas V 401 launch vehicle, the LOFTID mission officially began after the JPSS-2 payload was delivered to its orbit by the Centaur second stage. The LOFTID RV was flying solo on its spin-stabilized ballistic reentry trajectory about one hour after launch, and the flight ended approximately one hour later with a gentle splashdown under parachute in the Pacific Ocean off the east coast of Hawaii, where the RV was recovered and later shipped back to NASA Langley. LOFTID endured the harsh environments of atmospheric reentry while demonstrating stable aerodynamics through the entire spectrum of hypersonic, supersonic, transonic, and subsonic flight. The LOFTID RV was exposed to an aeroheating environment representative of many Mars and LEO HIAD applications, while successfully demonstrating the ability of the heat-affected inflatable structure to with-stand aerodynamic forces that exceeded those expected at Mars. This flight demonstration of a 6m diameter HIAD confirmed the technology structural and thermal performance as it protected the 1100kg RV entering Earth’s atmosphere at 8 km/s, reaching Mach 30, and experiencing 9g deceleration before deploying parachutes and splashing down in the Pacific Ocean. HIAD technology involves an aeroshell that can be hard packed into a small volume for launch and then deployed prior to atmospheric entry for a controlled deceleration through the atmosphere. Large deployable heat shields enable spacecraft to carry bigger, heavier payloads, including scientific instruments and human support systems for planetary landing and exploration. Much larger than traditional fixed diameter aeroshells that are constrained by the size of launch vehicle shrouds, inflatable decelerators create more drag and start the deceleration process in the upper reaches of the atmosphere with greater efficiency and stability. LOFTID’s successful demonstration of the HIAD technology has greatly expanded NASA’s options for future planetary missions and opened new commercial opportunities for lower-cost mission pay-load recovery including recovery of launch vehicle assets, or as a delivery system to return cargo from the International Space Station or cislunar space. The developments for some of these applications are al-ready underway. While LOFTID was indeed a first-of-a-kind flight for an inflatable heatshield, the largest blunt-body entry ever, its remarkable performance assured that it will not be the last of its kind.

John DiNonno↗

Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) Aeroshell Performance

On November 10, 2022, NASA launched the Low-earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) vehicle as a secondary payload mounted inside the launch vehicle adaptor on an Atlas V 401 out of the Vandenburg Space Force Base (VSFB). The primary payload, Joint Polar Satellite System-2 (JPSS-2), was delivered successfully to a sun synchronous trajectory shortly after launch, at which point the Centaur upper stage performed a burn to de-orbit the system. Once on the desired trajectory to enter the atmosphere the top of the payload adaptor was ejected to expose the LOFTID vehicle, then the LOFTID aeroshell, a Hypersonic Inflatable Aerodynamic Decelerator (HIAD), was deployed and inflated without issue. The Centaur pointed the LOFTID to the desired attitude to enter the atmosphere, spun the assembly to three rpm, separated the reentry vehicle, and finally performed a collision avoidance maneuver to prevent the Centaur from re-contacting the LOFTID after atmospheric entry. The LOFTID vehicle maintained the design attitude and spin rate from separation to atmospheric entry, roughly 30 minutes, demonstrating the aeroshell did not experience any energy damping from inflatable structure flexibility. The LOFTID vehicle entered the atmosphere over Alaska at >8km/sec and decelerated as designed demonstrating stable flight from hypersonic entry through subsonic parachute deployment. On-board visible light cameras captured the reactions of the heatshield through all phases of flight, and co-located infrared light cameras captured the temperature distribution of the aft side of the heat shield anchored to a distribution of thermocouples on the inflatable structure (IS) in the field of view. Thermocouples were also embedded in the forward side of the aeroshell both in the Flexible Thermal Protection System (FTPS) as well as the IS. This paper will discuss aeroshell response to the atmospheric entry. The visible light cameras captured mechanical response of the deployable aeroshell to the loads applied in the different phases of entry. Events seen on the visible light cameras correlate with the response of the load cell pins on webbing elements that attach the aeroshell to the centerbody structure. Thermocouple data captured verifies the aerothermal response of the aeroshell was in-kind with pre-flight analysis predictions although somewhat lower in most locations. This data will allow the improvement of the aeroshell modeling tools predictive capability. Post-flight inspection of the aeroshell after splash down and ocean recovery shows that all the aeroshell materials and manufacturing techniques developed over the past 15 years of HIAD technology development performed as designed at large scale, a scale which cannot be replicated in ground test facilities. The HIAD supported the LOFTID vehicle high in the water after touching down under parachute and maintained buoyancy and integrity for the hour it took to position the recovery vessel near the LOFTID after splash down. There was no indication the HIAD would have experienced an issue maintaining buoyancy for many more hours after water impact as the component maintained adequate inflation pressure more than 24 hours after water extraction with no additional inflation gas in tanks, as the inflation gas remaining in the tank was vented prior to impact.

Entry Descent Landing Atmospheric Entry Deployable↗

The development of inflatable array antennas

Inflatable array antennas are being developed to significantly reduce the mass, the launch vehicle's stowage volume, and the cost of future spacecraft systems. Three inflatable array antennas, recently developed for spacecraft applications, are a 3.3 m x 1.0 m L-band synthetic-aperture radar (SAR) array, a 1.0 m-diameter X-band telecom reflectarray, and a 3 m-diameter Ka-band telecom reflectarray. All three antennas are similar in construction, and each consists of an inflatable tubular frame that supports and tensions a multi-layer thin-membrane RF radiating surface with printed microstrip patches. The L-band SAR array achieved a bandwidth of 80 MHz, an aperture efficiency of 74%, and a total mass of 15 kg. The X-band reflectarray achieved an aperture efficiency of 37%, good radiation patterns, and a total mass of 1.2 kg (excluding the inflation system). The 3 m Ka-band reflectarray achieved a surface flatness of 0.1 mm RMS, good radiation patterns, and a total mass of 12.8 kg (excluding the inflation system). These antennas demonstrated that inflatable arrays are feasible across the microwave and millimeter-wave spectrums. Further developments of these antennas are deemed necessary, in particular, in the area of qualifying the inflatable structures for space-environment usage.

Inflatable array antennas↗

No-scale ripple inflation revisited

We revisit the no-scale ripple inflation model, where no-scale supergravity is modified by an additional term for the inflaton field in the Kähler potential. This term not only breaks one SU(N,1) symmetry explicitly, but also plays an important role for inflation. We generalize the superpotential in the no-scale ripple inflation model slightly. There exists a discrete Z{sub 2} symmetry/parity in the scalar potential in general, which can be preserved or violated by the non-canonical nomalized inflaton kinetic term. Thus, there are three inflation paths: one parity invariant path, and the left and right paths for parity violating scenario. We show that the inflations along the parity invariant path and right path are consistent with the Planck results. However, the gavitino mass for the parity invariant path is so large that the inflation results will be invalid if we consider the inflaton supersymmetry breaking soft mass term. Thus, only the inflation along the right path gives the correct and consistent results. Notably, the tensor-to-scalar ratio in such case can be large, with a value around 0.05, which may be probed by the future Planck experiment.

79 ASTRONOMY AND ASTROPHYSICS↗

Primordial anisotropies in gauged hybrid inflation

We study primordial anisotropies generated in the model of gauged hybrid inflation in which the complex waterfall field is charged under a U(1)gauge field. Primordial anisotropies are generated either actively during inflation or from inhomogeneities modulating the surface of end of inflation during waterfall transition. We present a consistent δN mechanism to calculate the anisotropic power spectrum and bispectrum. We show that the primordial anisotropies generated at the surface of end of inflation do not depend on the number of e-folds and therefore do not produce dangerously large anisotropies associated with the IR modes. Furthermore, one can find the parameter space that the anisotropies generated from the surface of end of inflation cancel the anisotropies generated during inflation, therefore relaxing the constrains on model parameters imposed from IR anisotropies. We also show that the gauge field fluctuations induce a red-tilted power spectrum so the averaged power spectrum from the gauge field can change the total power spectrum from blue to red. Therefore, hybrid inflation, once gauged under a U(1) field, can be consistent with the cosmological observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Toward inflation models compatible with the no-boundary proposal

In this paper, we investigate various inflation models in the context of the no-boundary proposal. We propose that a good inflation model should satisfy three conditions: observational constraints, plausible initial conditions, and naturalness of the model. For various inflation models, we assign the probability to each initial condition using the no-boundary proposal and define a quantitative standard, typicality, to check whether the model satisfies the observational constraints with probable initial conditions. There are three possible ways to satisfy the typicality criterion: there was pre-inflation near the high energy scale, the potential is finely tuned or the inflationary field space is unbounded, or there are sufficient number of fields that contribute to inflation. The no-boundary proposal rejects some of naive inflation models, explains some of traditional doubts on inflation, and possibly, can have observational consequences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Inflating an inhomogeneous universe

While cosmological inflation can erase primordial inhomogeneities, it is possible that inflation may not begin in a significantly inhomogeneous universe. This issue is particularly pressing in multifield scenarios, where even the homogeneous dynamics may depend sensitively on the initial configuration. This paper presents an initial survey of the onset of inflation in multifield models, via qualitative lattice-based simulations that do not include local gravitational backreaction. Using hybrid inflation as a test model, our results suggest that small subhorizon inhomogeneities do play a key role in determining whether inflation begins in multifield scenarios. Interestingly, some configurations which do not inflate in the homogeneous limit ''succeed'' after inhomogeneity is included, while other initial configurations which inflate in the homogeneous limit ''fail'' when inhomogeneity is added.

79 ASTRONOMY AND ASTROPHYSICS↗

The expected anisotropy in solid inflation

Solid inflation is an effective field theory of inflation in which isotropy and homogeneity are accomplished via a specific combination of anisotropic sources (three scalar fields that individually break isotropy). This results in specific observational signatures that are not found in standard models of inflation: a non-trivial angular dependence for the squeezed bispectrum, and a possibly long period of anisotropic inflation (to drive inflation, the ''solid'' must be very insensitive to any deformation, and thus background anisotropies are very slowly erased). In this paper we compute the expected level of statistical anisotropy in the power spectrum of the curvature perturbations of this model. To do so, we account for the classical background values of the three scalar fields that are generated on large (superhorizon) scales during inflation via a random walk sum, as the perturbation modes leave the horizon. Such an anisotropy is unavoidably generated, even starting from perfectly isotropic classical initial conditions. The expected level of anisotropy is related to the duration of inflation and to the amplitude of the squeezed bispectrum. If this amplitude is close to its current observational limit (so that one of the most interesting predictions of the model can be observed in the near future), we find that a level of statistical anisotropy F{sup 2} gives frozen and scale invariant vector perturbations on superhorizon scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Negative running can prevent eternal inflation

Current data from the Planck satellite and the BICEP2 telescope favor, at around the 2 σ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running α < 0, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on n{sub S} from Planck, this corresponds to an upper bound of the running α < −9 × 10{sup −5}, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as 10{sup 4} e-folds.

79 ASTRONOMY AND ASTROPHYSICS↗

Saving Natural Inflation

Slow-roll inflation requires the inflaton field to have an exceptionally flat potential, which combined with measurements of the scale of inflation demands some degree of fine-tuning. Alternatively, the flatness of the potential could be due to the inflaton's origin as a pseudo-Goldstone boson, as in Natural Inflation. Alas, consistency with Planck data places the original proposal of Natural Inflation in a tight spot, as it requires a trans-Planckian excursion of the inflaton. Although one can still tune the renormalizable potential to sub-Planckian values, higher order corrections from quantum gravity or sources of breaking of the Goldstone symmetry would ruin the predictivity of the model. In this paper we show how in more realistic models of Natural Inflation one could achieve inflation without a trans-Planckian excursion of the field. We show how a variant of Extra-natural inflation with bulk fermions can achieve the desired goal and discuss its four-dimensional duals. We also present a new type of four dimensional models inspired in Little Higgs and Composite Higgs models which can lead to sub-Planckian values of the inflaton field.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Intermediate inflation from a non-canonical scalar field

We study the intermediate inflation in a non-canonical scalar field framework with a power-like Lagrangian. We show that in contrast with the standard canonical intermediate inflation, our non-canonical model is compatible with the observational results of Planck 2015. Also, we estimate the equilateral non-Gaussianity parameter which is in well agreement with the prediction of Planck 2015. Then, we obtain an approximation for the energy scale at the initial time of inflation and show that it can be of order of the Planck energy scale, i.e. M{sub P} ∼ 10{sup 18}GeV. We will see that after a short period of time, inflation enters in the slow-roll regime that its energy scale is of order M{sub P}/100 ∼ 10{sup 16}GeV and the horizon exit takes place in this energy scale. We also examine an idea in our non-canonical model to overcome the central drawback of intermediate inflation which is the fact that inflation never ends. We solve this problem without disturbing significantly the nature of the intermediate inflation until the time of horizon exit.

79 ASTRONOMY AND ASTROPHYSICS↗

Cascading dust inflation in Born-Infeld gravity

In the framework of Born-Infeld inspired gravity theories, which deviates from General Relativity (GR) in the high curvature regime, we discuss the viability of Cosmic Inflation without scalar fields. For energy densities higher than the new mass scale of the theory, a gravitating dust component is shown to generically induce an accelerated expansion of the Universe. Within such a simple scenario, inflation gracefully exits when the GR regime is recovered, but the Universe would remain matter dominated. In order to implement a reheating era after inflation, we then consider inflation to be driven by a mixture of unstable dust species decaying into radiation. Because the speed of sound gravitates within the Born-Infeld model under consideration, our scenario ends up being predictive on various open questions of the inflationary paradigm. The total number of e-folds of acceleration is given by the lifetime of the unstable dust components and is related to the duration of reheating. As a result, inflation does not last much longer than the number of e-folds of deceleration allowing a small spatial curvature and large scale deviations to isotropy to be observable today. Energy densities are self-regulated as inflation can only start for a total energy density less than a threshold value, again related to the species' lifetime. Above this threshold, the Universe may bounce thereby avoiding a singularity. Another distinctive feature is that the accelerated expansion is of the superinflationary kind, namely the first Hubble flow function is negative. We show however that the tensor modes are never excited and the tensor-to-scalar ratio is always vanishing, independently of the energy scale of inflation.

79 ASTRONOMY AND ASTROPHYSICS↗

Differentiating G-inflation from string gas cosmology using the effective field theory approach

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes n {sub s} and that of tensor ones n {sub t} , which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.

79 ASTRONOMY AND ASTROPHYSICS↗

Probable or improbable universe? Correlating electroweak vacuum instability with the scale of inflation

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around Λ I ~ 10 11 GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than Λ I (as preferred by the recent BICEP 2 measurement). Here, we perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale of inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Gravitational production of heavy particles during and after inflation

Abstract We investigate the gravitational production of a scalar fieldχwith a mass exceeding the Hubble scale during inflationm χ ≳H I , employing both analytical and numerical approaches. We demonstrate that the steepest descent method effectively captures the epochs and yields of gravitational production in a compact and simple analytical framework. These analytical results align with the numerical solutions of the field equation. Our study covers three spacetime backgrounds: de Sitter, power-law inflation, and the Starobinsky inflation model. Within these models, we identify two distinct phases of particle production: during and after inflation. During inflation, we derive an accurate analytic expression for the particle production rate, accounting for a varying Hubble rate. After inflation, the additional burst of particle production depends on the inflaton mass around its minimum. When this mass is smaller than the Hubble scale during inflation,H I , there is no significant extra production. However, if the inflaton mass is larger, post-inflation production becomes the dominant contribution. Furthermore, we explore the implications of gravitationally produced heavy fields for dark matter abundance, assuming their cosmological stability.

Physics↗

Bispectrum from open inflation

We calculate the bispectrum of primordial curvature perturbations, ζ, generated during ''open inflation.'' Inflation occurs inside a bubble nucleated via quantum tunneling from the background false vacuum state. Our universe lives inside the bubble, which can be described as a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) universe with negative spatial curvature, undergoing slow-roll inflation. We pay special attention to the issue of an initial state for quantum fluctuations. A ''vacuum state'' defined by a positive-frequency mode in de Sitter space charted by open coordinates is different from the Euclidean vacuum (which is equivalent to the so-called ''Bunch-Davies vacuum'' defined by a positive-frequency mode in de Sitter space charted by flat coordinates). Quantum tunneling (bubble nucleation) then modifies the initial state away from the original Euclidean vacuum. While most of the previous study on modifications of the initial quantum state introduces, by hand, an initial time at which the quantum state is modified as well as the form of the modification, an effective initial time naturally emerges and the form is fixed by quantum tunneling in open inflation models. Therefore, open inflation enables a self-consistent computation of the effect of a modified initial state on the bispectrum. We find a term which goes as (ζ{sub k{sub 1}}ζ{sub k{sub 2}}ζ{sub k{sub 3}})∝1/k{sub 1}{sup 2}k{sub 3}{sup 4} in the so-called squeezed configurations, k{sub 3} << k{sub 1} ≈ k{sub 2}, in agreement with the previous study on modifications of the initial state. The bispectrum in the exact folded limit, e.g., k{sub 1} = k{sub 2}+k{sub 3}, is also enhanced and remains finite. However, these terms are exponentially suppressed when the wavelength of ζ is smaller than the curvature radius of the universe. The leading-order bispectrum is equal to the usual one from single-field slow-roll inflation; the terms specific for open inflation arise only in the sub-leading order when the wavelength of ζ is smaller than the curvature radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗