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At least 829 records · Page 46
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DOE OSTI2013

Atmospheric retrieval analysis of the directly imaged exoplanet HR 8799b

Directly imaged exoplanets are unexplored laboratories for the application of the spectral and temperature retrieval method, where the chemistry and composition of their atmospheres are inferred from inverse modeling of the available data. As a pilot study, we focus on the extrasolar gas giant HR 8799b, for which more than 50 data points are available. We upgrade our non-linear optimal estimation retrieval method to include a phenomenological model of clouds that requires the cloud optical depth and monodisperse particle size to be specified. Previous studies have focused on forward models with assumed values of the exoplanetary properties; there is no consensus on the best-fit values of the radius, mass, surface gravity, and effective temperature of HR 8799b. We show that cloud-free models produce reasonable fits to the data if the atmosphere is of super-solar metallicity and non-solar elemental abundances. Intermediate cloudy models with moderate values of the cloud optical depth and micron-sized particles provide an equally reasonable fit to the data and require a lower mean molecular weight. We report our best-fit values for the radius, mass, surface gravity, and effective temperature of HR 8799b. The mean molecular weight is about 3.8, while the carbon-to-oxygen ratio is about unity due to the prevalence of carbon monoxide. Our study emphasizes the need for robust claims about the nature of an exoplanetary atmosphere to be based on analyses involving both photometry and spectroscopy and inferred from beyond a few photometric data points, such as are typically reported for hot Jupiters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The ultraluminous GRB 110918A

GRB 110918A is the brightest long gamma-ray burst (GRB) detected by Konus-WIND during its almost 19 yr of continuous observations and the most luminous GRB ever observed since the beginning of the cosmological era in 1997. We report on the final Interplanetary Network localization of this event and its detailed multiwavelength study with a number of space-based instruments. The prompt emission is characterized by a typical duration, a moderate peak energy of the time-integrated spectrum, and strong hard-to-soft evolution. The high observed energy fluence yields, at z = 0.984, a huge isotropic-equivalent energy release E {sub iso} = (2.1 ± 0.1) × 10{sup 54} erg. The record-breaking energy flux observed at the peak of the short, bright, hard initial pulse results in an unprecedented isotropic-equivalent luminosity L {sub iso} = (4.7 ± 0.2) × 10{sup 54} erg s{sup –1}. A tail of the soft γ-ray emission was detected with temporal and spectral behavior typical of that predicted by the synchrotron forward-shock model. The Swift/X-Ray Telescope and the Swift/Ultraviolet Optical Telescope observed the bright afterglow from 1.2 to 48 days after the burst and revealed no evidence of a jet break. The post-break scenario for the afterglow is preferred from our analysis, with a hard underlying electron spectrum and interstellar-medium-like circumburst environment implied. We conclude that, among the multiple reasons investigated, the tight collimation of the jet must have been a key ingredient to produce this unusually bright burst. The inferred jet opening angle of 1.°7-3.°4 results in reasonable values of the collimation-corrected radiated energy and the peak luminosity, which, however, are still at the top of their distributions for such tightly collimated events. We estimate a detection horizon for a similar ultraluminous GRB of z ∼ 7.5 for Konus-WIND and z ∼ 12 for the Swift/Burst Alert Telescope, which stresses the importance of GRBs as probes of the early Universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A test of the millisecond magnetar central engine model of gamma-ray bursts with swift data

A rapidly spinning, strongly magnetized neutron star (magnetar) has been proposed as one possible candidate of the central engine of gamma-ray bursts (GRBs). We systematically analyze the Swift/XRT light curves of long GRBs detected before 2013 August, and characterize them into four categories based on how likely they may harbor a magnetar central engine: Gold, Silver, Aluminum, and Non-magnetar. We also independently analyze the data of short GRBs with a putative magnetar central engine. We then perform a statistical study of various properties of the magnetar samples and the non-magnetar sample, and investigate whether the data are consistent with the hypothesis that there exist two types of central engines. By deriving the physical parameters of the putative magnetars, we find that the observations of the Gold and Silver samples are generally consistent with the predictions of the magnetar model. For a reasonable beaming factor for long GRBs, the derived magnetar surface magnetic field B{sub p} and initial spin period P {sub 0} fall into the reasonable range. Magnetar winds in short GRBs, on the other hand, are consistent with being isotropic. No GRB in the magnetar sample has a beam-corrected total energy exceeding the maximum energy budget defined by the initial spin energy of the magnetar, while some non-magnetar GRBs do violate such a limit. With beaming correction, on average the non-magnetar sample is more energetic and luminous than the magnetar samples. Our analysis hints that millisecond magnetars are likely operating in a good fraction, but probably not all, GRBs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Synchrotron self-inverse Compton radiation from reverse shock on GRB 120326A

We present multi-wavelength observations of a typical long duration GRB 120326A at z = 1.798, including rapid observations using a Submillimeter Array (SMA) and a comprehensive monitoring in the X-ray and optical. The SMA observation provided the fastest detection to date among seven submillimeter afterglows at 230 GHz. The prompt spectral analysis, using Swift and Suzaku, yielded a spectral peak energy of E{sub peak}{sup src}=107.8{sub −15.3}{sup +15.3} keV and an equivalent isotropic energy of E{sub iso} as 3.18{sub −0.32}{sup +0.40}×10{sup 52} erg. The temporal evolution and spectral properties in the optical were consistent with the standard forward shock synchrotron with jet collimation (6.°69 ± 0.°16). The forward shock modeling, using a two-dimensional relativistic hydrodynamic jet simulation, was also determined by the reasonable burst explosion and the synchrotron radiation parameters for the optical afterglow. The X-ray light curve showed no apparent jet break and the temporal decay index relation between the X-ray and optical (αo – α{sub X} = –1.45 ± 0.10) indicated different radiation processes in each of them. Introducing synchrotron self-inverse Compton radiation from reverse shock is a possible solution, and the detection and slow decay of the afterglow in submillimeter supports that this is a plausible idea. The observed temporal evolution and spectral properties, as well as forward shock modeling parameters, enabled us to determine reasonable functions to describe the afterglow properties. Because half of the events share similar properties in the X-ray and optical as the current event, GRB 120326A will be a benchmark with further rapid follow-ups, using submillimeter instruments such as an SMA and the Atacama Large Millimeter/submillimeter Array.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD

In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A LIGHT CURVE ANALYSIS OF CLASSICAL NOVAE: FREE-FREE EMISSION VERSUS PHOTOSPHERIC EMISSION

We analyzed light curves of seven relatively slower novae, PW Vul, V705 Cas, GQ Mus, RR Pic, V5558 Sgr, HR Del, and V723 Cas, based on an optically thick wind theory of nova outbursts. For fast novae, free-free emission dominates the spectrum in optical bands rather than photospheric emission, and nova optical light curves follow the universal decline law. Faster novae blow stronger winds with larger mass-loss rates. Because the brightness of free-free emission depends directly on the wind mass-loss rate, faster novae show brighter optical maxima. In slower novae, however, we must take into account photospheric emission because of their lower wind mass-loss rates. We calculated three model light curves of free-free emission, photospheric emission, and their sum for various white dwarf (WD) masses with various chemical compositions of their envelopes and fitted reasonably with observational data of optical, near-IR (NIR), and UV bands. From light curve fittings of the seven novae, we estimated their absolute magnitudes, distances, and WD masses. In PW Vul and V705 Cas, free-free emission still dominates the spectrum in the optical and NIR bands. In the very slow novae, RR Pic, V5558 Sgr, HR Del, and V723 Cas, photospheric emission dominates the spectrum rather than free-free emission, which makes a deviation from the universal decline law. We have confirmed that the absolute brightnesses of our model light curves are consistent with the distance moduli of four classical novae with known distances (GK Per, V603 Aql, RR Pic, and DQ Her). We also discussed the reason why the very slow novae are about ∼1 mag brighter than the proposed maximum magnitude versus rate of decline relation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Structure of retrograde circumbinary accretion disks

We evaluate the interactions between a central equal mass binary and a surrounding retrograde circumbinary accretion disk in a three-dimensional, MHD simulation. We find (as widely expected) that the net torque expressed on a retrograde circumbinary disk by the central binary is much (more than two orders of magnitude) smaller than when the disk orbits in the prograde direction. For this reason, unlike the prograde case, there is no “gap” carved out of the retrograde disk, and accreting fluid can travel directly from the disk to the domain of the binary. For the same reason, retrograde disks do not develop the large-amplitude “lumps” generically seen near the inner edges of prograde disks. Although not directly treated in this simulation, the finite extent of accretion disks around the individual masses of the binary can lead to shocks between their outer edges and the circumbinary disk, potentially creating a photon signal modulated at the binary orbital period. The spectra of these shocks should peak in the hard X-ray band as is expected for prograde systems, but retrograde systems would not be expected to display a “notch” in the optical/UV band. Because the disk’s angular momentum is directed oppositely to that of the binary, accretion onto the binary causes a rapid increase in eccentricity. Lastly, we discuss the comparative rates of orbital evolution associated with accretion in prograde and retrograde circumbinary disks, finding that the principal contrast is that e-dot should be rather greater in the retrograde case.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

THE ROLE OF TURBULENCE AND MAGNETIC FIELDS IN SIMULATED FILAMENTARY STRUCTURE

We use numerical simulations of turbulent cluster-forming regions to study the nature of dense filamentary structures in star formation. Using four hydrodynamic and magnetohydrodynamic simulations chosen to match observations, we identify filaments in the resulting column density maps and analyze their properties. We calculate the radial column density profiles of the filaments every 0.05 Myr and fit the profiles with the modified isothermal and pressure-confined isothermal cylinder models, finding reasonable fits for either model. The filaments formed in the simulations have similar radial column density profiles to those observed. Magnetic fields provide additional pressure support to the filaments, making “puffier” filaments less prone to fragmentation than in the pure hydrodynamic case, which continue to condense at a slower rate. In the higher density simulations, the filaments grow faster through the increased importance of gravity. Not all of the filaments identified in the simulations will evolve to form stars: some expand and disperse. Given these different filament evolutionary paths, the trends in bulk filament width as a function of time, magnetic field strength, or density are weak, and all cases are reasonably consistent with the finding of a constant filament width in different star-forming regions. In the simulations, the mean FWHM lies between 0.06 and 0.26 pc for all times and initial conditions, with most lying between 0.1 to 0.15 pc; the range in FWHMs is however, larger than seen in typical Herschel analyses. Finally, the filaments display a wealth of substructure similar to the recent discovery of filament bundles in Taurus.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Supermassive Black Holes from Ultra Strongly Self Interacting Dark Matter

We consider the cosmological consequences if a small fraction (ƒ≲0.1) of the dark matter is ultra-strongly self-interacting, with an elastic self-interaction cross section per unit mass σ$\gg$1 cm 2 g -1 . This possibility evades all current constraints that assume that the self-interacting component makes up the majority of the dark matter. Nevertheless, even a small fraction of ultra-strongly self-interacting dark matter (uSIDM) can have observable consequences on astrophysical scales. In particular, the uSIDM subcomponent can undergo gravothermal collapse and form seed black holes in the center of a halo. These seed black holes, which form within several hundred halo interaction times, contain a few percent of the total uSIDM mass in the halo. For reasonable values of σƒ, these black holes can form at high enough redshifts to grow to ~10 9 M ⊙ quasars by z≳6, alleviating tension within the standard Λ cold dark matter cosmology. The ubiquitous formation of central black holes in halos could also create cores in dwarf galaxies by ejecting matter during binary black hole mergers, potentially resolving the “too big to fail” problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

QUASI-STATIC MODEL OF MAGNETICALLY COLLIMATED JETS AND RADIO LOBES. II. JET STRUCTURE AND STABILITY

This is the second in a series of companion papers showing that when an efficient dynamo can be maintained by accretion disks around supermassive black holes in active galactic nuclei, it can lead to the formation of a powerful, magnetically driven, and mediated helix that could explain both the observed radio jet/lobe structures and ultimately the enormous power inferred from the observed ultrahigh-energy cosmic rays. In the first paper, we showed self-consistently that minimizing viscous dissipation in the disk naturally leads to jets of maximum power with boundary conditions known to yield jets as a low-density, magnetically collimated tower, consistent with observational constraints of wire-like currents at distances far from the black hole. In this paper we show that these magnetic towers remain collimated as they grow in length at nonrelativistic velocities. Differences with relativistic jet models are explained by three-dimensional magnetic structures derived from a detailed examination of stability properties of the tower model, including a broad diffuse pinch with current profiles predicted by a detailed jet solution outside the collimated central column treated as an electric circuit. We justify our model in part by the derived jet dimensions in reasonable agreement with observations. Using these jet properties, we also discuss the implications for relativistic particle acceleration in nonrelativistically moving jets. The appendices justify the low jet densities yielding our results and speculate how to reconcile our nonrelativistic treatment with general relativistic MHD simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Global and pedestal confinement and pedestal structure in dimensionless collisionality scans of low-triangularity H-mode plasmas in JET-ILW

A dimensionless collisionality scan in low-triangularity plasmas in the Joint European Torus with the ITER-like wall (JET-ILW) has been performed. The increase of the normalized energy confinement (defined as the ratio between thermal energy confinement and Bohm confinement time) with decreasing collisionality is observed. Moreover, at low collisionality, a confinement factor H98, comparable to JET-C, is achieved. At high collisionality, the low normalized confinement is related to a degraded pedestal stability and a reduction in the density-profile peaking.The increase of normalized energy confinement is due to both an increase in the pedestal and in the core regions. The improvement in the pedestal is related to the increase of the stability. The improvement in the core is driven by (i) the core temperature increase via the temperature-profile stiffness and by (ii) the density-peaking increase driven by the low collisionality.Pedestal stability analysis performed with the ELITE (edge-localized instabilities in tokamak equilibria) code has a reasonable qualitative agreement with the experimental results. An improvement of the pedestal stability with decreasing collisionality is observed. The improvement is ascribed to the reduction of the pedestal width, the increase of the bootstrap current and the reduction of the relative shift between the positions of the pedestal density and pedestal temperature.The EPED1 model predictions for the pedestal pressure height are qualitatively well correlated with the experimental results. Quantitatively, EPED1 overestimates the experimental pressure by 15–35%. In terms of the pedestal width, a correct agreement (within 10–15%) between the EPED1 and the experimental width is found at low collisionality. The experimental pedestal width increases with collisionality. Nonetheless, an extrapolation to low-collisionality values suggests that the width predictions from the KBM constraint are reasonable for ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

CI+MBPT calculations of Ar I energies, g factors, and transition line strengths

Excited states of noble gas atoms present certain challenges to atomic theory for several reasons: first, relativistic effects are important and LS coupling is not optimal; second, energy intervals can be quite small, leading to strong mixing of states; third, many-body perturbation theory for hole states does not converge well. Previously, some attempts were made to solve this problem, using for example the all-order coupled-cluster approach and particle-hole configuration-interaction many-body perturbation theory (CI-MBPT) with modified denominators. However, while these approaches were promising, the accuracy was still limited. In this study, we calculate Ar I energies, g factors, and transition amplitudes using ab initio CI-MBPT with eight valence electrons to avoid the problem of slow convergence of MBPT due to strong interaction between 3p and 3s states. We also included in CI many dominant states obtained by double excitations of the ground state configuration. Thus perturbation corrections were needed only for 1s, 2s, 2p core electrons non-included in valence-valence CI, which are quite small. We found that energy, g factors, and electric dipole matrix elements are in reasonable agreement with experiments. It is noteworthy that the theory agreed well with accurately measured g factors. Finally, experimental oscillator strengths have large uncertainty, so in some cases we made a comparison with average values.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Halo model and halo properties in Galileon gravity cosmologies

We investigate the performance of semi-analytical modelling of large-scale structure in Galileon gravity cosmologies using results from N-body simulations. We focus on the Cubic and Quartic Galileon models that provide a reasonable fit to CMB, SNIa and BAO data. We demonstrate that the Sheth-Tormen mass function and linear halo bias can be calibrated to provide a very good fit to our simulation results. We also find that the halo concentration-mass relation is well fitted by a power law. The nonlinear matter power spectrum computed in the halo model approach is found to be inaccurate in the mildly nonlinear regime, but captures reasonably well the effects of the Vainshtein screening mechanism on small scales. In the Cubic model, the screening mechanism hides essentially all of the effects of the fifth force inside haloes. In the case of the Quartic model, the screening mechanism leaves behind residual modifications to gravity, which make the effective gravitational strength time-varying and smaller than the standard value. Compared to normal gravity, this causes a deficiency of massive haloes and leads to a weaker matter clustering on small scales. For both models, we show that there are realistic halo occupation distributions of Luminous Red Galaxies that can match both the observed large-scale clustering amplitude and the number density of these galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Supernova cooling in a dark matter smog

A light hidden gauge boson with kinetic mixing with the usual photon is a popular setup in theories of dark matter. The supernova cooling via radiating the hidden boson is known to put an important constraint on the mixing. I consider the possible role dark matter, which under reasonable assumptions naturally exists inside supernova, can play in the cooling picture. Because the interaction between the hidden gauge boson and DM is likely unsuppressed, even a small number of dark matter compared to protons inside the supernova could dramatically shorten the free streaming length of the hidden boson. A picture of a dark matter “smog” inside the supernova, which substantially relaxes the cooling constraint, is discussed in detail.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

The fate of ultrahigh energy nuclei in the immediate environment of young fast-rotating pulsars

Young, fast-rotating neutron stars are promising candidate sources for the production of ultrahigh energy cosmic rays (UHECRs). The interest in this model has recently been boosted by the latest chemical composition measurements of cosmic rays, that seem to show the presence of a heavy nuclear component at the highest energies. Neutrons stars, with their metal-rich surfaces, are potentially interesting sources of such nuclei, but some open issues remain: 1) is it possible to extract these nuclei from the star's surface? 2) Do the nuclei survive the severe conditions present in the magnetosphere of the neutron star? 3) What happens to the surviving nuclei once they enter the wind that is launched outside the light cylinder? In this paper we address these issues in a quantitative way, proving that for the most reasonable range of neutron star surface temperatures (T<10{sup 7} K), a large fraction of heavy nuclei survive photo-disintegration losses. These processes, together with curvature losses and acceleration in the star's electric potential, lead to injection of nuclei with a chemical composition that is mixed, even if only iron is extracted from the surface. We show that under certain conditions the chemical composition injected into the wind region is compatible with that required in previous work based on purely phenomenological arguments (typically ∼50% protons, ∼30% CNO and ∼20% Fe), and provides a reasonable explanation of the mass abundance inferred from ultra high energy data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Generalised form factor dark matter in the Sun

We study the effects of energy transport in the Sun by asymmetric dark matter with momentum and velocity-dependent interactions, with an eye to solving the decade-old Solar Abundance Problem. We study effective theories where the dark matter-nucleon scattering cross-section goes as v{sub rel}{sup 2n} and q{sup 2n} with n=−1,0,1 or 2, where v{sub rel} is the dark matter-nucleon relative velocity and q is the momentum exchanged in the collision. Such cross-sections can arise generically as leading terms from the most basic nonstandard DM-quark operators. We employ a high-precision solar simulation code to study the impact on solar neutrino rates, the sound speed profile, convective zone depth, surface helium abundance and small frequency separations. We find that the majority of models that improve agreement with the observed sound speed profile and depth of the convection zone also reduce neutrino fluxes beyond the level that can be reasonably accommodated by measurement and theory errors. However, a few specific points in parameter space yield a significant overall improvement. A 3–5 GeV DM particle with σ{sub SI}∝q{sup 2} is particularly appealing, yielding more than a 6σ improvement with respect to standard solar models, while being allowed by direct detection and collider limits. We provide full analytical capture expressions for q- and v{sub rel}-dependent scattering, as well as complete likelihood tables for all models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

A Micromegas-based low-background x-ray detector coupled to a slumped-glass telescope for axion research

Here, we report on the design, construction and operation of a low background x-ray detection line composed of a shielded Micromegas detector of the microbulk technology. The detector is made from radiopure materials and is placed at the focal point of a ~ 5 cm diameter, 1.5 m focal-length, cone-approximation Wolter I x-ray telescope (XRT) assembled from thermally-formed (or "slumped") glass substrates deposited with multilayer coatings. The system has been conceived as a technological pathfinder for the future International Axion Observatory (IAXO), as it combines two of the techniques (optic and detector) proposed in the conceptual design of the project. It is innovative for two reasons: it is the first time an x-ray optic has been designed and fabricated specifically for axion research, and the first time a Micromegas detector has been operated with an x-ray optic. The line has been installed at one end of the CERN Axion Solar Telescope (CAST) magnet and is currently looking for solar axions. Furthermore, the combination of the XRT and Micromegas detector provides the best signal-to-noise ratio obtained so far by any detection system of the CAST experiment with a background rate of 5.4×10 –3 counts per hour in the energy region-of-interest and signal spot area.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Stationary bubbles and their tunneling channels toward trivial geometry

In the path integral approach, one has to sum over all histories that start from the same initial condition in order to obtain the final condition as a superposition of histories. Applying this into black hole dynamics, we consider stable and unstable stationary bubbles as a reasonable and regular initial condition. We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon. We investigate the dynamics and tunneling channels of true vacuum bubbles for various tensions. In particular, in line with the idea of superposition of geometries, we build a classically stable stationary thin-shell solution in a Minkowski background where its fate is probabilistically given by non-perturbative effects. Since there exists a tunneling channel toward a trivial geometry in the entire path integral, the entire information is encoded in the wave function. This demonstrates that the unitarity is preserved and there is no loss of information when viewed from the entire wave function of the universe, whereas a semi-classical observer, who can see only a definitive geometry, would find an effective loss of information. Ultimately, this may provide a resolution to the information loss dilemma.

79 ASTRONOMY AND ASTROPHYSICS↗