The on-going X-ray all-sky survey with the eROSITA instrument will yield large galaxy cluster samples, which will bring strong constraints on cosmological parameters. In particular, the survey holds great promise to investigate the tension between CMB and low-redshift measurements. The current bottleneck preventing the full exploitation of the survey data is the systematics associated with the relation between survey observable and halo mass. Numerous recent studies have shown that gas mass and core-excised X-ray luminosity exhibit very low scatter at fixed mass. We propose a new method to reconstruct these quantities from low photon count data and validate the method using extensive eROSITA-like simulations. We find that even near the detection threshold of ~50 counts the core-excised luminosity and the gas mass can be recovered with 20-30% precision, which is substantially less than the scatter of the full integrated X-ray luminosity at fixed mass. When combined with an accurate calibration of the absolute mass scale (e.g. through weak gravitational lensing), our technique reduces the systematics on cosmological parameters induced by the mass calibration.

Guidance for assemblable parts is a promising field for augmented reality. Augmented reality assembly guidance requires 6D object poses of target objects in real time. Especially in time-critical medical or industrial settings, continuous and markerless tracking of individual parts is essential to visualize instructions superimposed on or next to the target object parts. In this regard, occlusions by the user's hand or other objects and the complexity of different assembly states complicate robust and real-time markerless multi-object tracking. To address this problem, we present Graph-based Object Tracking (GBOT), a novel graph-based single-view RGB-D tracking approach. The real-time markerless multi-object tracking is initialized via 6D pose estimation and updates the graph-based assembly poses. The tracking through various assembly states is achieved by our novel multi-state assembly graph. We update the multi-state assembly graph by utilizing the relative poses of the individual assembly parts. Linking the individual objects in this graph enables more robust object tracking during the assembly process. For evaluation, we introduce a synthetic dataset of publicly available and 3D printable assembly assets as a benchmark for future work. Quantitative experiments in synthetic data and further qualitative study in real test data show that GBOT can outperform existing work towards enabling context-aware augmented reality assembly guidance. Dataset and code will be made publically available.

Strong gravitational lenses with measured time delays between the multiple images allow a direct measurement of the time-delay distance to the lens, and thus a measure of cosmological parameters, particularly the Hubble constant, $H_{0}$. We present a blind lens model analysis of the quadruply-imaged quasar lens HE 0435-1223 using deep Hubble Space Telescope imaging, updated time-delay measurements from the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL), a measurement of the velocity dispersion of the lens galaxy based on Keck data, and a characterization of the mass distribution along the line of sight. HE 0435-1223 is the third lens analyzed as a part of the $H_{0}$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) project. We account for various sources of systematic uncertainty, including the detailed treatment of nearby perturbers, the parameterization of the galaxy light and mass profile, and the regions used for lens modeling. We constrain the effective time-delay distance to be $D_{\Delta t} = 2612_{-191}^{+208}~\mathrm{Mpc}$, a precision of 7.6%. From HE 0435-1223 alone, we infer a Hubble constant of $H_{0} = 73.1_{-6.0}^{+5.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$assuming a flat$\Lambda$CDM cosmology. The cosmographic inference based on the three lenses analyzed by H0LiCOW to date is presented in a companion paper (H0LiCOW Paper V).

Strong gravitational lens systems with time delays between the multiple images allow measurements of time-delay distances, which are primarily sensitive to the Hubble constant that is key to probing dark energy, neutrino physics, and the spatial curvature of the Universe, as well as discovering new physics. We present H0LiCOW ($H_0$ Lenses in COSMOGRAIL's Wellspring), a program that aims to measure $H_0$ with <3.5\% uncertainty from five lens systems (B1608+656, RXJ1131-1231, HE0435-1223, WFI2033-4723 and HE1104-1805). We have been acquiring (1) time delays through COSMOGRAIL and Very Large Array monitoring, (2) high-resolution Hubble Space Telescope imaging for the lens mass modeling, (3) wide-field imaging and spectroscopy to characterize the lens environment, and (4) moderate-resolution spectroscopy to obtain the stellar velocity dispersion of the lenses for mass modeling. In cosmological models with one-parameter extension to flat $\Lambda$CDM, we expect to measure $H_0$ to <3.5\% in most models, spatial curvature $\Omega_{\rm k}$ to 0.004, $w$ to 0.14, and the effective number of neutrino species to 0.2 (1$\sigma$ uncertainties) when combined with current CMB experiments. These are, respectively, a factor of $\sim15$, $\sim2$, and $\sim1.5$ tighter than CMB alone. Our data set will further enable us to study the stellar initial mass function of the lens galaxies, and the co-evolution of supermassive black holes and their host galaxies. This program will provide a foundation for extracting cosmological distances from the hundreds of time-delay lenses that are expected to be discovered in current and future surveys.

The microphysical, kinetic properties of astrophysical plasmas near accreting compact objects are still poorly understood. For instance, in modern general-relativistic magnetohydrodynamic simulations, the relation between the temperature of electrons $T_{e}$ and protons $T_{p}$ is prescribed in terms of simplified phenomenological models where the electron temperature is related to the proton temperature in terms of the ratio between the gas and magnetic pressures, or $\beta$ parameter. We here present a very comprehensive campaign of {two-dimensional} kinetic Particle-In-Cell (PIC) simulations of special-relativistic turbulence to investigate systematically the microphysical properties of the plasma in the trans-relativistic regime. Using a realistic mass ratio between electrons and protons, we analyze how the index of the electron energy distributions $\kappa$, the efficiency of nonthermal particle production $\mathcal{E}$, and the temperature ratio $\mathcal{T}:=T_{e}/T_{p}$, vary over a wide range of values of $\beta$ and $\sigma$. For each of these quantities, we provide two-dimensional fitting functions that describe their behaviour in the relevant space of parameters, thus connecting the microphysical properties of the plasma, $\kappa$, $\mathcal{E}$, and $\mathcal{T}$, with the macrophysical ones $\beta$ and $\sigma$. In this way, our results can find application in wide range of astrophysical scenarios, including the accretion and the jet emission onto supermassive black holes, such as M87* and Sgr A*.

We explore the enhanced self-calibration of photometric galaxy redshift distributions, $n(z)$, through the combination of up to six two-point functions. Our $\rm 3\times2pt$ configuration is comprised of photometric shear, spectroscopic galaxy clustering, and spectroscopic-photometric galaxy-galaxy lensing (GGL). We further include spectroscopic-photometric cross-clustering; photometric GGL; and photometric auto-clustering, using the photometric shear sample as density tracer. We perform simulated likelihood forecasts of the cosmological and nuisance parameter constraints for Stage-III- and Stage-IV-like surveys. For the Stage-III-like case, we employ realistic but perturbed redshift distributions, and distinguish between "coherent" shifting in one direction, versus more internal scattering and full-shape errors. For perfectly known $n(z)$, a $\rm 6\times2pt$ analysis gains $\sim40\%$ in Figure of Merit (FoM) in the $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ and $\Omega_{\rm m}$ plane relative to the $\rm 3\times2pt$ analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of $S_8$ and $\Omega_{\rm m}$, respectively. Employing bin-wise scalar shifts $\delta{z}_i$ in the tomographic mean redshifts reduces cosmological parameter biases, with a $\rm 6x2pt$ analysis constraining the shift parameters with $2-4$ times the precision of a photometric $\rm 3^{ph}\times2pt$ analysis. For the Stage-IV-like survey, a $\rm 6\times2pt$ analysis doubles the FoM($\sigma_8{-}\Omega_{\rm m}$) compared to any $\rm 3\times2pt$ or $\rm 3^{ph}\times2pt$analysis, and is only$8\%$ less constraining than if the $n(z)$ were perfectly known. A Gaussian mixture model for the $n(z)$ reduces mean-redshift errors and preserves the $n(z)$ shape. It also yields the most accurate and precise cosmological constraints for any $N\rm\times2pt$ configuration given $n(z)$ biases.

This thesis calculates the special-relativistic internal energy of a non-interacting gas. We derive an equation of state (EoS) which we apply to the Tollmann-Oppenheimer Volkoff (TOV) equation. Furthermore we present numerical results of the TOV equation for various configurations of a polytropic EoS. These results show that the zero values of the TOV equation compared to its non-relativistic counterpart, the Lane-Emden (LE) equation, are smaller for identical parameters. We present initial developments to a proof of this theorem. Furthermore, an additional exact solution and index $n=2$ of the LE equation was discovered.

The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the $\beta$-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving the trace of the energy-momentum tensor. We use the latter result to give a fully detailed proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also correspond to CFTs. We also clarify the relation between the matrix entering the gradient flow formula for the $\beta$-function and a manifestly positive metric in coupling space associated with matrix elements of the trace of the energy momentum tensor.

We use a modified version of the Peak Patch excursion set formalism to compute the mass and size distribution of QCD axion miniclusters from a fully non-Gaussian initial density field obtained from numerical simulations of axion string decay. We find strong agreement with N-Body simulations at a significantly lower computational cost. We employ a spherical collapse model and provide fitting functions for the modified barrier in the radiation era. The halo mass function at $z=629$ has a power-law distribution $M^{-0.6}$ for masses within the range $10^{-15}\lesssim M\lesssim 10^{-10}M_{\odot}$, with all masses scaling as $(m_a/50\mu\mathrm{eV})^{-0.5}$. We construct merger trees to estimate the collapse redshift and concentration mass relation, $C(M)$, which is well described using analytical results from the initial power spectrum and linear growth. Using the calibrated analytic results to extrapolate to $z=0$, our method predicts a mean concentration $C\sim \mathcal{O}(\text{few})\times10^4$. The low computational cost of our method makes future investigation of the statistics of rare, dense miniclusters easy to achieve.

We propose a new parametric framework to describe in generic metric theories of gravity the spacetime of spherically symmetric and slowly rotating black holes. In contrast to similar approaches proposed so far, we do not use a Taylor expansion in powers of M/r, where M and r are the mass of the black hole and a generic radial coordinate, respectively. Rather, we use a continued-fraction expansion in terms of a compactified radial coordinate. This choice leads to superior convergence properties and allows us to approximate a number of known metric theories with a much smaller set of coefficients. The measure of these coefficients via observations of near-horizon processes can be used to effectively constrain and compare arbitrary metric theories of gravity. Although our attention is here focussed on spherically symmetric black holes, we also discuss how our approach could be extended to rotating black holes.

The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in the regime of validity of semiclassical gravity and do not add additional assumptions that are not necessary for the Hawking calculation, the answer to the question in the title is NO. In other words, the black hole evaporation is certainly unitary as predicted by quantum field theory in curved spacetime. However, if additional assumptions are added, such as a universal area bound on the entropy, contradictions may arise even in regimes where we would expect the semiclassical approximation to be valid. We show that a contradiction indeed arises, but not between the laws of semiclassical general relativity and quantum mechanics, but rather between the former and the additional (holographic) requirement of the area limit, according to which an exterior observer describes a black hole as a quantum system whose entropy is bounded by its area.

Deep learning approaches have shown promising performance for compressed sensing-based Magnetic Resonance Imaging. While deep neural networks trained with mean squared error (MSE) loss functions can achieve high peak signal to noise ratio, the reconstructed images are often blurry and lack sharp details, especially for higher undersampling rates. Recently, adversarial and perceptual loss functions have been shown to achieve more visually appealing results. However, it remains an open question how to (1) optimally combine these loss functions with the MSE loss function and (2) evaluate such a perceptual enhancement. In this work, we propose a hybrid method, in which a visual refinement component is learnt on top of an MSE loss-based reconstruction network. In addition, we introduce a semantic interpretability score, measuring the visibility of the region of interest in both ground truth and reconstructed images, which allows us to objectively quantify the usefulness of the image quality for image post-processing and analysis. Applied on a large cardiac MRI dataset simulated with 8-fold undersampling, we demonstrate significant improvements (p<0.01) over the state-of-the-art in both a human observer study and the semantic interpretability score.

The Pacific Ocean Neutrino Experiment (P-ONE) is a new initiative with a vision towards constructing a multi-cubic kilometre neutrino telescope, to expand our observable window of the Universe to highest energies, installed within the deep Pacific Ocean underwater infrastructure of Ocean Networks Canada.

Using full 3+1 dimensional general-relativistic hydrodynamic simulations of equal- and unequal-mass neutron-star binaries with properties that are consistent with those inferred from the inspiral of GW170817, we perform a detailed study of the quark-formation processes that could take place after merger. We use three equations of state consistent with current pulsar observations derived from a novel finite-temperature framework based on V-QCD, a non-perturbative gauge/gravity model for Quantum Chromodynamics. In this way, we identify three different post-merger stages at which mixed baryonic and quark matter, as well as pure quark matter, are generated. A phase transition triggered collapse already $\lesssim 10\,\rm{ms}$ after the merger reveals that the softest version of our equations of state is actually inconsistent with the expected second-long post-merger lifetime of GW170817. Our results underline the impact that multi-messenger observations of binary neutron-star mergers can have in constraining the equation of state of nuclear matter, especially in its most extreme regimes.