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Future weak lensing analyses with the Nancy Grace Roman Space Telescope (Roman) will require highly realistic image simulations to control shear systematics at unprecedented precision. A key limitation of existing approaches is their reliance on analytic light-profile models, which cannot fully capture the complex, nonparametric morphologies revealed by high-resolution observations. We present a diffusion-based framework for generating realistic galaxy image simulations tailored to the weak lensing requirements of the Roman High Latitude Survey. We construct Roman-like galaxy images from multiband James Webb Space Telescope NIRCam observations of the GOODS-S and GOODS-N fields, transforming them into the Roman observing regime through point-spread function matching, pixel-scale conversion, and interloper masking that preserves correlated noise properties. These data are used to train a denoising diffusion probabilistic model to generate multiband galaxy postage stamps in the Roman Y, J, and H filters. We validate the generated sample against an independent dataset using a consistent photometric pipeline, comparing key galaxy observables including magnitude, size, ellipticity, peak surface brightness, and three-band colors. The generated galaxies reproduce both the marginal distributions and the covariance structure of these properties, with only modest deviations in low-occupancy regions of parameter space. These results demonstrate that diffusion models provide a scalable and physically motivated alternative to analytic simulations, enabling high-fidelity galaxy populations for Roman weak lensing calibration and, more generally, for survey preparation in upcoming cosmological experiments.

Understanding and mitigating measurement systematics in weak lensing (WL) analysis requires large data sets of realistic galaxies with diverse morphologies and colors. Missions like Euclid, the Nancy Roman Space Telescope, and Vera C. Rubin Observatory’s Legacy Survey of Space and Time will provide unprecedented statistical power and control over systematic uncertainties. Achieving the stringent shear measurement requirement of ∣m∣ < 10−3 demands analyzing 109 galaxies. Accurately modeling galaxy morphology is crucial, as it is shaped by complex astrophysical processes that are not yet fully understood. Subtle deviations in shape and structural parameters can introduce biases in shear calibration. The interplay between bulges, disks, star formation, and mergers contributes to morphological diversity, requiring simulations that faithfully reproduce these features to avoid systematics in shear measurements. Generating such a large and realistic data set efficiently is feasible using advanced generative models like denoising diffusion probabilistic models. In this work, we extend Hubble Space Telescope (HST) data across Euclid’s broad optical band using the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey and develop a generative AI tool to produce realistic Euclid-like galaxies while preserving morphological details. We validate our tool through visual inspection and quantitative analysis of galaxy parameters, demonstrating its capability to simulate realistic Euclid galaxy images, which will address WL challenges and enhance calibration for current and future cosmological missions.

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminary study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ansätz to finding useful solutions to Einstein's equations.

We study continuous groups of generalized Kerr–Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.

The Roman Space Telescope will have the first advanced coronagraph in space, with deformable mirrors for wavefront control, low-order wavefront sensing and maintenance, and a photon-counting detector. It is expected to be able to detect and characterize mature, giant exoplanets in reflected visible light. Over the past decade the performance of the coronagraph in its flight environment has been simulated with increasingly detailed diffraction and structural/thermal finite element modeling. With the instrument now being integrated in preparation for launch within the next few years, the present state of the end-to-end modeling is described, including the measured flight components such as deformable mirrors. The coronagraphic modes are thoroughly described, including characteristics most readily derived from modeling. The methods for diffraction propagation, wavefront control, and structural and thermal finite-element modeling are detailed. The techniques and procedures developed for the instrument will serve as a foundation for future coronagraphic missions such as the Habitable Worlds Observatory.

In this work we study in detail new kinds of motions of the metric tensor. The work is divided into two main parts. In the first part we study the general existence of Kerr-Schild motions — a recently introduced metric motion. We show that generically, Kerr-Schild motions give rise to finite dimensional Lie algebras and are isometrizable, i.e., they are in a one-to-one correspondence with a subset of isometries of a (usually different) spacetime. This is similar to conformal motions. There are however some exceptions that yield infinite dimensional algebras in any dimension of the manifold. We also show that Kerr-Schild motions may be interpreted as some kind of metric symmetries in the sense of having associated some geometrical invariants. In the second part, we suggest a scheme able to cope with other new candidates of metric motions from a geometrical viewpoint. We solve a set of new candidates which may be interpreted as the seeds of further developments and relate them with known methods of finding new solutions to Einstein's field equations. The results are similar to those of Kerr-Schild motions, yet a richer algebraic structure appears. In conclusion, even though several points still remain open, the wealth of results shows that the proposed concept of generalized metric motions is meaningful and likely to have a spin-off in gravitational physics. We end by listing and analyzing some of those open points.

Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure atmospheric properties. Previous calculations have shown that a change in the orbital phase would cause a spectral signal, but whether this signal may be used to characterize the atmosphere has not been shown. We simulate starshade-enabled observations of the planet 47 Uma b, using the to-date most realistic simulator SISTER to estimate the uncertainties due to residual starlight, solar glint, and exozodiacal light. We then use the Bayesian retrieval algorithm ExoReL\\(^\\) to determine the constraints on the atmospheric properties from observations using a Roman- or HabEx-like telescope, comparing the strategies to observe at multiple orbital phases or in multiple wavelength bands. With a \\(20\\%\\) bandwidth in 600 - 800 nm on a Roman-like telescope, the retrieval finds a degenerate scenario with a lower gas abundance and a deeper or absent cloud than the truth. Repeating the observation at a different orbital phase or at a second \\(20\\%\\) wavelength band in 800 - 1000 nm, with the same integration time and thus degraded S/N, would effectively eliminate this degenerate solution. Single observation with a HabEx-like telescope would yield high-precision constraints on the gas abundances and cloud properties, without the degenerate scenario. These results are also generally applicable to high-contrast spectroscopy with a coronagraph with a similar wavelength coverage and S/N, and can help design the wavelength bandwidth and the observation plan of exoplanet direct imaging experiments in the future.

Future weak lensing analyses with the Nancy Grace Roman Space Telescope will require highly realistic image simulations to control shear systematics at unprecedented precision. A key limitation of existing approaches is their reliance on analytic light-profile models, which cannot fully capture the complex, non-parametric morphologies revealed by high-resolution observations. We present a diffusion-based framework for generating realistic galaxy image simulations tailored to the weak lensing requirements of the Roman High Latitude Survey. We construct Roman-like galaxy images from multi-band JWST/NIRCam observations in the GOODS-S and GOODS-N fields, transforming them into the Roman observing regime through point-spread-function matching, pixel-scale conversion, and interloper masking that preserves correlated noise properties. These data are used to train a denoising diffusion probabilistic model to generate multi-band galaxy postage stamps in the Roman Y, J, and H filters. We validate the generated sample against an independent dataset using a consistent photometric pipeline, comparing key galaxy observables including magnitude, size, ellipticity, peak surface brightness, and three-band colors. The generated galaxies reproduce both the marginal distributions and the covariance structure of these properties, with only modest deviations in low-occupancy regions of parameter space. These results demonstrate that diffusion models provide a scalable and physically motivated alternative to analytic simulations, enabling high-fidelity galaxy populations for Roman weak lensing calibration and, more generally, for survey preparation in upcoming cosmological experiments.

Understanding and mitigating measurement systematics in weak lensing (WL) analysis requires large datasets of realistic galaxies with diverse morphologies and colors. Missions like Euclid, the Nancy Roman Space Telescope, and Vera C. Rubin Observatory's Legacy Survey of Space and Time will provide unprecedented statistical power and control over systematic uncertainties. Achieving the stringent shear measurement requirement of \\( m < 10^-3\\) demands analyzing \\(10^9\\) galaxies. Accurately modeling galaxy morphology is crucial, as it is shaped by complex astrophysical processes that are not yet fully understood. Subtle deviations in shape and structural parameters can introduce biases in shear calibration. The interplay between bulges, disks, star formation, and mergers contributes to morphological diversity, requiring simulations that faithfully reproduce these features to avoid systematics in shear measurements. Generating such a large and realistic dataset efficiently is feasible using advanced generative models like denoising diffusion probabilistic models (DDPMs). In this work, we extend Hubble Space Telescope (HST) data across Euclid's broad optical band using CANDELS and develop a generative AI tool to produce realistic Euclid-like galaxies while preserving morphological details. We validate our tool through visual inspection and quantitative analysis of galaxy parameters, demonstrating its capability to simulate realistic Euclid galaxy images, which will address WL challenges and enhance calibration for current and future cosmological missions.

Future direct imaging missions will primarily observe planets that have been previously detected, mostly via the radial velocity (RV) technique, to characterize planetary atmospheres. In the meantime, direct imaging may discover new planets within existing planetary systems that have bright enough reflected flux, yet with insufficient signals for other methods to detect. Here, we investigate the parameter space within which planets are unlikely to be detected by RV in the near future due to precision limitations, but could be discovered through reflected light with future direct imaging missions. We use the HD 134987 system as a working example, combine RV and direct imaging detection limit curves in the same parameter space through various assumptions, and insert a fictitious planet into the system while ensuring it lies between the RV and imaging detection limits. Planet validity tested through dynamical simulations and retrieval tests revealed that the planet could indeed be detected by imaging while remaining hidden from RV surveys. Direct imaging retrieval was carried out using starshade simulations for two mission concepts: the Starshade Rendezvous Probe that could be coupled with the Nancy Grace Roman Space Telescope, and the Habitable Exoplanet Observatory. This method is applicable to any other systems and high contrast direct imaging instruments, and could help inform future imaging observations and data analysis on the discovery of new exoplanets.