David M Goldberg

We present ARCH (Adaptive Reconstruction of Cluster Halos), a new gravitational lensing pipeline for cluster mass reconstruction that applies a joint shear-flexion analysis to JWST imaging. Previous approaches have explored joint shear+flexion reconstructions through forward modeling and Bayesian inference frameworks; in contrast, ARCH adopts a staged optimization strategy that incrementally filters and selects candidate halos rather than requiring a global likelihood model or strong priors. This design makes reconstruction computationally tractable and flexible, enabling systematic tests of multiple signal combinations within a unified framework. ARCH employs staged candidate generation, local optimization, filtering, forward selection, and global strength refinement, with a combined fit metric weighted by per-signal uncertainties. Applies to Abell 2744 and El Gordo, the pipeline recovers convergence maps and subcluster masses consistent with published weak+strong lensing results. In Abell 2744 the central core mass within 300 $h^{-1}$kpc is$2.1\times 10^{14} M_\odot h^{-1}$ , while in El Gordo the northwestern and southeastern clumps are recovered at$2.6\times 10^{14} M_\odot h^{-1}$and$2.3\times 10^{14} M_\odot h^{-1}$ . Jackknife resampling indicates typical 1 $σ$uncertainties of$10^{12}-10^{13} M_\odot h^{-1}$ , with the all signal and shear+ $\mathcal{F}$reconstructions providing the most stable results. These results demonstrate that flexion, when anchored by shear, enhances sensitivity to cluster substructure while maintaining stable cluster-scale mass recovery.

"Special relativity challenges one's physical intuition of space, time, matter, and energy in a way that few other topics in physics do. Yet the subject is often treated as an extra in undergraduate courses-something to be picked up in a few random lectures and presented as a combination of geometric and logical puzzles (seemingly with the premise of getting the novice student to concede that Einstein was a genius and that the universe is weird). But special relativity is absolutely fundamental to modern physics. It is the canvas on which electromagnetism, particle physics, field theory, and ultimately general relativity are based. For physics students, developing a relativistic intuition isn't just a luxury: it's a requirement. Physicist and popular author Dave Goldberg provides a rigorous but conversational introduction to fill this void in spacetime education. Employing the standard calculus a sophomore or junior university student in science, engineering, or computer science will have encountered, Goldberg connects relativity to a student's work ahead, acquainting them with topics like tensors, the development of new physical theories, and how relativity directly relates to other disciplines. But more than this, Goldberg welcomes lifelong learners who may have encountered special relativity in popular accounts, but are seeking a mathematical challenge to understand an elegant physical theory"--

We perform a flexion-based weak gravitational analysis of the first two Hubble Frontier Field clusters: Abell 2744 and MACS 0416. A parametric method for using radially projected flexion signals as a probe of cluster member mass is described in detail. The normalization and slope of a L - theta(E) (as a proxy for L - sigma) scaling relation in each cluster is determined using measured flexion signals. A parallel field analysis is undertaken concurrently to provide a baseline measure of method effectiveness. We find an agreement in the Faber-Jackson slope l associated with galaxy age and morphology for both clusters, as well as a theoretical distinction in the cluster normalization mass.

We calculate the Bayesian evidences for a class of Ekpyrotic universe models, and compare with a model of single field inflation with a Higgs-type potential. Combining parsimony and observational constraints, this gives us a systematic way to evaluate the degree to which Ekpyrotic models are constrained by CMB data from Planck. We integrate the equations of motion numerically to define a likelihood using Planck 2018 data and sample this likelihood to obtain Bayesian evidences. Priors are justified and used to put Ekpyrotic models and inflation on equal footing. We find reasonable preference for one of the considered Ekpyrotic models over the others, but that even this one is disfavored compared with Higgs inflation.

Canonically, elliptical galaxies might be expected to have a perfect rotational symmetry, making them ideal targets for flexion studies - however, this assumption has not been tested. We have undertaken an analysis of low- and high-redshift galaxy catalogues of known morphological type with a new gravitational lensing code, Lenser. Using colour measurements in the u - r bands and fit Sersic index values, objects with characteristics consistent with early-type galaxies are found to have a lower intrinsic scatter in flexion signal than late-type galaxies. We find this measured flexion noise can be reduced by more than a factor of two at both low and high redshift.

We present the first flexion-focused gravitational lensing analysis of the Hubble Frontier Field observations of Abell 2744 (z = 0.308). We apply a modified Analytic Image Model technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin(-2). By using flexion data alone, we are able to identify the primary mass structure aligned along the heart of the cluster in addition to two major substructure peaks, including an NE component that corresponds to previous lensing work and a new peak detection offset 1.43 arcmin from the cluster core towards the east. We generate two types of non-parametric reconstructions: flexion aperture mass maps, which identify central core, E, and NE substructure peaks with mass signal-to-noise contours peaking at 3.5 sigma, 2.7 sigma, and 2.3 sigma, respectively; and convergence maps derived directly from the smoothed flexion field. For the primary peak, we find a mass of (1.62 +/- 0.12) x 10(14) h(-1)M(circle dot) within a 33 arcsec (105 h(-1) kpc) aperture, a mass of (2.92 +/- 0.26) x 10(13) h(-1)M(circle dot) within a 16 arcsec (50h(-1) kpc) aperture for the north-eastern substructure, and (8.81 +/- 0.52) x 10(13) h(-1)M(circle dot) within a 25 arcsec (80 h(-1) kpc) aperture for the novel eastern substructure.

We present results for utilizing weak lensing analysis in the identification and classification of the dark matter substructure in galaxy clusters. Using a previously developed flexion analysis package (FLEXTOOL) gravitationally lensed images are analyzed for their flexion signal, the anisotropic inward "bowing" of a lensed object. The measured flexion signal can be decomposed toward a nearest-neighbor lensing galaxy as a means for identifying dark matter structure within the lensing galaxy cluster. A figure-of-merit is developed for classifying the underlying substructure using source object size, measured flexion strength and nearest-neighbor radial distance. The analysis is applied to the Abell 2744 and MACS J0416.1-2403 galaxy clusters in the HST Frontier Fields program. This is the first such work that directly identifies individual substructure using weak gravitational flexion.

For a theory as genuinely elegant as the Standard Model the current framework describing elementary particles and their forces it can sometimes appear to students to be little more than a complicated collection of particles and ranked list of interactions. The Standard Model in a Nutshell provides a comprehensive and uncommonly accessible introduction to one of the most important subjects in modern physics, revealing why, despite initial appearances, the entire framework really is as elegant as physicists say. Dave Goldberg uses a "just-in-time" approach to instruction that enables students to gradually develop a deep understanding of the Standard Model even if this is their first exposure to it. He covers everything from relativity, group theory, and relativistic quantum mechanics to the Higgs boson, unification schemes, and physics beyond the Standard Model. The book also looks at new avenues of research that could answer still-unresolved questions and features numerous worked examples, helpful illustrations, and more than 120 exercises. Provides an essential introduction to the Standard Model for graduate students and advanced undergraduates across the physical sciences. Requires no more than an undergraduate-level exposure to quantum mechanics, classical mechanics, and electromagnetism Uses a "just-in-time" approach to topics such as group theory, relativity, classical fields, Feynman diagrams, and quantum field theory Couched in a conversational tone to make reading and learning easier Ideal for a one-semester course or independent study Includes a wealth of examples, illustrations, and exercises Solutions manual (available only to professors)

We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing "cosmic telescope" galaxy clusters, observed as part of the Hubble Frontier Fields initiative. Using HST observations of Abell 2744 (z = 0.308), we apply a modified Analytic Image Model (AIM) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin$^{-2}$. By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43' from the cluster core. We generate two types of nonparametric reconstructions: a flexion aperture mass map, which identifies the central potential and substructure peak with mass signal-to-noise of 3.5$\sigma$ and 2.3$\sigma$ respectively; and a convergence map derived directly from the smoothed flexion field. For the primary peak we find a mass of $1.93\times10^{14}\,h^{-1}\,M_{\odot}$ within a 45" (145h$^{-1}$ kpc) aperture, and for the western substructure we find a mass of $7.12\times10^{13}\,h^{-1}\,M_{\odot}$ within a 25" (80h$^{-1}$ kpc) aperture. The associated peak velocity dispersions were determined to be $\sigma_v$ = 1630 km/s and $\sigma_v$ = 766 km/s, respectively, by fitting nonsingular isothermal sphere profiles to the flexion data. Additionally, we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure, and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions. Finally, we perform the same analysis on the Abell 2744 parallel sky field, and find no strong phantom signals in the noise reconstructions.