Understanding the formation and evolution of galaxies is a crucially important task in modern astronomy. It is well known that galaxy formation is strongly affected by the environments they reside in. Galaxy clusters, as the densest large-scale structures in the Universe, thus serve as ideal laboratories to study how galaxy formation proceeds in dense environments. Clusters already began to form at $z>2$, therefore to directly witness the early stage of galaxy formation in dense environments, it is necessary to identify progenitors of clusters (`protoclusters') and study their galaxy constituents within. In this thesis, I present two observational studies on high-redshift protoclusters at $z>3$. Utilizing multiwavelength data and different galaxy selection techniques, significant galaxy overdensities are found in the two protoclusters, which are predicted to evolve into Coma-like clusters by present day. Various types of galaxies are identified in the protocluster, such as normal star-forming galaxies, massive quiescent galaxies and post-starburst galaxies. Together with extreme and rare sources such as giant Lyman-alpha nebulae and brighest cluster galaxy, they paint a picture of how different galaxy populations trace the underlying dark matter halos. Finally, the environmental impact on galaxy properties appears to be a subtle one for these protoclusters, which might depend on the galaxy population one chooses to study.

<p dir="ltr">In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.</p>

<p dir="ltr">Fitting the background-subtracted spectral data of SN 1991T indicates that the gamma rays emitted by the 56Fe nuclei are shifted to lower energies at the 3.2σ statistical level. The average energy shift of both the first and second excited states is found to be δE/E = 0.023±0.007 where the uncertainty is given at one standard deviation. Assuming this energy shift is constant as the universe evolves over time implies that δ ˙ E/E = (5.2±1.7)×10−10 yr−1. It is assumed that this energy shift is caused by a dynamical pseudoscalar field Q that acts as dark energy with a coupling to the nucleons of atoms. This interaction would cause an apparent variation in the mass of the pion, thereby shifting the gamma ray energies. To relate the energy deviation to the pion mass and Q, the excited 56Fe nucleus is modeled as a deformed rigid rotor and vibrating liquid drop. The implied pion mass variation, indicated by the observed energy deviations, is found to be δ ˙ m/m=−(2.2±0.7)×10−10 yr−1, modeling the nucleus as a deformed rigid rotor, and δ ˙ m/m=−(2.5±0.8)×10−10 yr−1, modeling the nucleus as a vibrating liquid drop. It can also be used to determine the value of ˙ Q, which corresponds to the term of the dark energy field that changes as the universe evolves. This quantity will depend on the free parameters α and p, which are the decay constant coefficient of the field and the power of the quintessence tracking potential, respectively. The maximum value of ˙ Q will result for α = 0.1 and p = 1. These values are ˙ Q = (1.07±0.35)×108 GeV/yr for the nucleus as a rigid rotor and ˙ Q = (1.22 ± 0.39) × 108 GeV/yr for the nucleus as a vibrating liquid drop. The measured values of the dark energy equation of state parameter determined by DESI observations of the BAO and complemented by Planck observations of the CMB and SNe indicate that there exists an allowed α–p parameter space. This implies that the fractional kinetic energy densities determined by ˙ Q are consistent with cosmological observations under the assumptions that are used throughout this work. Here upper limits are also presented to take into account the possibility that the observed energy deviations are caused by an unknown systematic error.</p>

<p>This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist.</p>

<p>Entanglement entropy (EE) is a quantum information theoretic measure that quantifies the correlations between a region and its surroundings. We study this quantity in the following two setups : </p> <ul> <li>We look at the dynamics of a free minimally coupled, massless scalar field in a deSitter expansion, where the expansion stops after some time (i.e. we quench the expansion) and transitions to flat spacetime. We study the evolution of entanglement entropy (EE) and the Rényi entropy of a spatial region during the expansion and, more interestingly, after the expansion stops, calculating its time evolution numerically. The EE increases during the expansion but the growth is much more rapid after the expansion ends, finally saturating at late times, with saturation values obeying a volume law. The final state of the subregion is a partially thermalized state, reminiscent of a Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.</li> <li>We study the EE in a theory that is holographically dual to a BTZ black hole geometry in the presence of a scalar field, using the Ryu-Takayangi (RT) formula. Gaberdiel and Gopakumar had conjectured that the theory of N free fermions in 1+1 dimensions, for large N, is dual to a higher spin gravity theory with two scalar fields in 2+1 dimensions. So, we choose our boundary theory to be the theory of N free Dirac fermions with a uniformly winding mass, m e^iqx, in two spacetime dimensions (which describes for instance a superconducting current in an N-channel wire). However, to O(m²), thermodynamic quantities can be computed using Einstein gravity. We aim to check if the same holds true for entanglement entropy (EE). Doing calculations on both sides of the duality, we find that general relativity does indeed correctly account for EE of single intervals to O(m²).</li> </ul>