Proton radiotherapy has recently become a popular form of cancer treatment. For maximum effectiveness, accurate models are needed to calculate proton angular scattering and energy loss. Scattering events are statistically independent and may be calculated from the effective number of events per reciprocal multiple scattering angle or energy loss. It is shown that multiple scattering distributions from Molière’s scattering law can be convolved by depth for accurate numerical calculation of angular distributions in several example materials. This obviates the need for correction factors to the analytic solution and its approximations. It is also shown that numerically solving Molière’s scattering law in terms of the complete (non-small angle) differential cross section and large angle approximations extends the validity of Molière theory to large angles. To calculate probability energy loss distributions, Landau-Vavilov theory is adapted to Fourier transforms and extended to very thick targets through convolution over the probability energy loss distributions in each depth interval. When the depth is expressed in terms of the continuous slowing down approximation (CSDA) the resulting probability energy loss distributions rely on the mean excitation energy as the sole material dependent parameter. Through numerical calculation of the CSDA over the desired energy loss, this allows the energy loss cross section to vary across the distribution and accurately accounts for broadening and skewness for thick targets in a compact manner. An analytic, Fourier transform solution to Vavilov’s integral is shown. A single scattering nuclear model that calculates large angle dose distributions that have a similar functional form to FLUKA (FLUktuierende KAskade) Monte Carlo, is also introduced. For incorporation into Monte Carlo or a treatment planning system, lookup tables of the number of scattering events or cross sections for different clinical energies may be used to determine angular or energy loss distributions.

As a demonstration study of low-resolution spectrophotometry, the photometric redshift estimation with narrow-band optical photometry of nine galaxy clusters is presented in this thesis. A complete data reduction process of the photometryusing up to 16 10nm wide narrow-band optical filters from 490nm − 660nm are provided. Narrow-band photometry data are combined with broad-band photometry (SDSS/Pan-STARRS) for photometric redshift fitting. With available spectroscopic redshift data from eight of the fields, I evaluated the fitted photometric redshift results and showed that combining broad-band photometric data with narrow-band data result in improvements of factor 2-3, compared to redshift estimations from broad-band photometry alone. With 15 or 16 narrow-band data combined with SDSS (Sloan Digital Sky Survey) or Pan-STARRS1 (The Panoramic Survey Telescope and Rapid Response System) data, a Normalized Median Absolute Deviation of σNMAD ∼ 0.01−0.016 can be achieved. The multiband images of galaxy cluster ABELL 611 have been used to further study intracluster light around its brightest cluster galaxy (BCG). It can be shown here that fitting of BCG+ICL stellar properties using the averaged 1-dimensional radial profile is possible up to ∼ 100kpc within this cluster. The decreasing in age of the stellar population as a function of radius from the BCG+ICL profile, though not entirely conclusive, demonstrates possible future application of low-resolution spectrophotometry on the ICL studies. Finally, Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx) mission planning study are covered, and a methodology of visualization tool for target availability is described.

In this dissertation I discuss about calculating one-loop partition function on curved spacetimes and various approaches to build symmetries of gravitational systems, and extending the analysis to the large dimensional spacetimes. I show the calculations pertaining to the contributions to the one-loop determinant for transverse trace-less gravitons in an $n + 3$-dimensional Schwarzschild black hole background in the large dimension limit, due to the $SO(n+2)$-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly I find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter $\Delta$. I show that the behavior of the one-loop determinant at large $\Delta$ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit. I also find that the analysis of building one-loop determinants is similar to that of the AdS, thus serving as a motivation to explore this emergent symmetry in detail. For this, I first build these symmetries for Kerr-(A)dS black holes in arbitrary dimensions and then extend this analysis to the large dimensional Schwarzschild black hole. To study the former, in this dissertation, I discuss how to generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. I also discuss the results on building the $SL(2, R)$ generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. This construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: I use the Killing tower to build a novel tensor equation connecting the $SL(2,R)$ Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions I discuss that the previously known results that were obtained using the ``near-region'' limit and the monodromy method, were recovered. I also perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. Lastly, I discuss the work on extending this analysis to the large-dimensional Schwarzschild black hole as a step towards building a Large-D/CFT correspondence.

Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC. Using the same argument, I show logarithmic quantum corrections to the Bekenstein-Hawking entropy formula do not alter the form of the Ricci convergence condition, but obscure its connection to the NEC. Then, by attributing thermodynamics to the stretched horizon of future lightcones -- a timelike hypersurface generated by a collection of radially accelerating observers with constant and uniform proper acceleration -- I derive Einstein's equations from the Clausius relation. Based on this derivation I uncover a local first law of gravity, connecting gravitational entropy to matter energy and work. I then provide an entanglement interpretation of stretched lightcone thermodynamics by extending the entanglement equilibrium proposal. Specifically I show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. Using the AdS/CFT correspondence, I then provide a microscopic explanation of the 'thermodynamic volume' -- the conjugate variable to the pressure in extended black hole thermodynamics -- and reveal the super-entropicity of three-dimensional AdS black holes is due to the gravitational entropy overcounting the number of available dual CFT states. Finally, I conclude by providing a recent generlization of the extended first law of entanglement, and study its non-trivial 2+1- and 1+1-dimensional limits. This thesis is self-contained and pedagogical by including useful background content relevant to emergent gravity.

In this dissertation, I present the results from my recent

investigations into the interactions involving topological defects, such as

magnetic monopoles and strings, that may have been produced in the early

universe. I performed numerical studies on the interactions of twisted

monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of

values of the scalar to vector mass ratio. Sphaleron solution predicted by

Taubes was recovered, and I mapped out its energy and size as functions of

parameters. I also looked into the production, and decay modes of $U(1)$ gauge

and global strings. I demonstrated that strings can be produced upon evolution

of gauge wavepackets defined within a certain region of parameter space. The

numerical exploration of the decay modes of cosmic string loops led to the

conclusions that string loops emit particle radiation primarily due to kink

collisions, and that their decay time due to these losses is proportional to

$L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay

time due to gravitational radiation scales in proportion to $L$, and I

concluded that particle emission is the primary energy loss mechanism for loops

smaller than a critical length scale, while gravitational losses dominate for

larger loops. In addition, I analyzed the decay of cosmic global string loops

due to radiation of Goldstone bosons and massive scalar ($\chi$) particles.

The length of loops I studied ranges from 200-1000 times the width of the

string core. I found that the lifetime of a loop is approximately $1.4L$. The

energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$

is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is

the mass of $\chi$. The latter is a new feature and implies a peak at high

energies (MeV-GeV) in the cosmological distribution of QCD axions.

Chiral symmetry and its anomalous and spontaneous breaking play an important role

in particle physics, where it explains the origin of pion and hadron mass hierarchy

among other things.

Despite its microscopic origin chirality may also lead to observable effects

in macroscopic physical systems -- relativistic plasmas made of chiral

(spin-$\frac{1}{2}$) particles.

Such plasmas are called \textit{chiral}.

The effects include non-dissipative currents in external fields that could be present

even in quasi-equilibrium, such as the chiral magnetic (CME) and separation (CSE)

effects, as well as a number of inherently chiral collective modes

called the chiral magnetic (CMW) and vortical (CVW) waves.

Applications of chiral plasmas are truly interdisciplinary, ranging from

hot plasma filling the early Universe, to dense matter in neutron stars,

to electronic band structures in Dirac and Weyl semimetals, to quark-gluon plasma

produced in heavy-ion collisions.

The main focus of this dissertation is a search for traces of chiral physics

in the spectrum of collective modes in chiral plasmas.

I start from relativistic chiral kinetic theory and derive

first- and second-order chiral hydrodynamics.

Then I establish key features of an equilibrium state that describes many

physical chiral systems and use it to find the full spectrum of collective modes

in high-temperature and high-density cases.

Finally, I consider in detail the fate of the two inherently chiral waves, namely

the CMW and the CVW, and determine their detection prospects.

The main results of this dissertation are the formulation of a fully covariant

dissipative chiral hydrodynamics and the calculation of the spectrum of collective

modes in chiral plasmas.

It is found that the dissipative effects and dynamical electromagnetism play

an important role in most cases.

In particular, it is found that both the CMW and the CVW are heavily damped by the usual

Ohmic dissipation in charged plasmas and the diffusion effects in neutral plasmas.

These findings prompt a search for new physical observables in heavy-ion collisions,

as well as a revision of potential applications of chiral theories in

cosmology and solid-state physics.

The Cosmic Microwave Background (CMB) has provided precise information on the evolution of the Universe and the current cosmological paradigm. The CMB has not yet provided definitive information on the origin and strength of any primordial magnetic fields or how they affect the presence of magnetic fields observed throughout the cosmos. This work outlines an alternative method to investigating and identifying the presence of cosmic magnetic fields. This method searches for Faraday Rotation (FR) and specifically uses polarized CMB photons as back-light. I find that current generation CMB experiments may be not sensitive enough to detect FR but next generation experiments should be able to make highly significant detections. Identifying FR with the CMB will provide information on the component of magnetic fields along the line of sight of observation.

The 21cm emission from the hyperfine splitting of neutral Hydrogen in the early universe is predicted to provide precise information about the formation and evolution of cosmic structure, complementing the wealth of knowledge gained from the CMB.

21cm cosmology is a relatively new field, and precise measurements of the Epoch of Reionization (EoR) have not yet been achieved. In this work I present 2σ upper limits on the power spectrum of 21cm fluctuations (Δ²(k)) probed at the cosmological wave number k from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) 64 element deployment. I find upper limits on Δ²(k) in the range 0.3 < k < 0.6 h/Mpc to be (650 mK)², (450 mK)², (390 mK)², (250 mK)², (280mK)², (250 mK)² at redshifts z = 10.87, 9.93, 8.91, 8.37, 8.13 and 7.48 respectively

Building on the power spectrum analysis, I identify a major limiting factor in detecting the 21cm power spectrum.

This work is concluded by outlining a metric to evaluate the predisposition of redshifted 21cm interferometers to foreground contamination in power spectrum estimation. This will help inform the construction of future arrays and enable high fidelity imaging and

cross-correlation analysis with other high redshift cosmic probes like the CMB and other upcoming all sky surveys. I find future

arrays with uniform (u,v) coverage and small spectral evolution of their response in the (u,v,f) cube can minimize foreground leakage while pursuing 21cm imaging.

Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$ gravity allows for traversable wormholes among its vacuum solutions. This is surprising to find in such simple setting as these type of solutions usually requires fairly complex constructions to satisfy the equations of motion of a gravitational theory. The second idea is the matter bounce description of the early universe where a fairly unique feature of the model is identified. Consequences of this feature could allow the paradigm to distinguish itself from other alternative descriptions, such as inflation, through late time observations. An explicit example of this claim is worked out by studying a model involving an interaction in the dark sector. Results of a more astrophysical nature, where a careful analysis of the morphology of blazar halos is performed, are also presented in the Appendix. The analysis determined that the $Q$-statistic is an appropriate tool to probe the properties of the intergalactic magnetic fields responsible for the halos formation.

The work presented in this dissertation examines three different nonequilibrium particle physics processes that could play a role in answering the question “how was the particle content of today’s universe produced after the big bang?” Cosmic strings produced from spontaneous breaking of a hidden sector $U(1)_{\rm X}$ symmetry could couple to Standard Model fields through Higgs Portal or Kinetic Mixing operators and radiate particles that contribute to the diffuse gamma ray background. In this work we calculate the properties of these strings, including finding effective couplings between the strings and Standard Model fields. Explosive particle production after inflation, known as preheating, would have produced a stochastic background of gravitational waves (GW). This work shows how the presence of realistic additional fields and interactions can affect this prediction dramatically. Specifically, it considers the inflaton to be coupled to a light scalar field, and shows that even a very small quartic self-interaction term will reduce the amplitude of the gravitational wave spectrum. For self-coupling $\lambda_{\chi} \gtrsim g^2$, where $g^2$ is the inflaton-scalar coupling, the peak energy density goes as $\Omega_{\rm GW}^{(\lambda_{\chi})} / \Omega_{\rm GW}^{(\lambda_{\chi}=0)} \sim (g^2/\lambda_{\chi})^{2}$. Finally, leptonic charge-parity (CP) violation could be an important clue to understanding the origin of our universe's matter-antimatter asymmetry, and long-baseline neutrino oscillation experiments in the coming decade may uncover this. The CP violating effects of a possible fourth ``sterile" neutrino can interfere with the usual three neutrinos; this work shows how combinations of various measurements can help break those degeneracies.