For this project, the diffuse supernova neutrino background (DSNB) has been calculated based on the recent direct supernova rate measurements and neutrino spectrum from SN1987A. The estimated diffuse electron antineutrino flux is ∼ 0.10 – 0.59 /cm2/s at 99% confidence level, which is 5 times lower than the Super-Kamiokande 2012 upper limit of 3.0 /cm2/s, above energy threshold of 17.3 MeV. With a Megaton scale water detector, 40 events could be detected above the threshold per year. In addition, the detectability of neutrino bursts from direct black hole forming collapses (failed supernovae) at Megaton detectors is calculated. These neutrino bursts are energetic and with short time duration, ∼ 1s. They could be identified by the time coincidence of N ≥2 or N ≥3 events within 1s time window from nearby (4 – 5 Mpc) failed supernovae. The detection rate of these neutrino bursts could get up to one per decade. This is a realistic way to detect a failed supernova and gives a promising method for studying the physics of direct black hole formation mechanism. Finally, the absorption of ultra high energy (UHE) neutrinos by the cosmic neutrino background, with full inclusion of the effect of the thermal distribution of the background on the resonant annihilation channel, is discussed. Results are applied to serval models of UHE neutrino sources. Suppression effects are strong for sources that extend beyond z ∼ 10. This provides a fascinating probe of the physics of the relic neutrino background in the unexplored redshift interval z ∼ 10 – 100. Ultimately this research will examine the detectability of DSNB, neutrino bursts from failed supernovae and absorption effects in the neutrino spectrum.

Quark matter at sufficiently high density and low temperature is expected to be a color superconductor, and may exist in the interior of neutron stars. The properties of two simplest possible color-superconducting phases, i.e., the color-flavor-locked (CFL) and two-flavor superconducting (2SC) phases, are reviewed. The effect of a magnetic field on the pairing dynamics in two-flavor color-superconducting dense quark matter is investigated. A universal form of the gap equation for an arbitrary magnetic field is derived in the weakly coupled regime of QCD at asymptotically high density, using the framework of Schwinger-Dyson equation in the improved rainbow approximation. The results for the gap in two limiting cases, weak and strong magnetic fields, are obtained and discussed. It is shown that the superconducting gap function in the weak magnetic field limit develops a directional dependence in momentum space. This property of the gap parameter is argued to be a consequence of a long-range interaction in QCD.

There are many lines of evidence for anisotropy at all scales in the explosions of core collapse supernovae, e.g. visual inspection of the images of resolved supernova remnants, polarization measurements, velocity profiles, "natal kicks" of neutron stars, or spectroscopic observations of different regions of remnants. Theoretical stability considerations and detailed numerical simulations have shown that Rayleigh-Taylor (RT) instabilities arise in the star after the explosion, which leads to the early fragmentation of parts of the ejecta. The clumps thus created are of interest to a variety of topics, one of them being the formation environment of the solar system. There is a high probability that the solar system formed in the vicinity of a massive star that, shortly after its formation, exploded as a core collapse supernova. As argued in this thesis as well as other works, a core collapse supernova generally is a good candidate for chemically enriching the forming solar system with material. As forming proto--planetary systems in general have a high probability of being contaminated with supernova material, a method was developed for detecting tracer elements indicative supernova contamination in proto--planetary systems.The degree of the anisotropy of the supernova explosion can have dramatic effects on the mode of delivery of that material to the solar system, or proto--planetary systems in general. Thus it is of particular interest to be able to predict the structure of the supernova ejecta. Numerical simulations of the explosions of core collapse supernovae were done in 3 dimensions in order to study the formation of structure. It is found that RT instabilities result in clumps in the He- and C+O rich regions in the exploding star that are overdense by 1-2 orders of magnitude. These clumps are potential candidates for enriching the solar system with material. In the course of the further evolution of the supernova remnant, these RT clumps are likely to evolve into ejecta knots of the type observed in the Cassiopeia A supernova remnant.

Gamma-ray burst observations provide a great opportunity for cosmography in high redshift. Some tight correlations between different physical properties of GRBs are discovered and used for cosmography. However, data selection, assumptions, systematic uncertainty and some other issues affect most of them. Most importantly, until the physical origin of a relation is understood, one should be cautious to employ the relation to utilize Gamma ray bursts for cosmography. In the first part of this dissertation, I use Liang-Zhang correlation to constrain ¦« Cold Dark Matter standard cosmology and a particular class of brane cosmology (brane-induced gravity model). With the most probable model being ¦¸_m=0.23 and ¦¸_¦«=0.77 for flat ¦«CDM cosmology and ¦¸_m=0.18 and ¦¸_(r_c )=0.17 for flat brane-induced gravity cosmology, my result for the energy components of these two models is comparable with the result from SNIa observation. With average uncertainty of distance modulus being 0.2771, the two discussed cosmologies are indistinguishable using my current sample of GRB with redshift ranging between 0.1685 and 3.2. I argue that by expanding my sample and adding more low and high redshift GRBs and also with improvement in using GRB for cosmography, we might be able to distinguish between different cosmological models and tighten the most probable model. Looking into correlation and evolution of GRB prompt emission and afterglow has many advantages. It helps to open windows to comprehend the physics of GRBs and examine different GRB models. It is also possible to use GRB correlation as an accurate redshift estimator and more importantly to constrain the cosmological parameters. XRT flares of GRB afterglow are thought to be the result of central engine activity. Studying this component leads us to understand GRB flare and central engine nature. In the next part of this dissertation, I study the correlation and evolution of different prompt emission and afterglow GRB properties and some GRB flare-based quantities. Considering instrument bias and selection effect, I conclude some well-correlated correlations and establish some property evolution. The correlation between average luminosity and isotropic ¦Ã-ray energy, energy of plateau and isotropic ¦Ã-ray energy and luminosity at break time and break time and evolution of plateau energy are well established. It is also realized that the apparent evolution of isotropic ¦Ã-ray energy and average luminosity is due to the instrumental flux threshold. With expanding the sample of GRB and accommodating more GRBs with XRT flares to my sample, I can reevaluate my result more firmly and confirm or rule out some hard to assert results due to limited number of data. In search for physically motivated GRB relation, analyzing the thermal component of GRB prompt emission, I derive two well-correlated relations. They are between calculated and estimated flux of the GRB thermal component for the co-moving bolometric and co-moving detector band-pass range of spectrum. In this study, three samples of Swift, pre-Swift and combined samples are used. The quality of this correlation is comparable with the Ghirlanda relation in terms of Spearman rank correlation parameters (correlation coefficient and correlation significance) and reduced ¦Ö^2of best fit. These results for the Swift GRB sample for co-moving bolometric range of spectrum are 0.81, 4.07¡Á¡¼10¡½^(-7) and 0.66 respectively. The derived correlations also imply a E_(¦Ã,iso)-E_peak^4 relation that provides physical insight to E_¦Ã-E_peak Ghirlanda correlation. Three scaling coefficients are employed to study these correlations. Monte Carlo statistics indicates that the existing correlations are independent of these constants. For Swift and combined sample 73% - 84.8% successes are recorded. Therefore, it is expected by determining these constants, the tightness of these correlations will further improve.