The objective of this thesis is to derive a supersymmetric Lagrangian for fermionic fields with mass dimension one and to discuss their coupling to the O'Raifeartaigh model which is the simplest model permitting supersymmetry breaking. In addition it will be shown that eigenspinors of the charge conjugation operator (ELKO) exhibit a different transformation behaviour under discrete symmetries than previously assumed.<p> The calculations confirm that ELKO spinors are not eigenspinors of the parity operator and satisfy (<i>CPT</i>)² = - 1 which identifies them as representation of a nonstandard Wigner class. However, it is found that ELKO spinors transform symmetrically under parity instead of the previously assumed asymmetry. Furthermore, it is demonstrated that ELKO spinors transform asymmetrically under time reversal which is opposite to the previously reported symmetric behaviour. These changes affect the (anti)commutation relations that are satisfied by the operators acting on ELKO spinors. Therefore, ELKO spinors satisfy the same (anti)commutation relations as Dirac spinors, even though they belong to two different representations of the Lorentz group.<p> Afterwards, a supersymmetric model for fermionic fields with mass dimension one based on a general superfield with one spinor index is formulated. It includes the systematic derivation of all associated chiral and anti-chiral superfields up to third order in covariant derivatives. Starting from these fundamental superfields a supersymmetric on-shell Lagrangian that contains a kinetic term for the fermionic fields with mass dimension one is constructed. This on-shell Lagrangian is subsequently used to derive the on-shell supercurrent and to successfully formulate a consistent second quantisation for the component fields. In addition, the Hamiltonian in position space that corresponds to the supersymmetric Lagrangian is calculated. As the Lagrangian is by construction supersymmetric and the second quantisation of the component fields is consistent with their general supertranslations, the Hamiltonian is positive definite. This is confirmed by the results for the Hamiltonian in momentum space and the derivation of the creation and annihilation operators in momentum space. Based on these results, fermionic fields with mass dimension one represent an intriguing candidate for supersymmetric dark matter.<p> As an application the coupling of the fermionic fields with mass dimension one to the O'Raifeartaigh model is discussed. It turns out that the coupled model has two distinct solutions. The first solution representing a local minimum of the superpotential spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case the coupling to the fermionic sector restores supersymmetry. This is, however, achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension.<p> These results show that the presented model for fermionic fields with mass dimension one is a viable candidate for supersymmetric dark matter that could be accessible to experiments in the near future.

Different aspects of specific models in supersymmetry as well as constraints on decaying dark matter are analysed in this thesis. In chapter 1 we give a general introduction to supersymmetry, and briefly discuss some of the concepts that are used throughout the thesis. In chapter 2 we present a version of Gauge Mediated Supersymmetry Breaking which preserves an $R$-symmetry---the gauginos are Dirac particles, the $A$-terms are zero, and there are four Higgs doublets. This offers an alternative way for gauginos to acquire mass in the supersymmetry-breaking models of Intriligator, Seiberg, and Shih \cite{Intriligator:2006dd} . Additionally, we investigate the possibility of using $R$-symmetric gauge mediation to realise the spectrum and large sfermion mixing of the model of Kribs, Poppitz, and Weiner \cite{Kribs:2007ac}. In chapter 3 we investigate the Higgs sector of the $R$-symmetric model presented in chapter 2. Furthermore, a scan of the parameter space and sample spectra are provided. Other attributes like the tuning of the model are discussed. In chapter 4 we present a complete analysis of the cosmological constraints on decaying dark matter. In order to do this, we have updated and extended previous analyses to include Lyman-$\alpha$ forest, large scale structure, and weak lensing observations. Astrophysical constraints are not considered in this thesis. The bounds on the lifetime of decaying dark matter are dominated by either the late-time integrated Sachs-Wolfe effect for the scenario with weak reionization, or CMB polarisation observations when there is significant reionization. For the respective scenarios, the lifetimes for decaying dark matter are $\Gamma^{-1} \gtrsim 100$ Gyr and $ (f \Gamma) ^{-1} \gtrsim 5.3 \times 10^8$ Gyr (at 95.4\% confidence level), where the phenomenological parameter $f$ is the fraction of the decay energy deposited in baryonic gas. This allows us to constrain particle physics models with dark matter candidates through investigation of dark matter decays into Standard Model particles via effective operators. For decaying dark matter of $\sim 100$ GeV mass, we found that the size of the coupling constant in the effective dimension-4 operators responsible for dark matter decay has to generically be $ \lesssim 10^{-22}$.

We have investigated the use of the graphical processing unit to accelerate the software package DarkSUSY. DarkSUSY is, among other things, used for calculating the dark matter relic density -- an measurable quantity -- given the supersymmetric neutralino, χ, as a dark matter candidate. Supersymmetric theories have many free parameters and we want to calculate the relic density for large areas of the parameter space. The results can then be compared with observations and to constrain the parameters. A faster DarkSUSY would allow for larger searches in the parameter space. We modified DarkSUSY using Nvidia's CUDA platform and wrote a program that, by using the GPU, calculates the χ + χ &lt;-&gt; W+ + W- contribution to the annihilation cross-section. Our initial try was only negligible faster than our non-CUDA program due to under-utilization of the GPU, but solving that the program was 47 times faster than the reference program. We also report on difficulties we faced, both solved and unsolved so the reader can make an informed decision on the worth of rewriting so that the heavy calculations in DarkSUSY use the GPU. / Vi har undersökt om man kan använda grafikkortet för att få mjukvarupaketet DarkSUSY snabbare. DarkSUSY används, bland annat, för att beräkna relikdensiteten av mörk materia -- en mätbar kvantitet -- användandes den supersymmetriska neutralinon, χ, som mörk materia-kandidat. Supersymmetriska teorier har många fria parametrar och vi vill beräkna relikdensiteten för stora områden av parameterrummet. Resultaten kan sedan jämföras med observationer för att begränsa parametrarna. Ett snabbare DarkSUSY skulle tillåta större sökningar i parameterrummet. Vi modifierade DarkSUSY med hjälp av Nvidias CUDA-platform och skrev ett program som, genom att använda grafikkortet, beräknar χ + χ &lt;-&gt; W+ + W- kanalens bidrag till annihilationstvärsnittet. Vårt första försök var bara försumbart snabbare än vårt icke-CUDA program på grund av underanvändning av grafikkortet. Men med det åtgärdat så var programmet 47 gånger snabbare än referensprogrammet. Vi rapporterar också de problem vi stött på, både de vi löste och de vi inte löste. Detta så att läsaren kan avgöra värdet av att omarbeta så att alla de beräkningsintensiva delarna av DarkSUSY använder grafikkortet.

Though the arrival directions of ultra-high-energy cosmic rays (UHECRs) are distributed in a relatively isotropic manner, there is evidence of small-scale anisotropy. This, combined with the detection of cosmic rays with energies above the GZK cut-off, has motivated us to further investigate the idea that UHECRs are the result of a top-down mechanism involving the annihilation of superheavy dark matter particles in our galactic halo. To more precisely characterize the nature of dark matter, we have endeavoured to apply two different models to the leading UHECR spectra, namely those from the AGASA, High Resolution Flys Eye, and Pierre Auger Collaborations. First, we attempt a non-linear, least-squares fit of the particle physics fragmentation function to the spectra. Second, we propose that the observed cosmic ray spectrum above 3.5 × 10E+18 eV is the superposition of flux from two different sources: bottom-up acceleration via a simple power-law relation at lower energies and scattered particles from dark matter annihilation governed by fragmentation functions at higher energies. We find that while the former model does not provide a satisfactory fit to observatory data, the latter yields reduced χ2 values between 1.14 and 2.6. From the fragmentation function component of our second model, we are able to extract estimates of dark matter particle mass. We find values of (1.2 ± 0.6) 10E+21 eV, (5.0 ± 4.3) 10E+20 eV, and (2.6 ± 1.5) 10E+21 eV respectively for the AGASA, HiRes, and Pierre Auger data, which agree with earlier predictions based on a cosmological analysis of non-thermal particle production in an inflationary universe. Furthermore, we verify that the dark matter particle densities required by our two-source model are in line with current CDM theory.

Galaxies and clusters of galaxies are believed to be dominated by non-luminous non-baryonic dark matter. A favored candidate is a new type of Weakly Interacting Massive Particle (WIMP) with a mass of order 100 GeV/c^2. The ZEPLIN II experiment is a WIMP search experiment that attempts to directly detect WIMP interactions using the two-phase xenon approach. The detector measures both scintillation and ionization generated by interactions in a 31 kg liquid xenon target. This approach provides a powerful discrimination between nuclear recoils, as expected from WIMPs, and background electron recoils. In this work, we develop a new X^2 approach to determine the three dimensional event positions in an attempt to improve the background rejection. The optical properties of the PTFE reflectors and the grids of the detector were determined using the Geant4 simulation, and event positions were obtained by finding the best match to the amount of light in each photomultiplier. This was found to greatly improve the position resolution. The approach was then applied to the WIMP search data. It was found that one of the dominating background sources was events from the gas above the anode grid and not from the PTFE walls caused by the small signals as previously thought. WIMP search results were then obtained from the first 31 days of stable ZEPLIN II data using two methods. Although the X^2 method greatly improved position resolution, the number of background events was not significantly altered and the new limit agreed well with the limit published by the collaboration.

The most popular way to achieve accelerated expansion of the universe is by introducing a scalar field in which motion of state varies with time. The accelerated expanded universe was first observed by Type Ia supernovae and future confirmed by the latest of CMB (Cosmic Microwave Background). The reason for the accelerated universe is the existence of dark energy. In this dissertation, we discuss the relationship between dark matter, dark energy, reheating and the standard model, and we find that it is possible for us to unify dark energy, dark matter and a reheating field into one scalar field. There is a very important stage called inflationary, and we find that the residue of the inflationary field, which is also described by a scalar field, can form bubbles in our universe due to the gravity force. We discuss that these bubbles are stable since they are trapped in their potential wells, and the bubbles can be a candidate for dark matter. We also discuss the scalar singlet filed, with the simplest interaction with the Higgs field, and we find that a static, classical droplet can be formed. The physics picture of the droplet is natural, and it is almost the same as the formation of an oil droplet in water. We show that the droplet is absolutely stable. Due to the very weak interaction with the Standard Model particles, the droplet becomes a very promising candidate for dark matter.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 243-256).

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, December 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, August 2003. / Includes bibliographical references. Also available on the Internet.

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