In this master’s thesis the width of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> meson is studied as a function of temperature. We consider a background medium consisting of a pion gas and assume a vanishing net baryon chemical potential. The width is obtained in the framework of large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> chiral perturbation theory and we consider terms up to next-to-leading order in the effective Lagrangian. We use a low-density approximation to calculate the width increase due to scattering with pions from the heat bath. The results suggest that the in-medium width for the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may become of considerable size: at a temperature <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?T%5Capprox%2075" /> MeV we find a width increase of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%5CGamma%5Capprox%203-4" /> MeV, comparable to the inverse lifetime of the fireball created in a heavy-ion collision. The <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> is of particular interested since it is intimately connected to the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> anomaly of Quantum Chromodynamics (QCD). It has been speculated that <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> may become a symmetry of QCD at high temperatures and studies of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> could indicate if that is the case. Depending on for how large temperatures the results from large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> can be trusted, they indicate that the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may be possible to study experimentally in heavy-ion collisions due to its sizable in-medium width.

Communication using fiber optics is an integral part of modern societies and one of the most important parts of this is the grating filter of a laser. In this report we introduce both the periodic and the non-periodic grating filter and discuss how there can be resonance in these structures. We then provide an exact method for calculating the spectrum of these grating filters and study three different methods to calculate this approximately. The first one is the \emph{Fourier approximation} which is very simple. For the studied filters the fundamental form of the results for this method is correct, even though the details are not. The second method consists of calculating the spectrum exactly for some values and then use interpolation by splines. This method gives satisfactory results for the types of gratings analysed. Finally a method of perturbation is provided for the periodic grating filter as well as an outline for how this can be extended to the non-periodic grating filter. For the studied filters the results of this method are very promising. The method of perturbations may also give a deeper understanding of how a filter works and we therefore conclude that it would be of interest to study the method of perturbations further, while all the studied methods can be useful for computation of the spectrum depending on the required precision. / Fiberoptisk kommunikation utgör en viktig del i moderna samhällen och en av de grudläggande delarna av detta är Bragg-filter i lasrar. I den här rapporten introducerar vi både det periodiska och det icke-periodiska Bragg-filtret och diskuterar hur resonans kan uppstå i dessa. Vi presenterar sedan en exakt metod för att beräkna spektrumet av dessa filter samt studerar tre approximativa metoder för att beräkna spektrumet. Den första metoden är \emph{Fourier-approximationen} som är väldigt enkel. För de studerade filtrena blir de grundläggande formerna korrekta med Fourier-approximationen, medan detaljerna är fel. Den andra metoden består av att räkna ut spektrumet exakt för några punkter och sedan interpolera med hjälp av splines. Den här metoden ger mycket bra resultat för de studerade filtrena. Till sist presenteras en metod baserad på störningsteori för det periodiska filtret, samt en översikt över hur det här kan utökas till det icke-periodiska filtret. Denna metod ger mycket lovande resulat och den kan även ge djupare insikt i hur ett filter fungerar. Vi sluter oss därför till att det vore intressant att vidare studera metoder med störningar, men även att alla studerade metoder kan vara användabara för beräkningen av spektra beroende på vilken precision som krävs.

Experimental data suggest that the universe is homogeneous and isotropic on sufficiently large scales. An exact solution of the Einstein field equations exists for a homogeneous and isotropic universe, also known as a Friedmann-Lemaître-Robertson-Walker (FLRW) universe. However, this model is only a first approximation since we know that, locally, the universe has anisotropic and inhomogeneous structures such as galaxies and clusters of galaxies. In order to successfully introduce inhomogeneities and anisotropies to the model one uses perturbative methods. In cosmological perturbations the FLRW universe is considered the zeroth order term in a perturbation expansion and perturbation theory is used to derive higher order terms which one tries to match with observations. In this thesis I present a review of the main concepts of general relativity, discuss the 3+1 formalism which gives us the Einstein field equations in a useful form for the perturbative analysis, and lastly, I derive the first order scalar perturbations of the Einstein field equations.