Cosmological perturbations in a universe with an elastic component

In this work we studied the formation, evolution and observation of cosmological perturbations. All of these aspects are discussed in first part, which is meant as a pedagogical introduction and theoretical background to the chapter Extended model. First we introduced briefly the concept of cosmological inflation, after listing the three cosmological problems which are solved by it. A consequence of exponential expansion of the universe during the inflationary era is the formation of cosmological perturbations. We explained this process and the evolution of perturbations in general. Then we studied observational consequences of the presence of perturbations in our universe, the temperature and polarization anisotropies measured in CMB radiation. We modified the standard scenario in the fifth chapter called Extended model. An isotropic solid continuum with elastic properties was introduced there and its effect on the evolution of the perturbations was studied. It turned out that the elastic properties of such continuum can be parametrized by one parameter, shear modulus. All calculations were made in the proper-time comoving gauge, but then they were 'translated' to more commonly used gauge invariant variables first introduced by Bardeen. The main focus of the work was on a one-component universe, with constant ratio of shear modulus to energy density. The solutions for cosmological perturbations in such universe were expressed in terms of Bessel functions, which offered us new possibilities in the analysis of the solutions. The standard solutions found in the literature were shown to be a special case of our solutions. Solutions which could not be expressed in terms of Bessel functions were treated separately and physically motivated restrictions were imposed on the parameters. We presented asymptotic solutions with emphasis put on long-wavelength solutions. We found that perturbations above the horizon decrease and can even oscillate despite the arguments presented in the literature, provided the shear modulus of the continuum is sufficiently large. Then we modified the scenario. We added a specific time dependence of the shear stress to the theory, assuming that the initially zero shear stress parameter instantaneously increased to a final value at the moment of a phase transition. This modification brings some peculiarities to the evolution of the cosmological perturbations, which we have discussed. The complete solutions were found by matching the solutions before and after the phase transition. This scenario is advantageous in that that it allows to modify the evolution of cosmological perturbations without the need to modify the theory of their formation, so that the calculations presented in the theoretical introduction stay valid. We also included a very quick review of the models of elastic solid into the chapter 'Extended model', and supplemented our work by several appendices, meant to ease the orientation of the reader in the text. (author)