| Sažetak (engleski) | Accelerated expansion of the universe is one of key discoveries in modern cosmology. Even though the problem has been worked on for more than two decades, there is still no empirically confirmed theory that would sufficiently explain this phenomenon. In this work, a new methodology of modelling dark energy through implicit equation of state of cosmic fluid is developed: speed of sound is being modelled as a function of parameter w of the equation of state of cosmic fluids. The procedure is demonstrated through establishing new and analysis of already existing models. As can be seen in the equation of acceleration, value of component parameter of equation of state, w = p/ρ, is crucial for the behaviour of expansion of universe. If w > -1/3, the contribution to expansion is decelerating and if w < -1/3, the contribution to expansion is accelerating. The ΛCDM model presumes that w = -1 for dark energy throughout the history of the universe. This assumption, however, leads to some recently observationally established tensions, which is why a dynamic dark energy is investigated: several models and parametrizations are trying to establish a dynamic function where w changes with time. After the primary objective of this work, the development of new methodology, the secondary direction of this work is twofold. The first direction is investigating how much certain functions and parametrizations of w(a) yield results that conform with observation. The second is checking if dark energy in selected and also newly constructed models has the properties of barotropic fluid, i.e., if its pressure is the function of energy density only; also, this means verifying that the value of its speed of sound squared, cˇ2s is always between zero and speed of light squared. Methodology derived in this work will rely heavily on equations derived from the fluid continuity equation. Due to the nature of those equations, behaviour of parameter w around the value of -1 will be especially important because at that point cˇ2s, parameter w and/or other cosmic parameters often go through a singularity. In chapter 2 a model is presented that, in some cases, allows a smooth cosmological constant boundary crossing between areas w < -1 to w > -1. Some results of this model are then compared to observational data. Also, depending on model parameters, possible futures are discussed: Big Rip, Small Rip and transient dark energy. Some of the important parameter regimes show a wide range of scale factor a during which the parameter w is almost constant and close to -1, conforming to the current observational results. Another set of models introduced in this work is the one unifying dark matter and dark energy. Analytical function for c2s (w) yields results that describe behaviour of unified dark fluid that behaves like dark energy or dark matter through different stages of development of the universe: starting with dark matter stage, depending on model parameters, parameter w goes through the stage of dark energy to end up either as phantom energy (w < -1), dark energy with w asymptotically going to w* or shifting back into dark matter regime. The next part of the work deals with collecting around 40 models presented in literature and determining whether dark energy presented there has key properties of barotropic fluid. Analytical examination is performed in two cases and numerical analysis using two methods is performed in all of them, examining if speed of sound squared of the dark fluid remains between zero and speed of light squared for the whole interval of cosmic past (0 < a < a_0). Results show that many models developed since the discovery of accelerated expansion of the universe do not satisfy these conditions. Furthermore, newly constructed models of dark energy are examined through the model of purely kinetic k-essence, formulating it through Lagrange field theory which would connect cosmology with other areas of physics. In all introduced models there is a case of unification of dark matter and dark energy with w shifting from zero or near-zero (depending on model parameters) at a = 0 to w asymptotically going to -1 as a goes to infinity. Finally, observational data of orbital velocities of objects in Milky Way galaxy are examined and used to establish a method of checking if local dark fluid is in concord with properties of barotropic fluid. A model-independent method is derived for calculating speed of sound squared from the observed data using numerical calculation of first and second derivatives of orbital velocity on distance from the galaxy centre. The results mostly show the possibility of dark matter showing properties of barotropic fluid, however, there is significant room for improvement with regard to the accuracy of observed data. |
