Dark Energy, Hyperbolic Cosecant Cardassian and Virial Collapse for Power-style Cardassian

The problem of dark energy(DE) is the greatest challenge for modern physics, and therefore this thesis is dedicated to the modeling establishment of DE. In the first chapter, qualitative and descriptive methods are employed to draw a rough map for the cosmos in its finely analyzed era. Then the dynamical equations of cosmology based on the general relativity are introduced, together with the measuring methods and parameters. The second chapter reviews the results of cosmic microwave background radiation and supernova observations, which conclude the flat topology and accelerating expansion of cosmos, and give rise to existence of DE and the associated dynamical mechanism problem. Taking WMAP data as an example, we introduced the practical parameters. In the end we classify the existing DE models into three categories for further discussion. The first two chapters make up the basis for the whole thesis. Chapter 3 reviews the fundamental structures and research progress of two scalar fields, Quintessence and Phantom, which correspond to the case of EOS beyond -1 and below -1 respectively. Chapter 4 reviews the fundamental structures and research progress of another two scalar fields, Phantom and Quintom with non-canonical lagrangian, both of which have EOS crossing -1. But Phantom field is real, while Quintom complex. Chapter 5 reviews two non-scalar-field DE formalism of K-essence and Chaplygin gas, which are both rooted in modern quantum field theory. Totally six kinds of DE is analyzed, all of which have positive energy density, negative pressure and could drive the lately accelerating expansion. And they are compared and identified in details. New work gathers in Chapter 6 and Chapter 7. Firstly we make a comprehensive analysis of the existing work, pay particular attention to Gondolo and Freese’s idea of treating Cardassian energy term as relativistic perfect fluid(GF fluid), point out that a potential Cardassian term should meet three conditions, and review three existing Cardassian terms (power style, polytropic style and its modification, exponential style and its modification), and eventually put forward the newly found hyperbolic cosecant Cardassian. Then the Cardassian dynamical equations are introduced generally and logically under GF fluid scenario, together with the flowing process of constructing phase space and differential dynamical systems from Friedmann equation. Hyperbolic cosecant Cardassian term is employed for concrete computing. The analysis proceeds in two cases, namely a unified description of matter and radiation energy density (case 1) and a separate description of matter and radiation terms (case 2). Formalism of case 2 is more