A superfluid universe (Q2818809)

The book is devoted to the model of all-pervasive superfluid in the universe, developed by the author, and gives an introduction into the corresponding processes, including condensed matter physics, quantum field theory and general relativity. The book is divided into eleven chapters. Chapter 1 briefly defines the most important parameters and phenomena which are relative to superfluidity. In particular, the Bose-Einstein condensation, order parameter, spontaneous symmetry breaking, quantized vorticity, superconductivity, and the Higgs mechanism are considered. The quantum turbulence is discussed in Chapter 2 beginning with a consideration of the dynamics of quantum vorticity. It is shown that the Gross-Pitaevskii (GP) equation fully describes superfluid hydrodynamics, including vorticity. Then, the vortex reconnections and vortex tangle are presented, presenting quantum turbulence as a balance of the growth rate of new vortex loops due to external heating and the rate of degradation due to reconnections. As a result, the string theory of relativistic quantized vorticity is stated, based on the nonlinear Klein-Gordon equation. Chapter 3 reviews how the Higgs field is introduced to give a mass to the vector bosons that mediate the weak interactions. A vortex ring in the Higgs field is defined by the particle dubbed the vorticon, minimizing the energy of the lowest mode by varying the dimensions of the waveguide. The Higgs field is considered as order parameter, and relativistic superfluidity and the non-relativistic limit of a generic vacuum complex scalar field are considered. Chapter 4 presents the renormalization approach in the field theory. In particular, the Wilson's renormalization theory is presented, relying on a sharp high-momentum cutoff. Moreover, the Polchinski's equation is considered, describing an independent renormalization of the form of the cutoff, and a functional integro-differential equation for the interaction Lagrangian is obtained. Chapter 5 studies Gaussian fixed points of the renormalization group (RG) trajectories. Chapter 6 is devoted to the dynamics of spacetime, introducing the spacetime curvature and the Robertson-Walker (RW) metric, describing a spatially homogeneous and isotropic universe allowing a description of the expanding universe. Black holes are presented in Chapter 7 based on the Schwarzschild metric. The problem of the star collapse, defined by the Schwarzschild radius is defined on the base of Oppenheimer-Snyder solutions for inside and outside cases. Chapter 8 presents a big bang model, based on a Halpern-Huang scalar field, which can emerge from the Gaussian fixed point at the big bang due to the fact that it is asymptotically free. Chapter 9 discusses a creation of matter by using the Halpern-Huang scalar field, which being asymptotically free provides a possible initial state, but fails to efficiently create matter via conventional coupling. Chapter 10 explains that the dark energy is the energy density of the cosmic superfluid and dark matter arises from deviations of the superfluid density from its vacuum value. Finally, galaxy rotation and formation are in the centre of Chapter 11. In total, the book presents the author's interesting model for the description of superfluidity with the same approach on the scales from the nanolevel up to the universe. The book could be useful and interesting for undergraduate and graduate students, which study physics and mathematical background of this phenomenon.