Inflation and topological phase transition driven by exotic smoothness

In this paper we will discuss a model which describes the cause of inflation by a topological transition. The guiding principle is the choice of an exotic smoothness structure for the space-time. Here we consider a space-time with topology $S^{3}\times\mathbb{R}$. In case of an exotic $S^{3}\times\mathbb{R}$, there is a change in the spatial topology from a 3-sphere to a homology 3-sphere which can carry a hyperbolic structure. From the physical point of view, we will discuss the path integral for the Einstein-Hilbert action with respect to a decomposition of the space-time. The inclusion of the boundary terms produces fermionic contributions to the partition function. The expectation value of an area (with respect to some surface) shows an exponential increase, i.e. we obtain inflationary behavior. We will calculate the amount of this increase to be a topological invariant. Then we will describe this transition by an effective model, the Starobinski or $R^{2}$ model which is consistent with the current measurement of the Planck satellite. The spectral index and other observables are also calculated. Finally we obtain a realistic cosmological constant.Comment: 21 pages, no figures, iopart styla, accepted in Advances in High Energy Physics, special issue "Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects (QGEQ)

Composite particles in the Theory of Quantum Hall Effect

The formation of composite particles in the electron liquid under QHE conditions discussed by Jain in generalizing Laughlins many-particle state is considered by using a model for two-dimensional guiding center configurations. Describing the self-consistent field of electron repulsion by a negative parabolic potential on effective centers and an inter-center amount we show that with increasing magnetic field the ground state of so-called primary composite particles $\nu=\frac{1}{q}$, $q=1,3,5,...$, is given for higher negative quantum numbers of the total angular momentum. By clustering of primary composite particles due to absorption or emission of flux quanta we explain phenomenologically the quasi-particle structure behind the series of relevant filling factors $\nu=\frac{p}{q}$, $p=1,2,3,...$. Our considerations show that the complicate interplay of electron-magnetic field and electron-electron interactions in QHE systems may be understood in terms of adding flux quanta $\Phi_0$ to charges $e$ and binding of charges by flux quanta.Comment: RevTeX 3.0, LaTeX, 10 pages, one table at th en