Inflation and Topological Phase Transition Driven by Exotic Smoothness. (19th March 2014) - Asselmeyer-Maluga, Torsten; Król, Jerzy
Abstract : 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 × ℝ . In case of an exotic S 3 × 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; that is, 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.