Abstract
I give a review of predictions of values of spectral parameters for a large number of inflationary models. The present review includes detailed deductions and information about the approximations that have been made, written in a style that is suitable for text book authors. The Planck data have the power of falsifying several models of inflation as shown in the present paper. Furthermore, they fix the beginning of the inflationary era to a time about 10−36 s, and the typical energy of a particle at this point of time to 1016 GeV, only a few orders of magnitude less than the Planck energy, and at least 12 orders of magnitude larger than the most energetic particle produced by CERN’s particle accelerator, LHC. This is a phenomenological review with contents as given in the list below. It includes systematic presentations of the different types of slow roll parameters that have been in use, and also of the N-formalism.
Highlights
We have a so-called standard-model for the evolution of the universe
Equation (2.12) shows that the Hubble parameter is constant and there is exponential expansion for a constant inflaton field. This represents the case where the inflaton field behaves like Lorentz invariant vacuum energy (LIVE) with a constant density, which may be represented by a cosmological constant
The differences between the models cook down to specifying the potential by different functions of the potential, V(φ). In this connection one often classifies the models in three classes: Large field inflation: In these models the field strength at the end of the inflation is larger than an order of magnitude less than the Planck energy
Summary
We have a so-called standard-model for the evolution of the universe. According to this model, the universe started from a quantum fluctuation where the universe appeared in a state dominated by dark energy with extremely great density. The dark energy caused repulsive gravity and made the universe expand with great acceleration This state lasted for about 10−33 s, and the distances between reference points increased by 50–60 e-folds. At the beginning of the inflationary era, there were wildly changing patterns in the cosmic density distribution, and these changing shapes produced gravity waves. These gravity waves functioned as messengers telling about events that happened before the universe was 10−35 s old. In the present situation with new observations of the B-mode polarization pattern in the CMB radiation field expected the years, the predictions of spectral parameters from different inflationary models should be presented in a way suitable for chapters in text books and for teachers and students. The large classes of warm and tachyonic inflationary universe models are thoroughly reviewed
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