Narrow Results

In this paper, we show that a smooth dynamic evolution from an initial unstable de Sitter stage to the standard radiation phase can analytically be described by a dominant noncanonical scalar field. For all practical purposes, at the end of the vacuum decaying process, the remaining potential energy density is completely stored in the kinetic part of the field satisfying the radiation equation of state. In this model, the early universe is nonsingular, free of horizon and different from many inflationary variants none post-inflationary reheating is required since the formation of the thermal bath is concomitant with inflation. The thermodynamic evolution of the thermal bath is determined. It is also shown that the resulting noncanonical cosmology can be rigorously interpreted as a dynamical $\mathrm{\Lambda }$-model (vacuum fluid) whose spontaneous decaying process into radiation may be the origin of the primeval thermal bath.

The new model of modified F(R)-gravity theory with the function F(R) = R + (a/γ) arcsin(γR) is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We consider both the Jordan and Einstein frames, and the potential and the mass of the scalar degree of freedom are found. It was shown that the de Sitter space-time is unstable but the flat space-time is stable. We calculate the slow-roll parameters ϵ, η, and the e-fold number of the model. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are obtained and learned.