Reconstruction of scalar potentials in induced gravity and cosmology

Abstract

We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological constant, a Chaplygin gas and a modified Chaplygin gas are constructed explicitly.

The Complex Quantum and Classical Pseudo-Tachyonic Universe

“…Now, we have differentiate both sides with respect to "t" of the equation (90), we get, So, the impossibility of the changing the sign of ) (t   without the soft singularity crossing implies the inevitability of the approaching of the universe to this soft singularity. Also we have from equation (19) that the value of the Hubble parameter is decreasing during all the evolution. And,…”

“…We shall construct the complete classification of the cosmological evolutions (trajectories) of our model, using equation (16), (18) and (19) …”

“…Substituting the above expression of (t) in the equation (19) and then integrating, we get, , i.e., the sign of H B can be both positive or negative, hence, the universe can pass through this singularity in the phase of its expansion or of its contraction and where the energy density of the matter in the universe is different from zero. Again from the equation (90), it was noticed at the moment when  = 0, shows that after passing the zero value, the scalar-field is positive it cannot change the sign.…”

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

“…If we want to have a little bit more rich model for the analysis of its classical and quantum dynamics, we can use rather a standard procedure of the reconstruction of potentials of minimally coupled scalar fields [22,[35][36][37][38][39], reproducing a given cosmological evolution. This procedure is based on the use of two equations:…”

Arbitrary scalar-field and quintessence cosmological models

“…If inflation passes a consistency test, one can use observational information to constrain the inflationary potential. The key point in the reconstruction procedure is that the Hubble parameter is considered as a function of the scalar field, and this allows one to reconstruct the scalar-field potential and determine the dynamics of the field itself, without a priori knowing the Hubble parameter as a function of time or of the scale factor [76,77]. General solutions for flat Friedmann Universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity were also derived in [78].…”