Cosmological models in semi-classical and higher order gravitational theories (Q5931786)

From the authors' conclusions: We have investigated higher-order gravitational field equations, being either introduced by quantum corrections to the theory, or postulated in a generalised Lagrangian. In the first case we have studied several homogeneous isotropic semi-classical cosmological models with the presence of a self interacting classical scalar field. Considering a self interaction potential, we found exact solutions to this problem with a vacuum polarization term. In the case of exponential potentials we have shown the existence of inflationary power-law solutions when the range of the regularization parameters is \(0<\beta/\alpha< 3\). We have also shown that, unlike in the classical case, the vacuum polarization terms make the power law solutions unstable for every value of the exponent \(n\). In the second case of the Lagrangian models, we study the stability of the de Sitter space-time for the complete 6th-order theory. We have shown the detailed dependence of the stability of the de Sitter space-time upon the characteristic expansion scale (or the equivalent vacuum energy). Also, in our study of stability of Minkowski space-time (under isotropic and homogeneous perturbations) we have recovered the masses of the scalar fields appearing in the conformal picture given in [\textit{S. Gottlöber}, \textit{H.-J. Schmidt} and \textit{A. A. Starobinskij}, Classical Quantum Gravity 7, 893-900 (1990; Zbl 0693.53037)]. Note: One of the cited preprints now appeared as: \textit{S. Capozziello} and \textit{G. Lambiase}, Gen. Relativity Gravitation 32, 295-311 (2000; Zbl 0974.83036).