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Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This
We consider here the existence and structure of trapped surfaces, horizons and singularities in spherically symmetric static massless scalar field spacetimes. Earlier studies have shown that there exists no event horizon in such spacetimes if the sca
This paper treats nonrelativistic matter and a scalar field $phi$ with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lema^{i}tre-Robertson-Walker cosmology. The field equations are reformulated as a three-dimensi
The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the li
We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncert