On weakly B symmetric pseudo Riemannian manifolds and its applications

The object of the present paper is to study weakly B symmetric manifolds (WBS)n. At first some geometric properties of (WBS)n(n > 2) have been studied. Finally, we consider (WBS)4 spacetimes. They turn out to be both perfect and imperfect fluids Robertson-Walker space-times : an equation of state is provided in the first case, and in the second the nature of the bulk viscosity pressure is pointed out. Also, we construct an example of a (WBS)4.

Inflation and bounce from classical and loop quantum cosmology imperfect fluids

We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmologies. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the [Formula: see text] inflation scenario and two constant-roll inflation scenarios, and with regards to the bouncing cosmologies, we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of primordial curvature perturbations, the scalar-to-tensor ratio and the running of the spectral index and we compare the resulting picture with the Planck data. As we demonstrate, partial compatibility with the observational data is achieved in the imperfect fluid description, however none of the above scenarios is in full agreement with data. This result shows that although it is possible to realize various cosmological scenarios using different theoretical frameworks, it is not guaranteed that all the theoretical descriptions are viable.

STATIC ISOTROPIC SPACE–TIMES WITH RADIALLY IMPERFECT FLUIDS

When one is solving the equations of general relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress–energy. This implies that for static and isotropic space–times, the most general natural stress–energy tensor is a sum of a perfect fluid and a radially imperfect fluid component. In the special situations where the perfect fluid component vanishes or is a space–time constant, the solutions to Einstein's equations can be thought of as modified Schwarzschild and Schwarzschild–de Sitter spaces. Exact solutions of this type are derived and it is shown that whereas deviations from the unmodified solutions can be made small, among the manifestations of the imperfect fluid component is a shift in angular momentum scaling for orbiting test bodies at large radius. Based on this effect, the question of whether the imperfect fluid component can feasibly describe dark matter phenomenology is addressed.