The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G2 cosmologies. By using Darboux’s theory in order to study ordinary differential equations in the complex projective plane CP we solve the Bianchi V models totally. Moreover, we carry...

Bianchi type V bulk viscous fluid cosmological models are investigated. Using a generation technique (Camci et al., 2001), it is shown that the Einstein’s field equations are solvable for any arbitrary cosmic scale function. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. Solutions for particular forms of cosmic scale functions are also obtaine...

Bianchi type V bulk viscous fluid cosmological models are investigated. Using a generation technique (Camci et al., 2001), it is shown that the Einstein’s field equations are solvable for any arbitrary cosmic scale function. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. Solutions for particular forms of cosmic scale functions are also obtaine...

We analyze carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (=“homogeneity preserving diffeomorphisms”) given in the literature do not incorporate the crucial feature that local gauge transformations should be independent at each point of the manifold of the independent v...

A new class of LRS Bianchi type VI0 cosmological models with free gravitational fields and a variable cosmological term is investigated in presence of perfect fluid as well as bulk viscous fluid. To get the deterministic solution we have imposed the two different conditions over the free gravitational fields. In first case we consider the free gravitational field as magnetic type whereas in sec...

We present a reconstruction algorithm for cosmological models based on $f(\mathcal{Q})$ gravity. specifically focus Bianchi type I and Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes, obtaining exact solutions that might have application in variety of scenarios such as spontaneous isotropization models, dark energy, inflation, well pre-big bang cosmologies.