Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources

The scalar field degree of freedom in Einstein's plus Matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V(Phi), is provided by a perfect fluid obeying a general equation of state p =p(rho). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to 1st order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.Comment: latex2e source file,14 pages, no figures; (v3): minor corrections, to appear in J. Math. Phy

The General Solution of Bianchi Type VIIhVII_h Vacuum Cosmology

The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time re-parametrization symmetry. The application of the method to Type VII_h results in (a) obtaining the general solution of Type VII_0 with the aid of the third Painlev\'{e} transcendental (b) obtaining the general solution of Type $VII_h$ with the aid of the sixth Painlev\'{e} transcendental (c) the recovery of all known solutions (six in total) without a prior assumption of any extra symmetry (d) The discovery of a new solution (the line element given in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like hyper-surfaces, along with the emergence of the line element describing the flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure

Cosmological Solutions in Multiscalar Field Theory

We consider a cosmological model with two scalar fields minimally coupled to gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in our analysis. The coupling function and the potential function, which depend on one of the fields, characterize the model we study. We prove the existence of exact solutions that are of special interest for the cosmological evolution. Furthermore, we provide with a methodology that relates the scale factor behaviour to the free functions characterizing the scalar field kinetic term coupling and potential. We derive the necessary conditions that connect these two functions so that the relative cosmological solutions can be admitted. We find that unified dark matter and dark energy solutions are allowed by the theory in various scenarios involving the aforementioned functions.Comment: 15 pages, 3 figures, Latex2e source file, revised to agree with the accepted EPJC versio

Labour Market Dynamics in Greek Regions: a Bayesian Markov Chain Approach Using Proportions Data

This paper focuses on Greek labour market dynamics at a regional base, which comprises of 16 provinces, as defined by NUTS levels 1 and 2 (Eurostat, 2008), using Markov Chains for proportions data for the first time in the literature. We apply a Bayesian approach, which employs a Monte Carlo Integration procedure that uncovers the entire empirical posterior distribution of transition probabilities from full employment to part employment, unemployment and economically unregistered unemployment and vice a versa. Our results show that there are disparities in the transition probabilities across regions, implying that the convergence of the Greek labour market at a regional base is far from being considered as completed. However, some common patterns are observed as regions in the south of the country exhibit similar transition probabilities between different states of the labour marketGreek Regions, Employment, Unemployment, Markov Chains