Studies On Stability Of Einstein Static Universes

Since general relativity was formulated, it has withstood challenges from var-ious experiments and observations, influencing many disciplines profoundly. The standard big-bang cosmological model based on general relativity and the cosmo-logical principle can successfully explain the history of cosmic evolution from to the present one percent of a second after the big bang. However, the model confronts four theoretically unsolved problems:the horizon problem, the flatness problem, the magnetic monopole problem and the big-bang singularity problem. In 1980, American physicist Alan Quth initially proposed the cosmic inflation which indi-cates the universe in the very early epoch underwent a transient and exponentially rapid expansion. Cosmic inflation reasonably explains the horizon problem, the flatness problem, the magnetic monopole problem, leaving the big-bang singularity unsolved. According to the singularity theorem presented by Hawking and others, the universe must have a beginning which is the so-called big-bang singularity. At the singularity, all the physical theories are invalid because infinitely large are both the temperature and energy density of the universe. Thus, some theories should be attractive if they can circumvent the singularity. The emergent universe is a cosmological model without the singularity. It assumes that the universe originats from an Einstein static universe with finite scale rather than a singularity, and then enters the inflationary stage. So, the emergent theory can be accommodated with the standard cosmological model. Thus, it is quite crucial for emergent theo-ry whether Einstein static universes can keep stable past eternally. However, it is worth noting that an Einstein static universe is unstable within general relativity, and it will lose stability against some perturbations. Therefore, it cannot stay at the initial static state past eternally. Thus, it is worth to discuss the stability of Einstein static universes. Besides the emergent universe scenario, some interesting models are proposed to solve the singularity problem, such as cyclic scenarios in string/M theory and the oscillating universes.The stability of Einstein static universes attracted much attention a long time ago. In 1930, Eddington initially found that an Einstein static universe with the content of normal matter is unstable with respect to spatially homogeneous and isotropic scalar perturbations in the framework of general relativity. Since then, the stability of Einstein static universe in various theories of gravity—such as in loop quantum cosmology, braneworld scenario, f(T) gravity, f(R) gravity and massive gravity, has been investigated against different kinds of perturbations.Modified Gauss-Bonnet gravity is a modified theory of gravity which adds a f(G) term on the original Einstein-Hilbert action, where G is the Gauss-Bonnet invariant. In Chapter III, we investigate the stability of Einstein static universes within the framework of modified Gauss-Bonnet gravity. We assume that the matter component consists of a perfect fluid with a constant equation of state and a scalar field, respectively. For the scenario of perfect fluid, it is concluded that there are stable Einstein static solutions against homogeneous scalar perturbations and there exists no stable ES solution against homogeneous scalar perturbations since model parameter a has no stability region as wavenumber k approximates infinity. In the same way, For the case of a scalar field; it is shown that there are no stable Einstein static solutions against both homogeneous and inhomogeneous scalar perturbations. Finally, we must point out that since a successfully emergent scenario requires that the universe stays at a stable ES state past eternally, and furthermore, that it can naturally exit from this state and then enter an inflationary era, our analysis suggests that the emergent scenario that avoids the big bang singularity cannot be realized in the modified GB gravity since there are no stable ES solutions in the first place.The Jordan-Brans-Dicke (JBD) theory of gravity is a particular example of the scalar-tensor theories of gravity. The JBD theory of gravity may appear naturally in supergravity, Kaluza-Klein theory, and string theory and it has been employed to elucidate the cosmic expansion ranging from the early cosmic inflation to the late time cosmic acceleration. In Chapter IV, We assume that the matter con-tent consists of a perfect fluid with a constant equation of state and a scalar field, respectively. For the case of perfect fluid, we find that within the framework of the Jordan-Brans-Dicke (JBD) theory of gravity there exist stable Einstein static solutions against both homogeneous and inhomogeneous scalar perturbations. In the same way, if the matter content of the universe consists in a scalar field Ψ, there exist stable Einstein static solutions against homogeneous and inhomoge-neous scalar perturbations. Finally, we point out that the universe can exit from this stable state and then enter an inflationary phase naturally. As a result,the emergent scenario in the JBD theory may resolve the big bang singularity problem successfully.