Abstract:
In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogeneous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed that Einstein's fundamental equation also allowed dynamical worlds, and in 1927 Geroges Lemaitre, backed by observational evidence, concluded that our universe was expanding. Einstein impetuously rejected Friedman's as well as Lemaitre's findings. However, in 1931 he retracted his former static model in favour of a dynamic solution. This investigation follows Einstein on his hesitating path from a static to the expanding universe. Contrary to an often repeated belief the primary motive for his switch was not observational evidence, but the realisation that his static model was unstable.

Abstract:
Einstein's static model is the first relativistic cosmological model. The model is static, finite and of spherical spatial symmetry. I use the solution of Einstein's field equations in a homogeneous and isotropic universe -- Friedmann's equation -- to calculate the radius of curvature of the model (also known as "Einstein's universe"). Furthermore, I show, using a Newtonian analogy, the model's mostly known feature, namely, its instability under small perturbations on the state of equilibrium.

Abstract:
We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c_{s}^2>1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilise an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.

Abstract:
Starting from the assumption that general relativity might be an emergent phenomenon showing up at low-energies from an underlying microscopic structure, we re-analyze the stability of a static closed Universe filled with radiation. In this scenario, it is sensible to consider the effective general-relativistic configuration as in a thermal contact with an "environment" (the role of environment can be played, for example, by the higher-dimensional bulk or by the trans-Planckian degrees of freedom). We calculate the free energy at a fixed temperature of this radiation-filled static configuration. Then, by looking at the free energy we show that the static Einstein configuration is stable under the stated condition.

Abstract:
We study a possibility of the fate of universe, in which there is neither the rip singularity, which results in the disintegration of bound systems, nor the endless expansion, instead the universe will be quasi static. We discuss the parameterization of the corresponding evolution and the reconstruction of the scalar field model. We find, with the parameterization consistent with the current observation, that the current universe might arrive at a quasi static phase after less than 20Gyr.

Abstract:
In principle the geometry of the universe can be investigated by measuring the angular size of known objects as a function of distance. Thus the distribution of angular sizes provides a critical test of the stable and static model of the universe described by Crawford (1991,1993) that has a simple and explicit relationship between the angular size of an object and its redshift. The result is that the agreement with observations of galactic diameters and the size of double radio sources with the static model is much better than the standard (Big Bang) theory without evolution. However there is still a small discrepancy at large redshifts that could be due to selection effects.

Abstract:
We consider a cosmology in which the final stage of the Universe is neither accelerating nor decelerating, but approaches an asymptotic state where the scale factor becomes a constant value. In order to achieve this, we first bring in a scale factor with the desired property and then determine the details of the energy contents as a result of the cosmological evolution equations. We show that such a scenario can be realized if we introduce a generalized quintom model which consists of a scalar field and a phantom with a {\it negative} cosmological constant term. The standard cold dark matter with $w_m=0$ is also introduced. This is possible basically due to the balance between the matter and the {\it negative} cosmological constant which tend to attract and scalar field and phantom which repel in the asymptotic region. The stability analysis shows that this asymptotic solution is classically stable.

Abstract:
The gravitaional force produced by a point particle, like the sun, in the background of the static Einstein universe is studied. Both the approximate solution in the weak field limit and exact solution are obtained. The main properties of the solution are {\it i}) near the point particle, the metric approaches the Schwarzschild one and the radius of its singularity becomes larger than that of the Schwarzschild singularity, {\it ii}) far from the point particle, the metric approaches the static Einstein closed universe. The maximum length of the equator of the universe becomes smaller than that of the static Einstein universe due to the existence of the point particle. These properties show the strong correlation betweem the particle and the universe.

Abstract:
We demonstrate that as we extrapolate the current $\Lambda$CDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.

Abstract:
We demonstrate that as we extrapolate the current $\Lambda$CDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.