Narrow Results

We examine the homogeneous and isotropic models sourced by the fluid having an inhomogenous equation of state (EoS) using qualitative methods. The flat Friedmann–Lemaitre–Robertson–Walker (FLRW) model explains the accelerating universe expansion of the present era having past of decelerating era dominated by radiation and matter. The open FLRW model incorporates the radiation, matter and dark energy dominated era in order with the spatial curvature playing role just before the accelerated universe evolution. The dominating behaviors of radiation, matter and spatial curvature affect the evolution trajectories of the deceleration and effective EoS parameter, which are obtained by the numerical solutions of autonomous system. The model parameters affect the nature of dark energy and therefore the EoS parameter may also lie in the quintessence or phantom regions. The closed FLRW model having constant positive curvature may yield the bouncing and turnaround universe evolution with dark energy-dominated phase at late-times. The application of statefinder diagnostic in the cosmological dynamical systems highlights that the universe may approach the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }$CDM) universe as a particular case in the future.

The vacuum inflation with a boundary condition specified at a short distance scale in a generally primeval nonflat universe, and implications of the correspondingly modified primordial power spectrum via the WMAP data are investigated. We obtain a general form of the modified primordial power spectrum including the effects of both the possibly new physics scale and the spatial curvature. The modulation of the primordial power spectrum due to new physics is of the order H/Λ, where H is the Hubble parameter during inflation and Λ is the new physics scale which is key to inflation, while the modulation from the curvature effect is of the order K/k², where K is the spatial curvature before inflation and k is the comoving wave number. We also find that a closed universe before inflation is favored by WMAP five-year data.

We estimate the cosmological spatial curvature as generated by the actual matter content of the universe. The result is that the present day universe appears to be very nearly spatially flat due to the low density and the nonrelativistic peculiar velocities. The sign of the spatial curvature comes out as positive.

In this paper, we first deduce the Tolman–Oppenheimer–Volkoff (TOV) equations and Schwarzschild–de Sitter (SdS) constant-density interior solutions of perfect fluid spheres in hydrostatic equilibrium by the Einstein equations with a nonzero cosmological constant. The TOV equations and the spacetime properties of exact solutions inside uniform perfect fluid spheres with different spatial curvature and cosmological constants will be respectively analyzed in detail. Moreover, a brief comparison between the internal static solutions of the SdS type and the dynamical Einstein–Strauss–de Sitter (ESdS) vacuole spacetime is obtained.

As evidenced by a great number of works in the literature, it is common practice to assume that the universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the $\mathrm{\Lambda }$CDM cosmology, or extensions thereof. On the other hand, when data is fitted to models with a time-varying dark energy equation-of-state, it turns out that such models may accommodate a non-flat universe. Several authors caution that if the assumption of spatial flatness is wrong, it could greatly hinder our understanding of dark energy, even if the curvature is in reality very small. We thus consider a number of different dynamical dark energy models that represent the complete cosmological scenario, and investigate the effects of spatial curvature on the evolution. We find that for a closed universe, the transition to the epoch of decelerated expansion would be delayed with respect to the flat case. So would the start of the current dark energy-dominated era. This would be accompanied by a larger inflationary acceleration, as well as a larger subsequent deceleration. The opposite behavior is observed if the universe is open.

We consider the Little Rip (LR), Pseudo Rip (PR) and bounce cosmological models in the Friedmann–Robertson–Walker (FRW) metric with nonzero spatial curvature. We describe the evolution of the universe using a generalized equation of state (EoS) in the presence of a viscous fluid. The conditions of the occurrence of the LR, PR and bounce were obtained from the point of view of the parameters of the generalized EoS for the cosmic dark fluid, taking into account the spatial curvature. The analytical expressions for the spatial curvature were obtained. Asymptotic cases of the early and late universe are considered. A method of Darboux transformation (DT) was proposed in the case of models of an accelerating universe with viscosity.

The matter distribution of the universe is observed to be discrete in the form of stars, galaxies and clusters of galaxies. Due to the non-linearities of the Einstein field equations, the discrete nature of the matter implies modifications of the standard Friedmann cosmology paradigm. The modifications affect both the dynamics and the possible cosmological initial data. We discuss properties and restrictions for the intial data of a universe with a discrete matter distribution, in particular possible implications for the curvature and topology.

The main idea of this contribution is to calculate the average spatial curvature directly from the observed mass distribution of the universe. In short, our philosophy is that the curvature of the universe is generated solely by the matter it contains. Although this may seem as self-evident in the context of general relativity, the usual practice in cosmology is rather to use a top-down approach in which the curvature is calculated indirectly using a prescribed matter distribution as a source of the Einstein equations. By contrast, our approach may be seen as part of a bottom-up approach. In practical terms, we first calculate the far field spatial curvature generated by an isolated matter distribution which is in arbitrary motion. At this stage we obtain the result that the sign of the spatial curvature is necessarily positive. For the spatial curvature generated by multiple sources we show that it is sufficient to use linearized theory to compute the leading contributions. In the matter dominated era the spatial curvature is then seen to be generated by local sources at small redshifts. This fact makes it possible to calculate the total spatial curvature just by summing up the contributions from the observed discrete mass distribution. A crude estimate gives a very small value for the curvature.