The mechanism for the relaxation of the cosmological constant is studied and elaborated. In the model used for the analysis of the relaxation mechanism the universe contains two components: a cosmological constant of an arbitrary size and sign and a component with an inhomogeneous equation of state. Owing to the dynamics of the second component the universe asymptotically tends to a de Sitter phase of expansion characterized by a small effective positive cosmological constant. An analysis of the asymptotic expansion for a general inhomogeneous equation of state of the second component is made. Several concrete examples are presented and the stability and speed of convergence to their fixed points are analyzed. It is found that the speed of convergence to a fixed point is large whenever the absolute value of the cosmological constant is large.
In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically distributed dust overdensities. The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average space-times given by the Green-Wald and the Buchert frameworks respect…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe may undergo a topology change and in between is a mixture of two different Friedmann-Rob…
We investigate quasilocal horizons in inhomogeneous cosmological models, specifically concentrating on the notion of a trapping horizon defined by Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate and analyse these quasilocally defined horizons in two dynamical spacetimes used as inhomogeneous cosmological models with perfect fluid source of non-zero pressure. In the spherically symmetric Lemaître spacetime we discover that the horizons (future and past) are both null hypersurfaces provided that the Misner-Sharp mass is constant along the horizons. Under the same …
In this work we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, therefore spatially inhomogeneous. However we retain the conformal flatness property of the standard cosmological model (FRW) i.e. the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently [1].
This is the third paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. In this paper we consider a particular kind of cosmological perturbation theory which starts from a gauge fixed version of General Relativity. The gauge fixing is performed using a material reference system called Gaussian dust. The resulting system has no constraints any more but possesses a physical Hamiltonian that drives the dynamics of bot…
We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, {\sc CosmoGRaPH}, which employs the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism on a 3-dimensional grid. Using {\sc CosmoGRaPH}, we calculate the effect of an inhomogeneous matter distribution on the evolution of a spacetime. We also present the results of a set of standard stability tests to demonstrate the robustness of our simulations.
In a fully inhomogeneous, anisotropic cosmological simulation performed by solving Einstein's equations with numerical relativity, we find a local measurement of the effective Hubble parameter differs by less than 1\% compared to the global value. This variance is consistent with predictions from Newtonian gravity. We analyse the averaged local expansion rate on scales comparable to Type 1a supernova surveys, and find that local variance cannot resolve the tension between the \citet{riess2018b} and \citet{planck2018a} measurements.
This is the fourth paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. In this paper, we finally consider the gauge invariant scalar (Mukhanov-Sasaki) and tensor (primordial gravitational wave) inhomogeneous perturbations of General Relativity coupled to an inflaton field which arise from a careful constraint analysis of this system up to second order in the perturbations. The simultaneous quantisation of the hom…
While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, non-linear and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaïtre-Robertston-Walker (FLRW) behavior, however this universe also exhibits loca…
In this paper, we construct and study solutions of Einstein's equations in vacuum with a positive cosmological constant which can be considered as inhomogeneous generalizations of the Nariai cosmological model. Similar to this Nariai spacetime, our solutions are at the borderline between gravitational collapse and de-Sitter-like exponential expansion. Our studies focus in particular on the intriguing oscillatory dynamics which we discover. Our investigations are carried out both analytically (using heuristic mode analysis arguments) and numerically (using the numerical infrastructure recently …
