相关论文: Averaging from a global point of view

The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann-Lemaitre-Robertson-Walker (FLRW) line…

Using the superfield approach we construct the $n=2$ supersymmetric lagrangian for the FRW Universe with barotropic perfect fluid as matter field. The obtained supersymmetric algebra allowed us to take the square root of the Wheeler-DeWitt…

We construct cosmological models consisting of large numbers of identical, regularly spaced masses. These models do not rely on any averaging procedures, or on the existence of a global Friedmann-Robertson-Walker (FRW) background. They are…

The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…

We generalize Buchert's averaged equations [Gen. Rel. Grav. 32, 105 (2000); Gen. Rel. Grav. 33, 1381 (2001)] to LRS class II dust model in the sense that all Einstein equations are averaged, not only the trace part. We derive the relevant…

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This method requires only elementary techniques in Fourier analysis and shows…

Effects of inhomogeneities on observations have been vastly studied using both perturbative methods, N-body simulations and Swiss cheese solutions to the Einstein equations. In nearly all cases, such studied setups assume vanishing spatial…

We provide a comprehensive analytic study (rigorous and qualitative) of the conditions for the existence of a a positive kinematic back reaction term $\QQ>0$, in the context of Buchert's scalar averaging formalism applied to spherically…

Scalar field cosmologies with a generalized harmonic potential and matter with energy density $\rho_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(\gamma-1)\rho_m, \; \gamma\in[0,2]$ in Kantowski-Sachs (KS) and closed…

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers…

Deviations from the area law of the horizon entropy, in the cosmological setup, are known to lead to modified Friedmann equations governing the evolution of the universe. In this work, we propose that such modifications need not be…

Using the spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi dust solution, we study how the shear and the backreaction depend on the sharpness of the spatial transition between voids and walls and on the size of the voids. The voids…

Consider nonlinear wave equations in the spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime…

Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume-averaged quantities and only these can be compared with…

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally…

We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…

We consider the averaging principle for stochastic reaction-diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion.…

We study constant mean curvature Lorentzian hypersurfaces of $\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the…

The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. The non-linearity of the Einstein field equations raises concern over…