Related papers: Spatial averaging and a non-Gaussianity
Idealizing matter as a pressureless fluid and representing its motion by a peculiar--velocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain $\cal D$ to the…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…
Due to the non-commutation of spatial averaging and temporal evolution, inhomogeneities and anisotropies (cosmic structures) influence the evolution of the averaged Universe via the cosmological backreaction mechanism. We study the…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
The purpose of this study is to describe a perfect fluid matter distribution that leads to a constant curvature region, thanks to the effect of a non-minimal coupling. This distribution exhibits a density profile within the range found in…
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained…
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…
There is an ongoing debate in the literature as to whether the effects of averaging out inhomogeneities (``backreaction'') in Cosmology can be large enough to account for the acceleration of the scale factor in the FLRW models. In…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
We revisit the conformally coupled scalar gravitational theory. This is the simplest local-scale invariant theory of gravity which is linear in the curvature scalar. We demonstrate that, if incorporate local-scale symmetry into the…
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor…
We use the local curvature to investigate the possible existence of non-Gaussianity/asymmetry in the WMAP data. Considering the full sky we find results which are consistent with the Gaussian assumption. However, strong non-Gaussian…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…
A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity,…
We use multiscale-multispace correlations and Fourier transform techniques, to study some intermittent random field properties, which escape analysis by structure function scaling. These properties are parametrized in terms of a set of…
We demonstrate that local, scale-dependent non-Gaussianity can generate cosmic variance uncertainty in the observed spectral index of primordial curvature perturbations. In a universe much larger than our current Hubble volume, locally…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
The paper 0705.0332v1 seeks to study the effect of non-trivial spatial curvature in homogeneous and isotropic models. We note that the space considered is not homogeneous, and that the equations of motion used are inconsistent with the…
We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from…