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This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field…
We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional…
With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost…
Applying the Sachs formalism, the optical properties encoded in the distance modulus are studied along curves exhibiting local rotational symmetry for some closed inhomogeneous cosmological models whose mass content is discretized by…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
This work provides a general discussion of the spatially inhomogeneous Lema\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of…
Distance measurements are usually thought to probe the background metric of the universe, but in reality the presence of perturbations will lead to deviations from the result expected in an exactly homogeneous and isotropic universe. At…
It is proposed to use exact, cosmologically relevant solutions to Einstein's equations to accurately quantify the precision of ray tracing techniques through Newtonian N-body simulations. As an initial example of such a study, the recipe in…
We calculate the systematic inhomogeneity-induced correction to the cosmological constant that one would infer from an analysis of the luminosities and redshifts of Type Ia supernovae, assuming a homogeneous universe. The calculation…
The cosmological exploitation of modern photometric galaxy surveys requires both accurate (unbiased) and precise (narrow) redshift probability distributions derived from broadband photometry. Existing methodologies do not meet those…
The homogeneous, isotropic, and flat $\Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special…
Based on an analogy between diffraction integral formalism of classical field propagation and Feynman path integral approach to quantum field theory, we develop a quantum model for light and radiation in Rindler spacetime. The framework…
I discuss the spherically symmetric but inhomogeneous Lemaitre-Tolman- Bondi (LTB) metric, which provides an exact toy model for an inhomogeneous universe. Since we observe light rays from the past light cone, not the expansion of the…
Context: In astronomy, new approaches to process and analyze the exponentially increasing amount of data are inevitable. While classical approaches (e.g. template fitting) are fine for objects of well-known classes, alternative techniques…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…
A brief illustrative discussion of the shadows of black holes at local and cosmological distances is presented. Starting from definition of the term and discussion of recent observations, we then investigate shadows at large, cosmological…
A generalized quintessence model is presented which corresponds to a richer vacuum structure that, besides a time-dependent, slowly varying scalar field, contains a varying cosmological term. From first principles we determine a number of…
In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind…
We provide an analytical estimate of the effect of a spherical inhomogeneity on light beams that travel through it. We model the interior of the inhomogeneity in terms of the Lemaitre-Tolman-Bondi metric. We assume that the beam source is…