Related papers: Well-posedness of Einstein's Equation with Redshif…
The luminosity distance can be used to determine the properties of large scale structure around the observer. To this purpose we develop a new inversion method to map luminosity distance to a LTB metric based on the use of the exact…
Observations are studied in toy-models constituting exact cosmological solutions to the Einstein equation which are statistically homogeneous but locally inhomogeneous, without an a priori introduced FLRW background and with "structures"…
We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar…
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…
The inverse problem with Lema\^itre-Tolman-Bondi (LTB) universe models is discussed. The LTB solution for the Einstein equations describes the spherically symmetric dust-filled spacetime. The LTB solution has two physical functional degrees…
We consider the redshift drift and position drift associated with astrophysical sources in a formalism that is suitable for describing emitters and observers of light in an arbitrary spacetime geometry, while identifying emitters of a given…
The ultimate application of Einstein's field equations is to empirically determine the geometry of the Universe from its matter content, rather than simply assuming the Universe can be represented by a homogeneous model on all scales.…
We calculate the low red-shift Taylor expansion for the luminosity distance for an observer at the center of a spherically symmetric matter inhomogeneity with a non vanishing cosmological constant. We then test the accuracy of the formulas…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of…
We investigate the temporal evolution of the redshift and the luminosity distance within the standard Friedmann-Roberston-Walker cosmological model. The redshift and luminosity distance of sources evolve with time and we show that they tend…
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms…
Extending the approach developed by Ara\'ujo and Stoeger [1] and improved in Ara\'ujo {\it et al} [2], we have shown how to construct dust-filled $\Lambda \neq 0$ Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmological models from FLRW…
The cosmic distance duality relation (CDDR) has been test through several astronomical observations in the last years. This relation establishes a simple equation relating the angular diameter ($D_A$) and luminosity ($D_L$) distances at a…
The Einstein's field equations of FRW universes filled with a dissipative fluid described by full theory of causal transport equations are analyzed. New exact solutions are found using a non-local transformations on the nonlinear…
The Einstein Telescope and other third generation interferometric detectors of gravitational waves are projected to be operational post $2030$. The cosmological signatures of gravitational waves would undoubtedly shed light on any departure…
We propose an efficient analytical method for estimating the luminosity distance in a homogenous Friedmann-Lema\^itre-Robertson-Walker (FLRW) model of the Universe. This method is based on the homotopy perturbation method (HPM), which has…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
It is well known that positive values of redshift drift is a signature of dark energy within the conventionally studied Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe models. Here we show -- without making assumptions on the…
On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth…