The analysis of modern cosmological data is becoming an increasingly important task as the amount of data multiplies. An important goal is to extract geometric information, i.e. the metric of the cosmos, from observational data. The observer metric is adapted to the reality of observations: information received along the past null cone, and matter flowing along timelike lines. It provides a potentially very good candidate for developing a general numerical data reduction program. As a basis for this, we elucidate the spherically symmetric solution, for which there is to date single presentation that is complete and correct. With future numerical implementation in mind, we give a clear presentation of the mathematical solution in terms of 4 arbitrary functions, the solution algorithm given observational data on the past null cone, and we argue that the evolution from one null cone to the next necessarily involves integrating down each null cone. Phys. Rev. D,

Abstract. This paper presents the algorithm for determining the Lemaître-Tolman model that best fits given datasets for maximum stellar ages, and SNIa luminosities, both as functions of redshift. It then applies it to current cosmological data. Special attention must be given to the handling of the origin, and the region of the maximum diameter distances. As with a previous combination of datasets (galaxy number counts and luminosity distances versus redshift), there are relationships that must hold at the region of the maximum diameter distance, which are unlikely to be obeyed exactly by real data. We show how to make corrections that enable a self-consistent solution to be found. We address the questions of the best way to approximate discrete data with smooth functions, and how to estimate the uncertainties of the output -the 3 free functions that determine a specific Lemaître-Tolmanmetric. While current data does not permit any confidence in our results, we show that the method works well, and reasonable Lemaître-Tolman models do fit with or without a cosmological constant.

Abstract:We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological "constants". Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor a as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden-Fowler equation.The analysis of the models shows that, for a particular choice of parameters in our first model, the cosmological "constant" decreases whereas the Newtonian gravitational "constant" increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational "constants" decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.

The homogeneous and anisotropic Bianchi type-V cosmological model with variable gravitational and cosmological “constants” with a general (nonstiff) perfect fluid is investigated. The Einstein field equations (EFEs) are numerically integrated with the fourth-order Runge–Kutta method for different values of [Formula: see text] and [Formula: see text] parameters of quantum fields in a curved and expanding background. Three realistic models, namely matter, radiation and phantom dark energy models are also discussed. In all these models, it was found that the cosmological “constant” decreases with time, whereas the gravitational “constant” increases over time. It is shown that the universe in these models becomes isotropic at late times.