A relação de dualidade testada com aglomerados de galáxias e H (z).

Abstract

The so-called reciprocity relation, proved long ago by Etherington (1933), is of fundamental importance in cosmology. It states that if the source and the observer are in relative motion, solid angles subtended between the source and observer are related by geometrical invariants and a factor dependent of the source redshift. Its most useful version in the astronomical context is known as cosmic distance duality relation (CDDR), and relates the luminosity (DL) and angular diameter (DA) distances by the following expression: DL(z)(1 + z)􀀀�2=DA(z) = 1. This relation is completely general, valid for all cosmological models based on Riemannian geometry and is independent either upon Einstein eld equations other nature of matter. It only requires that source and observer be connected by null geodesics in a Riemannian spacetime and that the number of photons be conserved. In this work we propose a cosmological model-independent test for the CDDR by using galaxy clusters and expansion rate of the universe measurements, H(z). In a first analysis, we use gas mass fractions (fgas) and angular diameter distances measurements from a sample of 38 galaxy clusters jointly with H(z) measurements to test the validity of the CDDR. In a second analysis, we use 25 angular diameter distances sample, which were obtained by considering two diferent morphologies, in order to investigate the influence of the morphology used to describe the galaxy clusters on the test. In our analyzes, we consider the Ƞ parameter, as a function of the redshift, in two diferent ways: Ƞ(z) = 1+ Ƞ 0z e Ƞ (z) = 1+ Ƞ 0z=(1+z). The results showed that the value of Ƞ0 depend on the observable used in the test (gas mass fraction or angular diameter distance) and of the morphology considered to describe the clusters.