On Energy of the Friedman Universes in Conformally Flat Coordinates

Abstract

Recently many authors have calculated the energy of the Friedman universes by using double index energy-momentum complexes in Cartesian comoving coordinates $(t,x,y,z)$ and concluded that the flat and closed Friedman universes are energy-free. We show in this paper by using Einstein canonical energy-momentum complex and by doing calculations in conformally flat coordinates that such conclusion is incorrect. The results obtained in this paper are compatible with the results of the our previous paper \cite{Gar07} where we have used coordinate-independent averaged relative energy-momentum tensors to analyze Friedman universes.