arXiv:astro-ph/0209158v1 9 Sep 2002 On the time evolution of the redshift and the luminosity distance C. Barbachoux ∗ , G. Le Denmat † LERMA/UMR 8540, Universit´ e Pierre et Marie Curie, ERGA, Boˆ ıte 142, 4 place Jussieu, 75005 Paris Cedex 05, France. February 2, 2008 Abstract We investigate the temporal evolution of the redshift and the lu- minosity 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 to given values, namely the stable equilibrium states associated to the first order differential equation they verify. This suggests that the sources concentrate at about these values. Furthermore, as these values depend only on the cosmological parameters, their measure could provide a new approach to determine the value of the cosmological constant. 1 Introduction Much attention has been devoted to the study of the temporal evolution of the redshift and the luminosity distance, because of the alternative scheme they constitute to determine the values of the cosmological parameters in comparison with other approaches (White, Scoot & Silk 1994; Perlmutter et al 1998; Schmidt et al 1998; Riess et al 1998). First proposed by Sandage (Sandage 1962) in a pioneering work (including an important Appendix from * e-mail: barba@ccr.jussieu.fr † e-mail: gele@ccr.jussieu.fr 1