Redshift spherical shell energy in isotropic universes

We introduce the redshift spherical shell energy, which can be used to test in the redshift space the radial inhomogeneity of an isotropic universe, providing additional constraints for Lemaitre-Tolman-Bondi models, and a more general test of cosmic homogeneity.

Figure 1

$\Delta Z(z)$ is plotted as a function of the redshift for the LTB model considered (thick line) and for a FRW flat universe with ${\Omega }_{\Lambda }=0.7$, ${\Omega }_M=0.3$ (thin line).

Figure 2

${\rho }_0(z)={log}_{10}[{\rho }_{\mathrm{SS}}(z)/{\rho }_{\mathrm{SS}}(0)]$ is plotted as a function of the redshift for the LTB model considered (thick line) and for a FRW flat universe with ${\Omega }_{\Lambda }=0.7$, ${\Omega }_M=0.3$ (thin line).