Cosmic age test in inhomogeneous cosmological models mimicking ΛCDM on the light cone

The possibility of reconstructing a spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi (LTB) model with Lambda CDM observations has drawn much attention. Recently, an inhomogeneous LTB model having the same luminosity-distance and light-cone mass density of the homogeneous Lambda CDM model was reconstructed. From the Wilkinson microwave anisotropy probe 7-year measurements together with other cosmological observations, we calculate the cosmic age at our position in this LTB model, and obtain a constraint t(LTB) < 11.7 Gyr at 1 sigma confidence level. We find that this result is, although 2 Gyr younger compared with the age of the homogeneous Lambda CDM model, still within 1 sigma agreement with the constraint of cosmic age given by current astronomical measurements. We expect that in the future, with the help of more advanced observations, we can distinguish the reconstructed inhomogeneous LTB model from the homogeneous Lambda CDM model.