Distinguishing between the inhomogeneous model and ΛCDM model with cosmic age method

Cosmological observables could be used to construct cosmological models; however, a fixed number of observables limited to the light cone are not enough to uniquely determine a certain model. In this paper, we employ a reconstructed spherically symmetric, inhomogeneous model that shares the same angular-diameter–distance–redshift relationship dA(z)dA(z) and Hubble parameter H(z)H(z) besides ΛCDM model (which we call LTB-ΛCDM model in this paper), that may provide another solution. Cosmic age, which is off the light cone, could be used to distinguish between these two models. We derive the formulae for age calculation with origin conditions. From the data given by 9-year WMAP measurement, we compute the likelihood of the parameters in these two models respectively by using the Distance Prior method and perform likelihood analysis by generating Monte Carlo Markov Chain for the purpose of bringing tighter constraints on the parameters ΩmΩm and H0H0 (the parameters that we use for calculation). The results yield: tΛCDM=13.76±0.09 GyrtΛCDM=13.76±0.09 Gyr, tLTB-ΛCDM=11.38±0.15 GyrtLTB-ΛCDM=11.38±0.15 Gyr, both in 1σ agreement with the constraint of cosmic age given by metal-deficient stars.