Age Problem In Lema(?)tre-Tolman-Bondi Void Models

Various observations, such as SN Ia, cosmic microwave background (CMB) and baryonacoustic oscillation (BAO) measurements, indicate that our Universe is undergoing accel-erated expansion. The standard cosmological model (ΛCDM) can fit the observations verywell. However, it is still suffering from many difficulties. Different methods have been devel-oped to tackle the deficiencies arising from ΛCDM. These methods can be divided into threecategories: dynamical models of dark energy, modified gravity models and models violatingthe assumption of cosmological principle.For the dynamical models of dark energy, such as quintessence, phantom, k-essence,and so on, the dynamical evolution of dark energy can successfully explain the coincidenceproblem and fine-turning problem. Modified gravity models study the character of gravity bymodifying Einstein field equation so that they can mimic the observations. Typical modifiedgravity models include f (R) theory, scalar-tensor theory, and so on. The models violat-ing cosmological principle consider the impact of inhomogeneous and/or anisotropic matterdistributions on the observed acceleration of our Universe. Among them, inhomogeneousmodels, such as Szekeres model, Swiss-Cheese model and Lema tre-Tolman-Bondi (LTB)void model, are well studied. The fundamental theories on these models are described in thiswork.Inhomogeneous models assume that the Universe is inhomogeneous but isotropic onlarge scale and may not follow the cosmological principle. Based on this assumption, theobserved acceleration can be ascribed to the inhomogeneous mass distributions so that in-troducing dark energy or modifying gravity is unnecessary. The well-known models are theLTB void models. In LTB models, the Universe is spherically symmetric and radially inho-mogeneous, and we are living in a locally underdense void centered nearby our location. Inthe present work, we use the measured ages of three old high redshift objects (OHROs) toinvestigate different LTB void models. In basic idea is that our Universe cannot be youngerthan its constituents.We study three kinds of parameterized LTB void models: Gaussian model, constrainedGarcia-Bellido-Haugb lle (GBH) model and GBH model. The three OHROs are the3.5Gyr old galaxy LBDS53W091at z=1.55, the4.0Gyr old galaxy LBDS53W069at z=1.43and2.0Gyr old quasar APM08279+5255at z=3.91, respectively. The allowed parameterspaces are explored for the three models by fixing the redshifts and ages to that of OHROs.Compared to other observations (e.g. SN Ia and CMB), We conclude that these OHROs bringa serious crisis to the LTB void models.