Age Problem in Lemaitre-Tolman-Bondi Void Models
  As is well known, one can explain the current cosmic acceleration by
considering an inhomogeneous and/or anisotropic universe (which violates the
cosmological principle), without invoking dark energy or modified gravity. The
well-known one of this kind of models is the so-called
Lema\^{\i}tre-Tolman-Bondi (LTB) void model, in which the universe is
spherically symmetric and radially inhomogeneous, and we are living in a
locally underdense void centered nearby our location. In the present work, we
test various LTB void models with some old high redshift objects (OHROs).
Obviously, the universe cannot be younger than its constituents. We find that
an unusually large $r_0$ (characterizing the size of the void) is required to
accommodate these OHROs in LTB void models. There is a serious tension between
this unusually large $r_0$ and the much smaller $r_0$ inferred from other
observations (e.g. SNIa, CMB and so on). However, if we instead consider the
lowest limit 1.7\,Gyr for the quasar APM 08279+5255 at redshift $z=3.91$, this
tension could be greatly alleviated.
