A dynamical systems study of the inhomogeneous Lambda-CDM model
  We consider spherically symmetric inhomogeneous dust models with a positive
cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric.
These configurations provide a simple but useful generalization of the
Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which
seems to fit current cosmological observations. The dynamics of these models
can be fully described by scalar evolution equations that can be given in the
form of a proper dynamical system associated with a 4-dimensional phase space
whose critical points and invariant subspaces are examined and classified. The
phase space evolution of various configurations is studied in detail by means
of two 2-dimensional subspaces: a projection into the invariant homogeneous
subspace associated with Lambda-CDM solutions with FLRW metric, and a
projection into a subspace generated by suitably defined fluctuations that
convey the effects of inhomogeneity. We look at cases with perpetual expansion,
bouncing and loitering behavior, as well as configurations with "mixed"
kinematic patters, such as a collapsing region in an expanding background. In
all cases, phase space trajectories emerge from and converge to stable past and
future attractors in a qualitatively analogous way as in the case of the FLRW
limit. However, we can identify in both projections of the phase space various
qualitative features absent in the FLRW limit that can be useful in the
construction of toy models of astrophysical and cosmological inhomogeneities.
