Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy
  A wide range of large scale observations hint towards possible modifications
on the standard cosmological model which is based on a homogeneous and
isotropic universe with a small cosmological constant and matter. These
observations, also known as "cosmic anomalies" include unexpected Cosmic
Microwave Background perturbations on large angular scales, large dipolar
peculiar velocity flows of galaxies ("bulk flows"), the measurement of
inhomogenous values of the fine structure constant on cosmological scales
("alpha dipole") and other effects. The presence of the observational anomalies
could either be a large statistical fluctuation in the context of {\lcdm} or it
could indicate a non-trivial departure from the cosmological principle on
Hubble scales. Such a departure is very much constrained by cosmological
observations for matter. For dark energy however there are no significant
observational constraints for Hubble scale inhomogeneities. In this brief
review I discuss some of the theoretical models that can naturally lead to
inhomogeneous dark energy, their observational constraints and their potential
to explain the large scale cosmic anomalies.
