The cosmological constant and the relaxed universe
  We study the role of the cosmological constant (CC) as a component of dark
energy (DE). It is argued that the cosmological term is in general unavoidable
and it should not be ignored even when dynamical DE sources are considered.
From the theoretical point of view quantum zero-point energy and phase
transitions suggest a CC of large magnitude in contrast to its tiny observed
value. Simply relieving this disaccord with a counterterm requires extreme
fine-tuning which is referred to as the old CC problem. To avoid it, we discuss
some recent approaches for neutralising a large CC dynamically without adding a
fine-tuned counterterm. This can be realised by an effective DE component which
relaxes the cosmic expansion by counteracting the effect of the large CC.
Alternatively, a CC filter is constructed by modifying gravity to make it
insensitive to vacuum energy.
