The cosmological constant has a strange history.. It was first introduced by Einstein and then removed by himself, in order to describe a static universe. Einstein even qualified the removal of the Cosmological Constant (CC) as ‘the biggest blunder’ of his carreer, since he basically missed predicting the universe expansion. The existance of a CC is now well accepted and supported by the recent data released by the Planck mission, that favours the ‘ Cold Dark Matter -Lambda model’, Lambda refering to the (positive) CC.
During my Ph.D, I studied deformations of known solutions in asymptotically flat space by inclusion of a CC, both positive and negative. Adding this term can actually lead to drastic changes in the properties of the objects under consideration. For example, a braneworld (see next section) model with a positive CC on the brane and in the bulk turns out to have a closed geometry. Another example, better known is that small black holes (compared to the scale of the CC) have essentially the same properties that asymptotically flat black holes (they don’t feel the CC), while big black holes do feel the effect and have different thermodynamical properties, such as becoming thermally stable.