Could LIV/noncommutativity alleviate the cosmological constant problem

We test the hypothesis that in models with an explicit breaking of Lorentz invariance (LIV models) the problem with the cosmological constant may, if not already be solved, then at least may partially be mitigated by improving its UV behaviour. Certain class of noncommutative models that have a well defined dual momentum space geometry and in addition set up a suitable frame for developing the appropriate DSR models are also subject to the same test.