  We present an unconventional approach for addressing the old cosmological
constant (CC) problem in a class of F(R,G) models of modified gravity. For a CC
of arbitrary size and sign the corresponding cosmological evolution follows an
expansion history which strikingly resembles that of our real universe. The
effects of the large CC are relaxed dynamically and there is no fine-tuning at
any stage. In addition, the relaxation mechanism alleviates the coincidence
problem. The upshot is that a large cosmological constant and the observed
cosmic expansion history coexist peacefully in the Relaxed Universe. This model
universe can be thought of as an interesting preliminary solution of the
cosmological constant problem, in the sense that it provides a successful
dynamical mechanism able to completely avoid the fine-tuning problem (the
toughest aspect of the CC problem). However, since the Relaxed Universe is
formulated within the context of modified gravity, it may still suffer of some
of the known issues associated with these theories, and therefore it can be
viewed only as a toy-model proposal towards a final solution of the CC problem.
