Cosmological bounce and the cosmological constant problem

We discuss how the modifications of the standard Einstein's equations needed to support the cosmological bounce can at the same time lead to vanishing of the well known cosmological constant problem, while also studying the effects of spacetime fluctuations. We first concentrate on the case of the classical FLRW spacetime and show that in a bouncing cosmology, where the modification of the Einstein-Hilbert action can be represented by the most general function needed to support the bounce, the cosmological constant problem is absent if this function at late cosmological times approaches a sufficiently large value. We show that this result is general and does not depend on the details of modifications needed to support the cosmological bounce. Motivated by the recent studies of cosmological constant problem in the context of quantum vacuum and spacetime fluctuations in the standard cosmology, we then generalize our study to incorporate the effects of spacetime fluctuations. We show that some problems of the earlier proposals, like singularities and negative values of the scale factor, are also naturally resolved in the approach proposed here.Comment: 32 pages, 9 figure