Possible solution to the main cosmological constant problem
  A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the vector fields dynamically cancel an arbitrary cosmological constant, and flat Minkowski spacetime appears as the limit of attractor-type solutions of the field equations. Asymptotically, the field equations give rise to a standard Friedmann-Robertson-Walker universe and standard Newtonian gravitational dynamics of small systems. 
V. Emelyanov, F. R. Klinkhamer
hep-th gr-qc