The energy of vacuum is an ugly problem for QFT and string theory. Both in the theoretical side, the vacuum energy would be a lot greater than 0, and in the experimental side, the universe seems to be accelerating according to the famous last nineties observations. The observational side is less worrying: It is due to an imbalance among redshifth and brightness of supernovae. Well, one could try to imaginate an missing light theory (MLT) where some photons are lost in the travel from the distant supernovae to us. This would result in a lost of intensity that could explain the observations. The way to "loose photons" would be by means that some (very rare, of course) interaction with K gravitons in a warped scenario, or in F-theory like scenaries where unification of gauge bossons is in upper dimensional branes one could try to search ways to loose some photon in that branes. Ok, this an idea of myself, and I have not purchased it too much, there are good reasons to think it is not an excellent/important idea.
Or it could be that the accelerated expansios is real but not due to a cosmological constant. One way would be the entropic force scenarie of Gerge Smooth where the acceleration is due to a entropic force caused by the entropy of the cosmological horizon. Or, maybe some "dark energy" theorie.
All of those phenomemenological problems and solutions don't address the fundamental problem that there is a vacuum energy in QFT that should be great. The most extended way is a"landscape + antropic" solution based on the Weimberg ideas and developed by Polchinsky, Bousso, etc and has derived in the multiverse scenario.
Reading the articles in the CC problem (for example, this of WItten: The Cosmological Constant From The Viewpoint Of String Theory or this other of Polchinsky: The Cosmological Constant and the String Landscape ) one can learn that the main objective is to get an small vacuum energy. But I thin that there is another alternative. To put the vacuum energy out of the reach of gravity. That sound like a hard problem because gravity couples to everything, that seems to be one of the most imprtant insights of general relativity. Well, of course I have not a mechanism to hide the vacuum energy for gravity or I would be trying to publish the paper where I develop it to some important review (and it would be in the arxiv just now), butt he key point is that if there is a way to do so it would give an elegant solution to a long standing problem and it could be, possibly, consistent with all the cosmological constraints, including accelerated expansion, inflation, CMB, etc. Well, maybe one could try to relate the mechanism to the observation that some people has made among the CC (presumably) observed value and the neutrino masses. Or, better, to try to relate it to the (presumably) recent observation of different masses among a neutrino and an antineutrino.Or one could forget neutrinos at all, of course.
Well, it is a pre-idea, as I said. For the most conservative readers my recommendation is to look at the two papers I linked (if they haven't already made it) and forget my comments ;-).