Solutions to the cosmological constant problems - art. no. 023517

We critically review several recent approaches to solving the two cosmologi cal constant problems. The "old" problem is the discrepancy between the obs erved value of rho (Lambda) and the large values suggested by particle phys ics models. The second problem is the "time coincidence" between the epoch of galaxy formation t(G) and the epoch of Lambda domination t(Lambda). It i s conceivable that the "old" problem can be resolved by fundamental physics alone, but we argue that in order to explain the ''time coincidence'' we m ust account for anthropic selection effects. Our main focus here is on the discrete-Lambda models in which Lambda can change through nucleation of bra nes. We consider the cosmology of this type of model in the context of infl ation and discuss the observational constraints on the model parameters. Th e issue of multiple brane nucleation raised by Feng et al. is discussed in some detail. We also review continuous-Lambda models in which the role of t he cosmological constant is played by a slowly varying potential of a scala r field. We find that both continuous and discrete models can in principle solve both cosmological constant problems, although the required values of the parameters do not appear very natural. M-theory-motivated brane models, in which the brane tension is determined by the brane coupling to the four -form field, do not seem to be viable, except perhaps in a very tight corne r of the parameter space. Finally, we point out that the time coincidence c an also be explained in models where Lambda is fixed, but the primordial de nsity contrast Q = delta rho/rho is treated as a random variable.