C. de-Sitter Space as a Solution to M-Theory

One interesting development to come out of the particle physics-cosmology interface is the role of de-Sitter space in M-theory. If inflationary theory is correct, then the universe must go through an accelerating (perhaps quasi-de-Sitter) phase at early times. However, the successes of the standard cosmology (not to mention our presence in the universe today) imply that this was a transient phase. However, the recent observations of type IA supernovae [Perlmutter et al.(1999), Riess et al.(1998b)] point to a second accelerating epoch, beginning at the present time. Taking this data at face value, there are two interesting possibilities: the acceleration could be caused by a small non-zero cosmological constant, or by some type of energy that redshifts sufficiently slowly as to cause acceleration, but that will eventually cease to act. Let us focus on the former possibility. If there exists a true cosmological constant in the universe, then the late-time space-time will approach de-Sitter space. This would seem to imply that de-Sitter space was a vacuum of the underlying theory. In the context of string theory this may be a problematic conclusion. Several authors [Hellerman et al.(2001), Fischler et al.(2001)] have recently pointed out that de-Sitter space seems to be incompatible with string theory, at least at the level of perturbation theory. Other arguments, based on upper bound on entropy in de-Sitter space [Banks(2000)] also challenge the viablity of string theory (or any theory with infinite degrees fo freedom) in a universe with a real cosmological constant. If, as measurements of the equation of state of the dark energy are refined, and string (or M) theory matures and its non-perturbative structure is understood, this tension remains, this may be a a way for cosmology to constrain our fundamental theories.