This is the claim of a paper appearing in today's Cornell archives. Not as long as expected but long enough. The collapse mechanism depends on dark energy.

http://arxiv.org/

http://arxiv.org/abs/astro-ph/0307185

Observational Bounds on Cosmic Doomsday
Authors: Renata Kallosh, Jan Kratochvil, Andrei Linde, Eric V. Linder, Marina Shmakova
Comments: 11 pages, 6 figures, revtex4
Report-no: SLAC-PUB-10032
Recently it was found, in a broad class of models, that the dark energy density may change its sign during the evolution of the universe. This may lead to a global collapse of the universe within the time t_c ~ 10^{10}-10^{11} years. Our goal is to find what bounds on the future lifetime of the universe can be placed by the next generation of cosmological observations. As an example, we investigate the simplest model of dark energy with a linear potential V(\phi) =V_0(1+\alpha\phi). This model can describe the present stage of acceleration of the universe if \alpha is small enough. However, eventually the field \phi rolls down, V(\phi) becomes negative, and the universe collapses. The existing observational data indicate that the universe described by this model will collapse not earlier than t_c > 10 billion years from the present moment. We show that the data from SNAP and Planck satellites may extend the bound on the "doomsday" time to t_c > 40 billion years at the 95% confidence level.