Could our Universe have begun with Negative Lambda?
  In this paper we present an informal description of the Cyclic Inflation scenario which allows our universe to "start" with a negative potential energy, inflate, and then gracefully exit to a positive potential energy universe. We discuss how this scenario fares in comparison with the standard inflationary paradigm with respect to the classic cosmological puzzles associated with the horizon, flatness and isotropy of our current universe. We also discuss some of the most debilitating problems of cyclic cosmologies, Tolman's entropy problem, and the problem with the overproduction of blackholes. We also sketch the calculation of the primordial spectrum in these models and possible observable signatures. We end with a special focus on the exit mechanism where the universe can transition from the negative to a positive potential region. The treatise is based on an ongoing collaboration between the authors and closely follows conference presentations given on the subject by TB. 
Tirthabir Biswas, Tomi Koivisto, and Anupam Mazumdar
astro-ph.CO gr-qc