where τ$_{n}$ is the time period of the nth cycle. Imagining τ$_{n}$ ≈ τ , every cycle leads to moderate inflation with the scale factor increasing with every cycle; a$_{n}$$_{+1}$/a$_{n}$ ≈ exp N . On average the Hubble expansion rate remains constant over many cycles. The exit of inflation happens when the universe leaves the negative cosmological constant to the positive cosmological constant via a dynamical scalar potential [150]. 

## Acknowledgments 

It is a pleasure to thank Rouzbeh Allahverdi, Borut Bajc, Anders Basboll, Tirthabir Biswas, Robert Brandenberger, Cliff Burgess, Michele Cicoli, Hael Collins, Pratika Dayal, Jean-Francois Dufaux, Kostas Dimopoulos, Bhaskar Dutta, Kari Enqvist, Andrew Frey, Juan Garcia-Bellido, Kazunori Kohri, Alex Kusenko, David Lyth, Tuomas Multamaki, Jerome Martin, Narendra Sahu, Philip Stephens, and Horace Stoica for fruitful discussions and comments. A.M. is also thankful to SISSA, Niels Bohr Academy, and ULB Brussels for their kind hospitality, where various parts of the review have been written. A.M. is partly supported by the Marie Curie Research and Training Network UniverseNet (MRTN-CT- 2006-035863). J.R. is funded in part by IISN and Belgian Science Policy IAP VI/11. 

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