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Such dignataries as Andre Linde and Maldacena and a few other similar types wrote a paper a few years ago suggesting that work be done on linking compactification and inflation. Since then we have had several papers on the link and then some others on multiple inflations, not related to compactification. The most recent 'link' paper is:
http://arxiv.org/PS_cache/hep-th/pdf/0508/0508139.pdf
Stringy Effects during Inflation and Reheating.
Andrew Frey
Likewise, the most recent paper on multiple inflations is:
http://arxiv.org/abs/hep-th/0501125
Multiple Inflation, Cosmic String Networks and the String Landscape
C.P. Burgess, Richard Easther, Anupam Mazumdar, David F. Mota, Tuomas Multamaki
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