Astroparticle Physics

12.4 How Inflation Works 251the predicted monopoles. Foremost among these is that theenergy density would be so high that the universe wouldhave recollapsed long ago. Given the currently observed expansionrate and photon density, the predicted contributionfrom monopoles would lead to a recollapse in a matter ofdays.So, here is not merely a failure to explain the universe’sinitial conditions, but a real contradiction between a predictionand what one observes. One could always argue, ofcourse, that Grand Unified Theories are not correct, and indeedthere is no direct evidence that requires such a pictureto be true. One can also try to arrange for types of GUTswhich do not produce monopoles, but these sorts of the theoryare usually disfavoured for other reasons. Historically,the monopole problem was one of the factors that motivatedAlan Guth to propose the mechanism of inflation, an acceleratingphase in the early universe. In the next sections itwill first be defined more formally what inflation is and howit could come about, and then it will be shown how it solvesnot only the monopole problem but also the horizon and flatnessproblems as well.recollapsedue to magnetic monopolesmonopole probleminflation solves the puzzles12.4 How Inflation Works“No point is more central than this, thatempty space is not empty. It is the seatof the most violent physics.”John Archibald WheelerInflation is defined as meaning a period of accelerating expansion,i.e., where ¨R >0. In this section it will be investigatedhow this can arise. Recall first the Friedmann equation,which can be written asṘ 2R 2 + k R 2 = 8πG ϱ, (12.12)3where here the term ϱ is understood to include all formsof energy including that of the vacuum, ϱ v .Itwasshownin Chap. 8 that this arises if one considers a cosmologicalconstant Λ. This gives rise to a constant contribution to thevacuum which can be interpreted as vacuum energy densityof the formϱ v =Λ8πG . (12.13)vacuum energycosmological constant