Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

infinity in inflationary cosmology 179V ()MFTFigure 8.1. A double-well inflationary potential V (φ). For a homogeneous cosmological scalarfield in such a potential, the field dynamics are much like a ball on a corresponding landscape:there is an acceleration proportional to the steepness of the slope and a friction term opposingthe velocity. Thus, the field at a point will generally evolve from its initial value “down thehill” to oscillate around, then settle into, a minimum. With quantum effects, tunneling througha barrier can also occur in a potential like this one. In this model, V (φ F ) corresponds to aninflationary vacuum energy, and V (φ T ) corresponds to our observed vacuum energy. A bubbleforms as the field tunnels through the barrier to the field value φ = φ M . Inflation within thebubble can occur as the bubble rolls down the potential, ending when the field nears the trueminimum at φ t .the early universe included a brief phase of exponential expansion, driven by vacuumenergy (in the form of the potential energy V (φ) of a scalar field φ). Alan Guthshowed that such a phase, which he dubbed “inflation,” would lead to a universe thatis large, homogeneous, of very nearly flat spatial geometry, and free of troublesomepreinflationary relics such as magnetic monopoles Guth (1981).In subsequently developed pictures of inflation, the exponential expansion endswhen φ (the “inflaton” field) relaxes to near a minimum of its potential V (φ). Thispicture is slightly complicated by quantum fluctuations: as the inflaton classically“rolls” to the minimum (Fig. 8.1), it also undergoes quantum fluctuations up and downthe potential. These are an important feature: they lead inflation to end in slightlydifferent times in different nearby places. This translates into density perturbations ofjust the type (nearly scale-invariant, Gaussian, and adiabatic) that are required to seedgalaxy formation later and that are observed in the temperature inhomogeneities of thecosmic microwave background (CMB).The ability of inflation to give rise to just the sort of early state that explains ourobserved universe has led to fairly widespread acceptance of it as an indispensableingredient of modern cosmology (see, e.g., Guth (2004), Linde (2007a) for recentreviews), and the evidence in its favor appears to keep improving. Most recently, thethree- and five-year data from the WMAP observations of the CMB indicate a slightdeparture from scale invariance in the density perturbations, which is a generic predictionof inflation models (Komatsu et al. 2008). There are some candidate alternativesto inflation, but I think that it is safe to say that none are anywhere near as compelling,at least in the minds of the vast majority of cosmologists, as inflation.But inflation, if accepted, comes with a certain amount of rather heavy baggage.