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

infinity is not enough 203Let’s now assume that we do live in a simply connected universe. Let’s suppose thatfuture experiments will be sufficiently precise to detect a slight deviation, either positiveor negative, from the Euclidean space (k ≠ 0, 0 ≠ 1). Indeed, that would be a greatdiscovery. However, even in that case we would not be able to draw strong conclusionson the universe as a whole. A small curvature might be a “local” effect rather than aglobal feature – just as a valley is a local concave shape on the overall spherical surfaceof a planet. Our view of the universe is similar to that of a sailor in the middle of theocean with a visibility limited by mist at large distance (resembling the last scatteringsurface). Waves in the real ocean are typically at a given length; this preferential scalemay correspond to the size of galaxies in the real universe. However, CMB observationstell us that in the early cosmic plasma, waves were present on all scales with nearlyconstant amplitude (the so-called Harrison-Zel’dovich scale-invariant spectrum). Thismeans that even on the largest dimensions we do expect deviations from the unperturbedscenario. 20 It’s as if our sailor saw waves of all possible lengths, including some soextended that they encompass the entire horizon and beyond. If the sailor happened tobe in the valley of a very long cosmic wave, a precision measurement of the curvature ofthe water surface would lead him to the erroneous conclusion that the earth is negativelycurved or flat and infinite in extent.It is clear that strong claims on the infinity of space based on the apparent spatialflatness of the observable universe might be as naive as those ancient ideas on theflatness of the earth based on local and inaccurate observation, but with an importantdifference: in the case of cosmic space, the ambiguity would remain even with infinitelyaccurate data. This is because our cosmic horizon, unlike the visibility horizon on theearth surface, is a fundamental boundary (Barrow 1999; Ellis 2006) not surmountablewith improved instruments or more refined theory.9.5 Infinity Is Not EnoughEven if we assume the flat infinite universe, we are still confronted with the questionof why something like life (here and now at least) is actually happening. Even thoughany system with nonzero probability would occur infinitely often in such a universe,this doesn’t mean that anything can happen: the possibility of something happeningdepends on the ingredients and the physical laws of that universe. A lattice structurerepeating itself in all directions, such as that pictured by Maurits C. Escher in his famousCubic Space Division (Escher 1952), makes an infinite universe with a very sharp –and low – limit to complexity. In an infinite FLRW universe, complexity and life wouldnot appear unless the physics has highly specialized characteristics. In fact, it turns outthat many basic parameters in our universe, such as the value of coupling constants, themass and charge of elementary particles, the rate of cosmic expansion, the amplitude ofdensity perturbations in the early universe, the number of space and time dimensions,and the form of physical laws, are extremely sensitive to life-supporting conditions. Infact, their measured values turn out to be precisely tuned for complex structures andlife to emerge (Barrow and Tipler 1986).20 These largest fluctuations have not been processed during the history of the universe because they are outsidethe causal horizon.