tailieunhanh - The Philosophy of Vacuum Part 20

The Philosophy of Vacuum Part 20. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | The Vacuum and Unification 183 where GN is Newton s constant 10-38 GeV-2 in units h c l and p is the energy density. Generally p is considered to be either radiation- or matter-dominated. In particular it has no constant part which would correspond to a cosmological constant term. To see the effect of such a term suppose p is a constant and set y GNp A . 2 Then it is easy to see from 1 that the scale size grows exponentially with time as R t R0 exp A1 2 t-t0 J. 3 Current observations are consistent with matter-dominated expansion which grows as t2 3. This gives a very severe bound on the possible magnitude of a A 1 2 10 42 GeV. 4 On the other hand we have just argued that a Higgs vacuum leads precisely to a constant p of order 4 where is order 1015 GeV for grand unification and 250 GeV for electroweak unification. From 2 these give a j2 1011 GeV. 5 a v2 10-14 GeV. 6 Even 6 is 28 orders of magnitude away from 3 . Of course this vacuum potential energy density is a constant and we might feel that we are free to cancel it away by subtracting the appropriate constant value from V. But again this is another and worse fine-tuning problem. Actually exponential growth in R which is called inflation is believed to be a highly desirable feature in the very early stages of the evolution of the universe see . Ross 1985 sec. Guth and Steinhardt 1984 Aitchison 1985 sec. . A typical value of f required via p fA for this very early inflation is of order 1016 GeV not very different from the grand unified fu. Perhaps this is significant. At all events the fact remains that the vacuum value of Chad better be pretty nearly zero now. The idea that the value of the effective potential energy can change as a system evolves is familiar in a 184 I. J. R. Aitchison condensed matter context. A system may cool down for example so as to pass through a critical temperature where a phase transition occurs. Such a change in phase can be modelled in terms of an appropriately chosen K