By P. Galeotti, David N. Schramm

Court cases of the NATO complicated learn Institute, Erice, Italy, may possibly 20-30, 1986

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**Sample text**

The scalar field

The first models of new inflation were 53 based upon Coleman-Weinberg potentials, which exhibit weakly-first order transitions. , the 4> = 0 state is never metastable) will work just as we1l 92 • Most of the models for inflation now do not involve SSB, at least directly, they just involve the evolution of a scalar field which is initially displaced from the minimum of its potential. ] Since the fields involved are very weakly coupled, thermal corrections can no longer be relied upon to set the initial value of 4>.

El where IV"I ~ 9H 2 , IV'mp';VI ~ (4811V/ 2 • 45 T~ T c ----~----------~--~¢ Figure 15: In SUSY /SUGR models < cP >T is not necessarily equal to zero. If < cP >T> 0, then there is the danger that < cP >T smoothly evolves into the zero temperature minimum of the potential, thereby eliminating the possibility of inflation (upper figure). A sure way of preventing this is to design the potential so that < cP >T::; 0 (lower figure). (2) The length of the interval where ¢ evolves slowly should be much greater than H /27r, the scale of the quantum fluctuations, so that the semi-classical approximation makes sense.