Double Inflation Page: 17 of 31
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of e-folds of inflation in each successive episode of inflation tumbles downward with the
last ‘hitting’ at value of order 10-100.
(3) Late Chaos. For our purposes, Linde’s chaotic inflation21 has the attractive feature
that the number of e-folds of inflation N ~ 7r(</>i/rop()2. That means for <pi ~ 0[few mpi)
inflation lasts 30 or so e-folds-just the number we want! In this model we make the scalar
field <f>2 the chaotic inflater.
Again we have two weakly-coupled scalar fields 4>\ and 4>2 with scalar potentials
Vi(*i) =; \\GA(2 + A1<^i4[ln(0i2/cr2) - 1/2] (2.12)
V2{4>2) ^ A2024 (2.13)
where Ai ~ 10-12, a ~ 300mp(, and A2 cs 10-8. The initial values of the scalar fields <f\
and <f>2 are taken to be: <f>n ~ <^2* — few mpi.
In this model scalar field <f>\ inflates first and produces density perturbations of order
10-4 on large scales. Then field <f>2 inflates, producing density perturbations of order
0.01 — 0.1 on scales smaller than Maeed. The quantum fluctuations in 02 produced during
the first episode of inflation are smaller than the initial value we have chosen for <f>2 and
so thereby do not affect the initial value of <^2. The second episode of inflation lasts the
requisite number of e-folds because the initial value of is of the order of a few mpi.
This model is really a toy model and we will not attempt to tie it to any particle physics
phenomenology. We present it as another qualitatively different way to achieve 40-50
e-folds of inflation during the second episode of inflation.
(4) Bubbles. Finally, we mention a very speculative possibility. Heretofore, we have
considered potentials without barriers between the initial value of <f> and the value of at
the minimum of its potential. Suppose the potential for (j>2 had such a barrier. Then the
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Silk, J. & Turner, M. S. Double Inflation, report, April 1, 1986; United States. (https://digital.library.unt.edu/ark:/67531/metadc1094833/m1/17/?rotate=90: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.