Abstract
We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak’s classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infinity, are strong. Hence stringy corrections are inevitable in the very early stage of these inflation models. We also find that the initial singularity of the hill top inflation could be weak for non-slow roll case.
Highlights
The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and it is not clear that stringy effects become significant around it
With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak’s classification
We find that the initial singularity of the hill top inflation could be weak for non-slow roll case
Summary
We focus on an inflationary universe which approaches flat de Sitter Universe in the limit t → −∞, a(t) eHt + · · · This scale factor satisfies the assumptions which we have assumed above: vanishing scale factor at t → ti := −∞ and the incompleteness of the null geodesics. An interesting property of this Universe is that the metric components are well defined in the limit u → 0, gμν dxμdxν u∼→0. Note that this scale factor can be expressed by the comoving time t as a(t) eHt κHβ−2 (2 − β) e(3−β)Ht. From the expression (2.17), the curvature component A(u) can be evaluated as a (u) κ A(u) = a(u) = − uβ + · · ·. The metric components are well defined in the limit u → 0 as expected
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