2012-02-27

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Tomohiro Nakama (RESCEU)

14:00-

Title:
Setting up the initial condition for the formation of
primordial black holes by asymptotic expansion

Abstract:
We constitute a solution of the Einstein equations for a spherically
symmetric perturbed region in the radiation dominated Friedmann
Universe in order to set up the initial condition for the formation of
primordial black holes. The analytic solution is obtained in terms of
the asymptotic expansion with respect to the ratio of the size of the
perturbed region to the Hubble radius, and it is fully determined by
the initial profile of the superhorizon curvature perturbations. Solv-
ing the recurrence formulae up to the eighth order in the expansion
parameter, we show that the errors associated with truncation remain
small enough for various initial curvature profiles to provide the ini-
tial condition for the full numerical analysis of primordial black hole
formation.