Gauge-Invariant Metric Perturbations in the Inflationary Universe

Accession number;03A0275218
Title;Gauge-Invariant Metric Perturbations in the Inflationary Universe
Author;WATANABE TOMOKI(Tokai Univ.)   HAYASHI MITSUO(Tokai Univ.)   
Journal Title;Proc Sch Sci Tokai Univ
Journal Code:S0439A
ISSN:0919-5025
VOL.38;NO.;PAGE.97-151(2003)
Figure&Table&Reference;FIG.1, REF.20
Pub. Country;Japan
Language;Japanese
Abstract;The tiny anisotropies of cosmic microwave background(CMB) originate from geometrical inhomogeneity in the early universe, and such inhomogeneity is considered as a candidate for the origin of structure. In this paper, we strictly treat the geometrical perturbations, which are caused by the quantum fluctuation of scalar fields in the inflationary universe, and look into their evolution under the general relativity. General perturbations are not invariant under the gauge transformation. So in order to manage the freedom of gauge choice, we reconstruct the perturbed Einstein equations from the gauge-invariant quantities. The equation of motion for only metric perturbation is derived from the Einstein equations contained the matter and the geometrical quantity, and can be solved in the limit case. Here, in order to clarify a constraint from the matter to geometry, we calculate the second-order action of gravity and scalar field. Giving attention to this constraint and applying the accelerated-expansion of the universe, we find that the evolution of metric perturbation will "freeze-in" in the midst of inflation, and that its spectrum is determined by potential of scalar field. By comparing with the observation of the CMB anisotropy, in the case of m2.PHI.2 potential, it is concluded that the inflaton mass is ordered-1013 GeV, and in the case of .LAMBDA..PHI.4 potential, the coupling constant is ordered-10-12, which is very weak. Finally, as a future view, we briefly discuss hybrid inflation model in the context of supersymmetry which seems to play an elementary role in the early unverse. (author abst.)