Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-09-04
Phys.Rev. D63 (2001) 044013
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages
Scientific paper
10.1103/PhysRevD.63.044013
We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.
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