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Effective equations in quantum cosmology by Barvinsky, Nesterov.

By Barvinsky, Nesterov.

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Lett. B 117 (1982) 25. D. D. Linde, Lett. A. Rubakov, Phys. Lett. B 148 (1984) 280; A. Vilenkin, Phys. Rev. B. A. Starobinsky, Sov. Astron. Lett. 10 (1984) 135. O. Yu. Kamenshchik, Phys. Lett. B 332 (1994) 270. O. Yu. V. Mishakov, Nucl. Phys. B 491 (1997) 387. [8] J. , Aph. J. 396 (1992) L1. [9] I. Strukov, A. Brukhanov, D. Skulachev, M. Sazhin, Pis’ma A. Zh. 18 (1992) 387; I. Strukov, A. Brukhanov, D. Skulachev, M. Sazhin, Mon. Not. R. Astron. Soc. 258 (1992) 37. O. Barvinsky, Open inflation without anthropic principle, hep-th/9806093.

11) Since δ ϕ¯ contains ϕ˙¯ in the denominator, all the other perturbations in the minimal frame ¯ ψ) ¯ ∼ O( )δ ϕ/m δ ϕ/m ¯ P . Therefore, in view of are much smaller in magnitude, (A, ¯ P Eqs. 18) the perturbations in the nonminimal frame read A −ψ 4π δ ϕ¯ , 3 mP δϕ 4π ϕ δ ϕ, ¯ 3 mP Ht 1. 12) Another important property of the perturbations in both frames is that to the leading order in slow roll they are constant in time for H t 1. This follows from Eqs. O. V. Nesterov / Nuclear Physics B 608 (2001) 333–374 371 containing the exponentially growing functions of time in both of its numerator and denominator (respectively Q and a).

43). 42) vanishes, but the only effect that the positive F q (0) can produce in this case is that it shifts the equilibrium point eff (ϕ∗ ) = 0, at which again from ϕI to slightly higher value of the inflaton ϕ∗ , F q (0) + FNB the system will undergo endless inflation. 8. 2) with the Hubble constant H (ϕ) approximately linear in ϕ. In the Einstein frame, it looks ¯ = similar with the Hubble constant which is practically independent of the inflaton H 2 (ϕ) 2 2 /96π|ξ |2 , the cosmic time parameters being related in both frames 8π V (ϕ)/3m ¯ λm P √ P by t¯ t 8π|ξ |ϕ/mP .

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