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This quantity is made out of electronic pictures from the Cornell collage Library historic arithmetic Monographs assortment.
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Extra resources for An elementary treatise on the theory of equations: with a collection of examples.
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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 .