Inflationary predictions Sample Clauses

Inflationary predictions. ‌ s To have a successful inflationary scenario, we need enough e-folds (at least 50-60) and we need to obtain the right perturbations ∆2 and spectral tilt ns 50-60 e-folds before the end of inflation. As shown in the previous section, more than 60 e-folds of expansion can be obtained very easily in this scenario - the scale of inflation H can be set to be much smaller than the Xxxxxx mass, so s 1 continues for many e-folds before H differs significantly from the value at symmetry breaking HSB, meaning that we get enough inflation. Here we show how the perturbations are generated once the field is classically rolling to the minimum. The perturbations in the spatially flat gauge (Ψ = 0) are defined as [22] (Eq. (1.64)) H Hϕ˙ δϕ ζ = − ρ¯˙ δρ = − ρ + p , (2.38) where we use δρ = V jδφ and also 3Hφ˙ = −V j but as opposed to what we did after Eq. (1.64), we can not say ρ + p = ϕ˙2. We note the pertubations in our model will lead to the usual expression encountered in models of warm inflation [108]. More explicitly, in our theory, the Hawking temperature is given by the vacuum solution of a conformal field inside the horizon, but, as well, for any conformal scalar field, the effective mass term of the Ricci scalar makes the field fluctuations around its mean value exponentially small, therefore we do not need to consider the temperature fluctuations in the calculation of the scalar perturbations. The power spectrum takes the form ∆2 = (ζζ) = . Hϕ˙ Σ2 . H Σ2 . Hϕ˙ . H ΣΣ2 P , (2.39) s ρ + p 2π −2H˙ M 2 2π = where from now on we set ϕ2 ≡ (φ2). In contrast to single field slow roll inflation −2H˙ M 2 = 4 N π2 T 4 , in the current setting the perturbations and the tilt are given P 3 30 H by ∆2 = . Hϕ˙ . H ΣΣ2 = .180π ϕ˙ Σ2 = .60π m2ϕ + λϕ3 Σ2 (, 2.40) s 4 N π2 T 4 2π NH2 NH3