Lyth bound of inflation with a tilt

Abstract

We provide strong evidence for universality of the inflationary field range: given an accurate measurement of ðn s ; rÞ, one can infer Δϕ in a model-independent way in the sub-Planckian regime for a range of universality classes of inflationary models. Both the tensor-to-scalar ratio as well as the spectral tilt are essential for the field range. Given the Planck constraints on n s , the Lyth bound is strengthened by two orders of magnitude: whereas the original bound gives a sub-Planckian field range for r ≲ 2 × 10 −3 , we find that n s ¼ 0.96 brings this down to r ≲ 2 × 10 −5 .

Inflationary field excursion in broad classes of scalar field models

“…At present it is in excellent agreement with the experimental results. The technique followed in this work has been proposed in the context of chaotic inflation as the benchmark model [14]. However the recent Planck data release rules out values of r > 0.09 while for quadratic potential in the chaotic class r = 0.16.…”

“…Lyth bound gives a guideline for the minimal single field slow roll scenario. Depending on whether one considers to vary or not during the horizon exit to the end of inflation more stringent constraints of Lyth bound can be imposed [18]. In this analysis we retain the considerations originally used to define the field excursion.…”

“…Most importantly this model can be understood in the context of supergravity, viewed as an effective theory. It has been the general practice earlier [14] to choose the chaotic inflationary scenario [15] as benchmark. However the minimal chaotic models are almost ruled out after Planck 2015 for not satisfying the bound on stochastic gravity wave amplitude (for the chaotic model r > 0.09).…”

Predictions of Spectral Parameters by Several Inflationary Universe Models in Light of the Planck Results

“…They calculated the spectral parameters from the expressions (4.63) and found the r, δ ns − relation 68) where the value of sin(2θ) must either be assumed or determined from measured values of the spectral parameters, and [65], and Garcia-Bellido and Roest [66,67] have independently of each other introduced a new so-called N-formalism, which is useful in calculating the physical parameters characterizing the observable properties of the CMB-radiation. It has been further developed by Bamba and Odintsov [68].…”

“…Using the N-formalism Roest [70], Mukhanov [71], and Garcia-Bellido et al [66,67] have recently classified a large number of inflationary universe models into so-called universality classes. In these classes the slow roll parameters ε, η and ξ have an asymptotic power law dependence on the number N of e-folds.…”