The upper bound on the tensor-to-scalar ratio consistent with quantum gravity. (20th May 2021) - Wu, Lina; Gao, Qing; Gong, Yungui; Jia, Yiding; Li, Tianjun
Abstract: We consider the polynomial inflation with the tensor-to-scalar ratio as large as possible which can be consistent with the quantum gravity (QG) corrections and effective field theory (EFT). To get a minimal field excursion Δ ϕ for enough e-folding number N, the inflaton field traverses an extremely flat part of the scalar potential, which results in the Lyth bound to be violated. We get a CMB signal consistent with Planck data by numerically computing the equation of motion for inflaton ϕ and using Mukhanov–Sasaki formalism for primordial spectrum. Inflation ends at Hubble slow-roll parameter ϵ 1 H = 1 or a ̈ = 0 . Interestingly, we find an excellent practical bound on the inflaton excursion in the format a + b r, where a is a tiny real number and b is at the order 1. To be consistent with QG/EFT and suppress the high-dimensional operators, we show that the concrete condition on inflaton excursion is Δ ϕ M Pl < 0.2 × 10 ≃ 0.632 . For n s = 0.9649, N e = 55, and Δ ϕ M Pl < 0.632, we predict that the tensor-to-scalar ratio is smaller than 0.0012 for such polynomial inflation to be consistent with QG/EFT.