The upper bound on the tensor-to-scalar ratio consistent with quantum gravity. (20th May 2021)

• Record Type: Journal Article
• Authors: Wu, Lina; Gao, Qing; Gong, Yungui; Jia, Yiding; Li, Tianjun
• Is Part Of: Communications in theoretical physics. Volume 73:Number 7(2021)
• Publication Date: 2021-05-20
• Subjects: polynomail inflation -- Lyth bound -- tensor-to-scalar ratio; Physics -- Periodicals; 530.105
• DOI: 10.1088/1572-9494/abf824
• Languages: English
• ISSNs: 0253-6102

Abstract

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.