论文标题
与量子重力一致的张量与量表比的上限
The Upper Bound on the Tensor-to-Scalar Ratio Consistent with Quantum Gravity
论文作者
论文摘要
我们认为，尽可能大的张量与尺度比率的多项式通胀可以与量子重力（QG）校正和有效场理论（EFT）一致。为了获得最小的场游览$ δϕ $，用于足够的电子折叠数$ n $，Inflaton场遍历标量潜力的极平坦的部分，这导致否则违反了lyth。我们通过数值计算Aftraton $ ϕ $的运动方程并将Mukhanov-Sasaki形式主义用于原始频谱来获得与Planck数据一致的CMB信号。通货膨胀以hubble慢速参数$ε_1^h = 1 $或$ \ ddot {a} = 0 $结束。 Interestingly, we find an excellent practical bound on the inflaton excursion in the format $a+b{\sqrt r}$, 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 $ \ frac {δϕ} {m _ {\ rm pl}} <0.2 \ times \ sqrt {10} \ simeq 0.632 $。对于$ n_s = 0.9649 $，$ n_e = 55 $，和$ \ frac {δϕ} {m _ {\ rm pl}} <0.632 $，我们预测，张量 - 标准比率为0.0012，用于与qg/eft的这种多态通信的0.0012。
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 $Δϕ$ 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 $\ddot{a}=0$. Interestingly, we find an excellent practical bound on the inflaton excursion in the format $a+b{\sqrt r}$, 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 $\frac{Δϕ}{M_{\rm Pl}} < 0.2 \times \sqrt{10}\simeq 0.632$. For $n_s=0.9649$, $N_e=55$, and $\frac{Δϕ}{M_{\rm Pl}} < 0.632$, we predict that the tensor-to-scalar ratio is smaller than 0.0012 for such polynomial inflation to be consistent with QG/EFT.
