论文标题
使用$ e $ -MMODEL $α$ -ATTRACTOR EFTRATON电位的宇宙学扰动模式分析
Mode analysis of cosmological perturbations with the $E$-model $α$-attractor inflaton potentials
论文作者
论文摘要
我们已经对单次弹性通货膨胀扰动进行了详细的$ k $模式分析，包括量子波动，通过设置非线性耦合的Aftraton场（$ ϕ $），其扰动（$ δϕ $）和$ $ $ $ $ $ $ $ $）（$）的（$ δϕ $），并计算出（$）的数量（$），计算，计算均计算频谱索引（$ n_s $），张频谱索引（$ n_h $），标量功率谱（$δ_s$），张量功率谱（$δ_H$），张量表与尺度比率（$ r $）和hubble参数（$ h $）的不同$ k $值在地平线上。在这些计算中，我们采用了$ e $ -model $α$ -Attractor的电位，这些电位显示出显示缓慢的行为。我们获得的$ n_s $和$ r $的值与众所周知的通用$α$ -Attractor公式的值一致。我们得到$ n_s = 0.956908 $和$ r = 0.005571 $ at $ k = 10^6 $ planck单位，用于潜在参数$ n = 1 $的价值。可以将这些与Planck-2018 Data相提并论，即$ n_s = 0.9649 \ pm 0.0042 $，$ 68 \％$ cl，$ r <0.064 $ at $ 95 \％\％$ $ cl和ACT-2020 Data viz。
We have carried out detailed $k$-mode analysis of single-inflaton slow-roll inflationary perturbations including quantum fluctuations by setting up non-linear coupled differential equations of inflaton field ($ϕ$), its perturbation ($δϕ$) and the metric perturbation (the Bardeen potential, $Φ_B$), and calculated the number of e-folds ($N$), scalar spectral index ($n_s$), tensor spectral index ($n_h$), scalar power spectrum ($Δ_s$), tensor power spectrum ($Δ_h$), tensor-to-scalar ratio ($r$) and the Hubble parameter ($H$) for different $k$ values at the horizon crossing. In these calculations we have employed the $E$-model $α$-attractor potentials which are found to display slow-roll behaviour. The values of $n_s$ and $r$ obtained by us are consistent with those given by the well-known universal $α$-attractor formulae. We got $n_s = 0.956908$ and $r= 0.005571 $ at $k = 10^6$ Planck unit for the value of the potential parameter $n = 1$. These can be compared with the Planck-2018 data viz., $n_s = 0.9649\pm 0.0042$ at $68\%$ CL, $r<0.064$ at $95\%$ CL and ACT-2020 data viz., $n_s = 0.9691\pm 0.0041$ at $68\%$ CL.
