Small field models with gravitational wave signature supported by CMB data

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index ns, the running of the scalar index nrun and the tensor to scalar ratio r. We find that for non-vanishing nrun and for r as small as r = 0.001, the precisely calculated values of ns and nrun deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of ns and nrun for values of r that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable r while conforming to known CMB observables.

我们针对一类可产生高张量-标量比的小尺寸单场暴胀模型，研究了其宇宙微波背景（cosmic microwave background, CMB）功率谱的尺度依赖性。本文所考虑的暴胀子势能为五次多项式，我们精确计算了该类势能下的功率谱，并提取出三项宇宙学参数：标量谱指数（scalar index, $n_s$）、标量谱指数跑动量（running of the scalar index, $n_{ ext{run}}$）以及张量-标量比（tensor to scalar ratio, $r$）。研究发现，当$n_{ ext{run}}$非零且$r$低至0.001时，$n_s$与$n_{ ext{run}}$的精确计算值与标准解析处理的预测结果存在显著偏差。我们对该类偏差展开了细致研究，并探讨了其潜在成因。据此，此前所有已被研究的此类模型均基于不准确的假设前提。我们扫描了势能参数的可行取值空间，使得对应的宇宙学参数处于观测允许的区间内。该五参数模型族能够在$r$高达0.001的情况下，复现$n_s$与$n_{ ext{run}}$的所有允许取值。本研究通过构建符合已知宇宙微波背景观测结果且可产生可观张量-标量比的模型，一举驳斥了此前基于解析Stewart-Lyth项构建的同类模型，并重新激活了小场暴胀模型的研究方向。