We introduce a set of generic conditions for the slow contracting Universe and for a narrowed-down category of models called fast-roll models. We present general conditions for superhorizon freeze-out of scalar and tensor perturbations and show that any fast-roll model satisfies them, as in the case of inflation. We are interested in the “Sourced Bounce” scenario, where perturbations are sourced by a U(1) gauge field coupled to a bouncer scalar field. The requirement of a slightly red tilted scalar spectrum greatly restricts the allowed couplings between the scalar and the gauge field. We show that a viable slightly red scalar spectrum is achievable. However, within the fast-roll approximation the tensor-to-scalar ratio is in general r ≃ 1/9, inconsistent with current observations. We demonstrate the general result with an explicit example we dub "Intermediate contraction". We prove that small modifications in fast-roll that do not alter the Green's functions, do not result in r < 0.06 consistent with the data for more than an e-fold. Hence, a successful “Sourced Bounce” requires a different source or a significant deviation from fast-roll.

我们为缓慢收缩的宇宙和称为快速滚动模型的缩小模型类别引入了一组通用条件。我们提出了标量和张量扰动的超地平线冻结的一般条件，并表明任何快速滚动模型都满足它们，就像在暴胀的情况下一样。我们对“Sourced Bounce”场景感兴趣，其中扰动由耦合到弹跳标量场的 U(1) 规范场产生。对略微偏红的标量谱的要求极大地限制了标量和规范场之间允许的耦合。我们表明可以实现可行的略带红色的标量光谱。然而，在快滚近似中，张量与标量之比通常为r≃ 1/9，与目前的观察不一致。我们用一个我们称之为“中间收缩”的明确例子来展示一般结果。我们证明快速滚动中的小修改不会改变格林函数，不会导致r < 0.06 与超过 e-fold 的数据一致。因此，成功的“Sourced Bounce”需要不同的来源或与快速滚动的显着偏差。