标题： 循环宇宙中的引力波：通过周期和真空中振荡的韧性 显示英文标题

标题： Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state

摘要： 我们提出了一个关于循环宇宙中原初张量扰动谱的广义计算方法，不对理论的真空态做任何假设，并考虑了前一循环暗能量阶段产生的张量模式的贡献。 我们表明，这些模式对当前循环所观测到的谱几乎没有影响，除非是在接近目前共动哈勃半径尺度上的修正。 这些修正来自于暗能量阶段末期产生的视界内模式，在下一循环的ekpyrotic（灾变性膨胀）阶段作为额外的量子持续存在。 关于真空态问题，我们论证了非Bunch-Davies量子可能轻易超过驱动暗能量阶段的能量密度，从而可能危及该模型。 因此，为了避免反作用效应，在这一阶段对偏离Bunch-Davies真空的偏差设置了严格的限制，限制了在循环宇宙中考虑替代真空态的整体自由度。 显示英文摘要

摘要： We present a generalised calculation for the spectrum of primordial tensor perturbations in a cyclic Universe, making no assumptions about the vacuum state of the theory and accounting for the contribution of tensor modes produced in the dark energy phase of the previous cycle. We show that these modes have minimal impact on the spectrum observed in the current cycle, except for corrections on scales as large as the comoving Hubble radius today. These corrections are due to sub-horizon modes produced towards the end of the dark energy phase, persisting into the ekpyrotic phase of the next cycle as additional quanta. In relation to the vacuum state, we argue that non-Bunch-Davies quanta can easily overwhelm the energy density driving the dark energy phase, potentially compromising the model. Therefore, avoiding backreaction effects sets restrictive constraints on deviations away from the Bunch-Davies vacuum during this phase, limiting the overall freedom to consider alternative vacua in the cyclic Universe.