Stationary processes do not accurately describe the diffuse backgrounds of relic gravitons whose correlations are homogeneous in space (i.e. only dependent upon the distance between the two spatial locations) but not in time. The symmetries of the autocorrelations ultimately reflect the quantum mechanical origin of the diffuse backgrounds and lead to non-stationary observables at late time. In particular, large oscillations are believed to arise in the spectral energy density that is customarily (but approximately) related to the tensor power spectrum. When the full expression of the spectral energy density is employed the amplitudes of oscillation are instead suppressed in the large-scale limit and the non-stationary features of the late-time signal practically disappear. For similar reasons the relations between the spectral energy density and the spectral amplitude are ambiguous in the presence of non-stationary features. While it is debatable if the non-stationary features are (or will be) directly detectable, we argue that the spectral amplitude following from the Wiener-Khintchine theorem is generally inappropriate for a consistent description of the relic signal. Nevertheless the strong oscillatory behaviour of the late-time observables is naturally smeared out provided the spectral energy density is selected as pivotal variable.

中文翻译：

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遗迹引力子和非平稳过程


平稳过程并不能准确描述遗迹引力子的漫反射背景，这些引力子的相关性在空间上是同质的（即仅取决于两个空间位置之间的距离），但在时间上不是。自相关的对称性最终反映了漫反射背景的量子力学起源，并导致后期出现非平稳可观察对象。特别是，人们认为光谱能量密度会出现大的振荡，这通常（但大致）与张量功率谱相关。当采用光谱能量密度的完全表达式时，振荡幅度反而被抑制在大尺度极限内，后期信号的非平稳特性实际上消失了。出于类似的原因，在存在非平稳特征的情况下，光谱能量密度和光谱振幅之间的关系是模糊的。虽然非平稳特征是否能够（或将要）直接可检测到存在争议，但我们认为，遵循 Wiener-Khintchine 定理的频谱振幅通常不适合对遗迹信号的一致描述。然而，如果选择光谱能量密度作为关键变量，则后期可观测物的强烈振荡行为自然会被消除。