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arXiv 2005.04962hep-thastro-ph.COgr-qchep-ph
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残余引力子谱能量密度高阶贡献的伪规范不变性

Spurious gauge-invariance of higher-order contributions to the spectral energy density of the relic gravitons

Massimo Giovannini

摘要:

与几何张量模相关的能量密度改变曲率扰动的演化方式相同,标量模也可能通过诱导仅表面规范不变的高阶修正来间接影响残余引力子的宇宙背景。当在不同的坐标系中计算的有效各向异性应力被初步表示为仅取决于定义在同动正交超曲面上的曲率不均匀性及其相应的时间导数的形式时,这种虚假的规范不变性变得明显。使用这种观察,我们证明了在一般条件下,高阶的贡献来自不同的坐标系一致时,波长小于定义的曲率不均匀性的演变的声音地平线,但他们导致急剧不同的结果在相反的限制。当残余引力子的能量密度是由相互竞争的能量-动量赝张量导出时,也会出现类似的缺点,在相关的唯象讨论中应该始终考虑到这一点。

英文摘要:

In the same way as the energy density associated with the tensor modes of the geometry modifies the evolution of the curvature perturbations, the scalar modes may also indirectly affect the cosmic backgrounds of relic gravitons by inducing higher-order corrections that are only superficially gauge-invariant. This spurious gauge-invariance gets manifest when the effective anisotropic stresses, computed in different coordinate systems, are preliminarily expressed in a form that only depends on the curvature inhomogeneities defined on comoving orthogonal hypersurfaces and on their corresponding time derivatives. Using this observation we demonstrate in general terms that the higher-order contributions derived in diverse coordinate systems coincide when the wavelengths are smaller than the sound horizon defining the evolution of the curvature inhomogeneities but they lead to sharply different results in the opposite limit. A similar drawback arises when the energy density of the relic gravitons is derived from competing energy-momentum pseudo-tensors and should be consistently taken into account in the related phenomenological discussions.

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