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arXiv 1812.06970gr-qcastro-ph.COhep-phhep-th
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弹跳宇宙学中的源标量涨落

Sourced Scalar Fluctuations in Bouncing Cosmology

Ido Ben-Dayan, Judy Kupferman

摘要:

我们计算的标量功率谱的源波动,由于标量场之间的耦合,它拥有宇宙的大部分能量密度,和一个规范场一般FLRW度量。为此,我们计算了规范场存在时的二阶曲率微扰,并证明了规范场的行为类似于一个附加的势项。然后,我们将分析应用于缓慢收缩的情况。由于标量场和规范场之间的相互作用,产生了额外的“源”张量谱和标量谱。由此产生的光谱是手性的,略带蓝色,任意接近标度不变性。张量谱和标量谱之间的唯一区别是具有${\mathcal O}(1)$数值系数的耦合常数和一些动量空间极化矢量。因此,光谱的倾斜是相同的。对于近似尺度不变的情况,动量积分给出了相同的主导贡献。因此,$r\simeq 1/9$,其中与该值的偏差由与标度不变性的偏差控制,并且与CMB观测不一致。与近尺度不变性有很大的偏差,并考虑到$n_T>0.12$的蓝色倾斜,该模型不能解释CMB观测,但可以在未来被LIGO和/或LISA检测到。

英文摘要:

We calculate the scalar power spectrum generated by sourced fluctuations due to coupling between the scalar field, which holds most of the energy density of the universe, and a gauge field for a general FLRW metric. For this purpose we calculate the curvature perturbation to second order in the presence of gauge fields, and show that the gauge fields behave like an additional potential term. We then apply the analysis to the case of slow-contraction. Due to the interaction between the scalar field and gauge fields additional 'sourced' tensor and scalar spectra are generated. The resulting spectra are chiral, slightly blue and arbitrarily close to scale invariance. The only difference between the tensor and scalar spectra is the coupling constant with an ${\mathcal O}(1)$ numerical coefficient, and some momentum space polarization vectors. As a result the tilt of the spectra are the same. For the nearly scale invariant case, the momentum integration gives the same leading contribution. Hence, $r\simeq 1/9$ where the deviation from this value is controlled by the deviation from scale invariance, and is not in agreement with CMB observations. Deviating considerably from near scale invariance, and considering a bluer tilt with $n_T>0.12$, the model cannot account for CMB observations, but can be detected by LIGO and/or LISA in the future.

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