宇宙学扰动理论中的光学膨胀标量
The Optical Expansion Scalar in Cosmological Perturbation Theory
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中文总结 AI 辅助
本文在几何光学近似下引入光学膨胀标量可观测量 $\vartheta$，推导其在标量扰动FLRW宇宙中的线性表达式与角功率谱，虽无显著优势，但各向异性对速度与势敏感，可用于一致性检验及探测修正引力。
中文摘要 AI 辅助
在几何光学近似下，光学膨胀标量描述了波振幅或穿过宇宙的光束面积的局部变化率。因此，它对于描述我们在宇宙学中进行的几乎所有观测都至关重要。最近有人指出，这一量原则上可以从角直径距离 $D_A$ 和有效观测膨胀率 $\mathfrak{H}$ 的测量中重建。受这一可能性的启发，我们引入了可观测量 $\vartheta \equiv \theta/\omega_o$，其中 $\theta$ 是萨克斯光学膨胀标量，$\omega_o$ 是观测到的光子频率。然后，我们在具有标量扰动的平坦FLRW宇宙中推导了 $\vartheta$ 的线性扰动表达式和角功率谱。将功率谱与 $D_A$ 涨落的功率谱以及相对论性N体模拟的功率谱进行比较，发现研究 $\vartheta$ 的涨落相对于 $D_A$ 的涨落没有立即显现的显著优势。然而，$\vartheta$ 的各向异性确实表现出几个独特的性质，例如对 peculiar 速度和相对论性势的增强敏感性。我们建议，我们的结果可能暗示 $\vartheta$ 有助于开发宇宙学观测的一致性检验，并可能探测对FLRW宇宙学和修正引力理论的偏离。本文开发并呈现的形式体系为未来研究这些可能性提供了基础。
英文摘要
Within the geometric optics approximation, the optical expansion scalar describes the local rate of change in the amplitude of a wave or the area of a light bundle propagating through the Universe. As such, it is fundamental for describing almost all the observations we make in cosmology. It was recently pointed out that this quantity can, in principle, be reconstructed from measurements of the angular diameter distance $D_A$ and the effective observed expansion rate $\mathfrak{H}$. Motivated by this possibility, we introduce the observable $\vartheta \equiv θ/ω_o$, where $θ$ is Sachs' optical expansion scalar, and $ω_o$ the observed photon frequency. We then derive the linear perturbative expression and angular power spectrum for $\vartheta$ in a flat FLRW universe with scalar perturbations. Comparing the power spectra with those of the fluctuations in $D_A$ and with power spectra from relativistic N-body simulations reveals no immediate striking advantage of studying the fluctuations of $\vartheta$ to those of $D_A$. However, the anisotropies of $\vartheta$ do exhibit several unique qualities such as an enhanced sensitivity to the peculiar velocity and relativistic potentials. We suggest that our results may hint at $\vartheta$ being useful for developing consistency tests of cosmological observations and possibly probing departures from FLRW cosmology and modified gravity theories. The formalism developed and presented here provides the foundation for future studies into these possibilities.
发表机构
- CP3-Origins, University of Southern Denmark（南丹麦大学 CP3-起源中心）
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