We study the fluctuation-dissipation relation for sound waves in the cosmic microwave background (CMB), employing effective field theory (EFT) for fluctuating hydrodynamics. Treating sound waves as the linear response to thermal radiation, we establish the fluctuation-dissipation relation within a cosmological framework. While dissipation is elucidated in established linear cosmological perturbation theory, the standard Boltzmann theory overlooks the associated noise, possibly contributing to inconsistencies in Lambda Cold Dark Matter ($Λ$CDM) cosmology. This paper employs EFT for fluctuating hydrodynamics in cosmological perturbation theory, deriving sound wave noise. Notably, the long-time limit of the noise spectrum is independent of viscosity details, resembling a Brownian motion bounded in a harmonic potential. The net energy transfer between the sound wave system and the radiation environment reaches a balance within Hubble time, suggesting the thermal equilibrium of the sound waves themselves. The induced density power spectrum is characterized as white noise dependent on the inverse of the entropy density, which is negligibly small on the CMB scale. The energy density of the entire sound wave system scales as $a^{-4}$, akin to radiation. While the numerical factor is not determined in the present calculation, the back reaction of the sound wave system to the background radiation may not be negligible, serving as a potential source for various fitting issues in $Λ$CDM cosmology.
A Cosmic Microwave Background feature consistent with a cosmic texture
宇宙微波背景提供了我们最古老的宇宙图像，也是我们研究宇宙早期演化的最佳工具。高能物理学理论预言在极早期宇宙中会形成各种类型的拓扑缺陷，包括在宇宙微波背景中产生热点和冷点的宇宙结构。我们通过贝叶斯统计分析表明，在全天空图像中观察到的最突出的5度半径冷点，这是很难解释的，与纹理引起的是兼容的。从这个模型中，我们将基本对称性破缺能标限制为phi_0 ~ 8.7 x 10^（15）GeV。如果得到证实，这种对宇宙缺陷的探测将在能量上探测物理学，超过任何可以想象的地球实验。
