Vorticity generation at second order in cosmological perturbation theory
Adam J. Christopherson, Karim A. Malik, David R. Matravers
我们证明了在二阶宇宙学扰动理论中涡度的产生是由熵梯度引起的。这是克罗克定理在宇宙学背景下的延伸。
We show that at second order in cosmological perturbation theory vorticity generation is sourced by entropy gradients. This is an extension of Crocco's theorem to a cosmological setting.
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Clustering of a perfect fluid does not lead to the generation of vorticity. It is the collisionless nature of dark matter, inducing velocity dispersion and shell crossing, which is at the origin of cosmological vorticity generation. In this paper we investigate the generation of vorticity during the formation of cosmological large scale structure using the public relativistic N-body code $\textit{gevolution}$. We test several methods to compute the vorticity power spectrum and we study its convergence with respect to the mass and grid resolution of our simulations. We determine the power spect…
Estimating the amount of vorticity generated by cosmological perturbations in the early universe
我们从一阶能量密度和非绝热压力或熵扰动之间的耦合来估计宇宙学扰动理论中二阶产生的涡量。假设源项的输入谱为幂律，并在辐射背景下工作，计算了涡度功率谱及其振幅与波数的关系。我们表明，这种机制所产生的涡度是不可忽略的小尺度，因此，应考虑在当前和未来的CMB实验。
Can cosmological perturbations produce early universe vorticity?
在这篇特刊文章中，我们根据GR19会议B5（理论和数学宇宙学）的同名谈话，回顾了使用宇宙学扰动理论的宇宙学中的涡度产生情况。我们发现，而在线性阶涡度演化方程没有源项的情况下，各向异性应力，在二阶涡度是由熵梯度和能量密度扰动。然后，我们提出了一些估计的大小和尺度依赖的涡度功率谱使用简单的输入功率谱的能量密度和熵扰动。最后，我们关闭与未来工作的可能方向，其次是一些提示对观测的重要性，这样产生的涡度，和原始磁场产生的可能性。
Observational searches for large-scale vorticity modes in the late time Universe are underexplored. Within the standard $Λ$CDM model, this is well motivated given the observed properties of the cosmic microwave background (CMB). However, this means that searches for cosmic vorticity modes can serve as a powerful consistency test of our cosmological model. We show that through combining CMB measurements of the kinetic Sunyaev-Zel'dovich and the moving lens effects with galaxy survey data we can constrain vorticity fields independently from the large scale cosmic velocity field. This approach ca…
In this paper I review some recent, interlinked, work undertaken using cosmological perturbation theory -- a powerful technique for modelling inhomogeneities in the Universe. The common theme which underpins these pieces of work is the presence of non-adiabatic pressure, or entropy, perturbations. After a brief introduction covering the standard techniques of describing inhomogeneities in both Newtonian and relativistic cosmology, I discuss the generation of vorticity. As in classical fluid mechanics, vorticity is not present in linearized perturbation theory (unless included as an initial con…
Vorticity survival in magnetised Friedmann universes
本文用广义相对论方法研究了宇宙辐射期和尘埃期弱宇宙磁场对线性转动扰动的影响。这包括普通的运动学涡度，以及宇宙介质密度分布中的涡状不均匀性。我们的研究证实，磁场可以产生这两种类型的扰动，并表明它们的存在也有助于宇宙旋转生存更长的时间。在协议与以前的牛顿的研究，我们发现，在尘埃时代的涡度衰减慢于非磁化宇宙学。在均分之前，磁效应更加明显，因为它有助于上述旋转失真保持恒定的大小。总的来说，磁化宇宙似乎比无磁宇宙提供了更好的宇宙涡旋生存环境。
We study the nonlinear gravitational dynamics of a universe filled with a pressureless fluid and a cosmological constant $Λ$ in the context of Newtonian gravity, and in the relativistic post-Friedmann approach proposed in paper I [I. Milillo et al., Phys. Rev. D 92, 023519 (2015).]. The post-Friedmann approximation scheme is based on the $1/c$ expansion of the space-time metric and the energy-momentum tensor, and includes nonlinear Newtonian cosmology. Here we establish the nonlinear post-Friedmann framework in the Lagrangian-coordinates approach for structure formation. For this we first iden…
Vorticity from isocurvature in the early universe
涡在自然界中是普遍存在的，然而，迄今为止，宇宙学和早期宇宙中的涡的研究已经相当罕见。本文根据第13届Marcel Grossmann会议CM-1上的一次讲话，讨论了理想流体系统标量宇宙学扰动的涡度产生。我们表明，在二阶微扰理论，涡源之间的耦合能量密度和熵梯度，从而扩展了一个众所周知的功能，经典流体动力学的相对论宇宙学框架。这种诱导涡度，来源于等曲率扰动，可能会证明在未来有用的作为一个额外的膨胀模型之间的连接。
We compute the generation of vorticity from velocity dispersion in the dark matter fluid. For dark matter at zero temperature Helmholtz's theorem dictates that no vorticity is generated and we therefore allow the dark matter fluid to have a non-vanishing velocity dispersion. This implies a modification to the usual hydrodynamical system (continuity and Euler equations): we have to consider the Boltzmann hierarchy up to the second moment. This means that the Euler equation is modified with a source term that describes the effect of non-zero velocity dispersion. We write an equation for the Eule…
Applications of Cosmological Perturbation Theory
宇宙学扰动理论对于我们理解宇宙至关重要。线性理论已经被很好地理解了一段时间，然而发展和应用超越线性秩序的理论是目前理论宇宙学研究的前沿。本论文研究微扰论在宇宙学，特别是早期宇宙中的应用。从一些背景材料介绍了久经考验的“标准模型”的宇宙学，我们移动到发展的形式主义微扰理论的二阶给出所有类型的标量，矢量和张量扰动的演化方程，无论是在规范依赖和规范不变的形式。然后，我们移动到论文的主要结果，表明，在第二阶微扰理论，涡是由耦合项二次在能量密度和熵扰动的来源。这个源项意味着与线性序有质的区别。因此，当线性阶涡量随着宇宙膨胀而衰减时，高阶涡量则不然。这将对未来测量宇宙微波背景的极化产生重要影响，并可能导致原始种子磁场的产生。导出这个定性的结果，然后，我们估计的尺度依赖性和涡度功率谱的大小，发现，简单的幂律输入一个小的，蓝色的频谱。本文的最后一部分是高阶微扰理论，首次导出了完全一般的三阶微扰的度规张量、规范变换规则和控制方程。最后，我们讨论了这项工作的自然延伸和其他可能的想法，在这个不断增长的领域的射击项目。
We study the effect of coarse-graining the dynamics of a pressureless selfgravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, both in the Eulerian und Lagrangian framework. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse-graining is illustrated by means of power and cross spectra for density and velocity that are computed up to 1-loop order. In particular, the large scale vorticity power spectrum that arises na…
Cosmological magnetic fields from inflation in extended electromagnetism
在这项工作中，我们考虑了一个扩展的电磁理论，其中的标量状态，这通常是由洛伦兹条件消除允许传播。在标准暴胀宇宙学的背景下，这种状态已经被证明会产生一个小的宇宙学常数。在这里，我们表明，通常的洛伦兹规范破缺项现在起着有效的电磁流的作用。这种电流是在膨胀期间从量子涨落产生的，并产生随机的有效电荷密度分布。由于膨胀后宇宙等离子体的高导电性，电荷密度产生电流，从而产生亚哈勃尺度的涡旋和磁场。由宇宙微波背景辐射温度各向异性引起的涡度上限被转换为宇宙磁场的下限。我们发现，对于一个近尺度不变的涡度谱，磁场$B_λ> 10^{-12}$ G通常产生的相干长度范围从亚星系尺度到目前的哈勃半径。这些场可以作为银河发电机的种子，甚至可以通过原银河云的坍缩和差异旋转来解释观测结果。
Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity
我们证明，在无限光速极限（即，非相对论性和亚视界极限），在零剪切规范和均匀膨胀规范两种规范条件下的相对论性完全非线性宇宙学扰动方程精确地再现了宇宙学背景下的牛顿流体动力学微扰方程;因此，在同样的两种规范条件下，牛顿流体动力学微扰方程精确地恢复到闵可夫斯基背景下。
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and te…
Cosmological Perturbation Theory With Background Anisotropic Curvature
将宇宙学扰动理论推广到各向同性膨胀但曲率各向异性的时空。在一般规范下导出了有质量粒子和无质量粒子的微扰爱因斯坦方程和玻尔兹曼方程，并提出了微扰的简谐模和矩的分解。推广的情况下，各向异性膨胀也存在于背景中进行了讨论。
We investigate the cosmological perturbations in the context of a Scalar-Tensor-Vector theory of Gravity known as MOG in the literature. Recent investigations show that MOG reproduces a viable background cosmological evolution comparable to $Λ$CDM. However, the matter-dominated era is slightly different. In this paper, we study the linear matter perturbations and estimate the relevant modified gravity parameters. We show that MOG reduces the growth rate of the perturbations and comparing with the RSD data reveals that MOG suggests a higher value for $σ_8$, compare to $Λ$CDM. This point, consti…
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more b…
Cosmic curl -- Features and convergence of the vorticity power spectrum in $N$-body simulations
针对宇宙速度场模拟中涡度场受离散化效应难以完全收敛的问题，本研究利用CONCEPT代码，仅通过4组不同粒子数的N体模拟就可靠外推出宇宙涡度功率谱，精度达5%以内，并探究了涡度的时间演化及与散度的比值。
FRW Cosmological Perturbations in Massive Bigravity
本文详细研究了无鬼质量双引力中FRW解的宇宙学扰动，其中也包括第二物质扇区。在早期，我们发现亚视界指数不稳定性是不可避免的，它导致了宇宙学扰动的过早脱离。
Perfect fluids are modeled by using an effective field theory approach which naturally gives a self-consistent and unambiguous description of the intrinsic non-adiabatic contribution to pressure variations. We study the impact of intrinsic entropy perturbation on the superhorizon dynamics of the curvature perturbation ${\cal R}$ in the dark sector. The dark sector, made of dark matter and dark energy is described as a single perfect fluid. The non-perturbative vorticity's dynamics and the Weinberg theorem violation for perfect fluids are also studied.
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal in…
Cosmological perturbations from statistical thermal fluctuations
计算了由任意状态方程描述的单一流体中统计热涨落引起的宇宙学扰动。导出了在给定温度下标量谱、张量扰动谱和非高斯性参数的计算公式。这些结果是相关的任何宇宙学的情况下，宇宙结构可能已经播种热，而不是纯粹起源于量子真空波动。
The cosmological perturbation theory in loop cosmology with holonomy corrections
本文在圈量子宇宙学的半经典框架下，研究了考虑完整性修正时，空间平坦FRW时空中一阶度规扰动的标量模.通过对哈密顿量的求导，得到了纵向规范下的宇宙学扰动方程。结果表明，在存在度规微扰的情况下，完整性效应对背景和微扰都有影响，并贡献了宇宙学扰动方程中的非平凡项$S_{h1}$和$S_{h2}$.
Cosmological Perturbations in the Projectable Version of Horava-Lifshitz Gravity
我们考虑线性扰动的均匀和各向同性的宇宙学背景中的可投影版本的Hoenava-Lifshitz引力。从宇宙学扰动的作用量出发，我们确定了正则归一化的涨落变量。我们发现，与非可投射版本的理论相反，额外标量宇宙学扰动模式在线性微扰的水平上已经是动力学的。当参数$λ$的值在$1/3 < λ< 1$范围内时，额外模式是类重影模式，当$1 < λ$和$λ< 1/3$值时，额外模式是快子模式。这表明了可投影版本的霍洛维茨-利夫希茨引力的问题。
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
Cosmological perturbations in SFT inspired non-local scalar field models
我们研究了具有单个非定域标量场的模型中的宇宙学扰动，该场起源于滚动快子动力学的弦场论描述。我们构造了非定域标量场的能量密度扰动方程，并明确证明了对于自由场，它与具有多个（可能是无穷多个）定域自由标量场的特定模型中的定域宇宙学扰动方程组是相同的.
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
An inflationary universe scenario in the context of tachyon field is studied. This study is done from an ansantz for the effective potential of cosmological perturbations $U(η)$. We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different ansantz in the effective potential of cosmological perturbations; the Easther's model and an effective potential similar to power law inflation. Also we find from the background equations that the effective tachyonic potential $V(φ)$, in both models satisfy the properties of a tachyonic potential. We consider …
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.
Inflation and Birth of Cosmological Perturbations
本文综述了暴胀理论的最新进展以及暴胀产生的宇宙学扰动。在简单介绍了标准的单场慢卷暴胀以及由此产生的曲率和张量扰动之后，我们讨论了其他暴胀模型中非线性、非高斯扰动的可能来源。然后，我们描述了所谓的$δN$形式主义，这是一个强大的工具，用于评估超哈勃尺度上的非线性曲率扰动。
Perturbation theory with dispersion and higher cumulants: non-linear regime
提出包含色散与高阶累积量的Vlasov微扰理论非线性解，通过UV模式屏蔽机制克服SPT发散，在单圈和双圈阶与N-body结果良好匹配，证明暗物质微扰技术可系统性改进。
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.
TASI Lectures on Cosmological Perturbations
我们提出了一个自成一体的线性宇宙学扰动理论的总结。我们着重讨论了最小宇宙模型的六个参数对宇宙微波背景温度各向异性谱和线性物质功率谱的影响。最后，我们简要回顾了一些非最小暗物质和暗能量模型的可能影响。
The super-horizon second-order density perturbations corresponding to cosmological random fluctuations are considered, their non-vanishing spatial average is shown to be useful in solving the serious problem on the cosmological tension between measured Hubble constants at present and those at the early stage, and the difference from previous works on the backreaction is discussed.
We discuss the effect of super-Hubble cosmological fluctuations on the locally measured Hubble expansion rate. We consider a large bare cosmological constant in the early universe in the presence of scalar field matter (the dominant matter component), which would lead to a scale-invariant primordial spectrum of cosmological fluctuations. Using the leading order gradient expansion we show that the expansion rate measured by a (secondary) clock field which is not comoving with the dominant matter component obtains a negative contribution from infrared fluctuations, a contribution whose absolute …
Cosmological Perturbations and the Running Cosmological Constant Model
利用纵向规范的线性微扰研究了运行宇宙学常数（RCC）模型中物质密度的涨落。利用该观测值计算了结构的增长率和物质的功率谱，并与$SDSS$数据和其他可用的线性增长率数据进行了比较。坍缩结构的分布也可能限制了暗能量的模型。结果表明，RCC模型增强偏离$ΛCDM$模型的集群数和累积集群数预测。一般而言，增加特征参数$ν$导致簇数目的显著增长。总的来说，我们发现微扰理论提供了一个很好的工具来区分新模型$RCC$的标准宇宙学模型$ΛCDM$。
In this work we construct a model where the first order vector perturbations can be generated during inflationary expansion. For the non-standard spinors, known as ELKO, we show that the components of the first order perturbed energy-momentum tensor of the ELKO is non-zero for pure vector part of the metric perturbation ($B_{i}$). We show that vector perturbations do not decay in the super-Hubble scale and for a specific super-inflation background model we show that the vector perturbations are nearly scale invariant, while its amplitude is smaller than the primordial scalar perturbations. We …
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