Cosmological perturbation theory: meeting the challenges set by current and future observations

宇宙微扰理论：应对当前和未来观测带来的挑战

• 批准号: ST/G002150/1
• 负责人: Karim Malik
• 金额: $ 40.21万
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=ST%2FG002150%2F1
• 关键词: Cosmological; perturbation; theory; meeting; challenges

In the cosmological standard model small inhomogeneities are generated in the early universe during a period of exponential expansion of space, called inflation. These small inhomogeneities, only at the level of 1 in 100000, are imprinted in the 'primordial density perturbation' which has mainly three observable effects today: it causes the Cosmic Microwave Radiation (CMB) radiation to be slightly anisotropic and polarised which can be observed with microwave telescopes such as the WMAP and PLANCK satellites. The second effect is to generate anisotropies also in the distribution of the neutral hydrogen left over from the big bang. These anisotropies can today be mapped with radio telescopes such as LOFAR through the 21cm transition of the hydrogen. The third effect of the primordial fluctuations is to act as seeds for the formation of large scale structure, the distribution of galaxies, galaxy clusters and even bigger structures in the sky, which we can measure in galaxy surveys. These structures form through gravitational collapse, when matter 'falls' into the potential wells of the primordial fluctuations. This model of structure formation needs another ingredient, dark matter, which makes itself only noticed through its gravitational interaction with normal matter, and which enhances the gravitational attraction of the primordial fluctuations. The primordial density perturbation is generated from the vacuum fluctuations of the scalar fields present during inflation: either from the field responsible for inflation itself, the 'inflaton', or from a separate scalar field, the 'curvaton'. However, there might be more fields involved, depending on the early universe model. In order to find the correct model, we have to compare the theoretical predictions to the observational data. In recent years the amount of data available and its quality have improved significantly, in particular with maps of the CMB by WMAP and other experiments and the 2dF and SDSS large scale structure surveys. The PLANCK satellite, to be launched in 2008, will improve the data on the CMB even further. Recently, however, it has been realised that on small scales the mapping of neutral hydrogen via its 21cm transition could provide a new and potentially even richer source of data about the early universe. The radio telescope LOFAR, scheduled for completion in 2009, has begun to take data in April 2007, and more experiments are planned. Each model of the early universe makes different observable predictions, such as the distribution and size of hot and cold spots in the CMB, the 'spectrum' of the CMB anisotropies, and their statistical properties. If the fields interact with each other, or with the gravitational field, this will result in yet another observational consequence, non-gaussianity. Whereas to calculate the spectrum linear (first-order) perturbation theory is sufficient since we are dealing with quantities proportional to the field fluctuations, to get a handle on non-gaussianity we need second-order perturbation theory because now we have to deal with quantities quadratic in the field fluctuations. Second-order perturbation theory is still in its infancy today, but is essential for the calculation of non-gaussianity and other higher-order effects. We will therefore calculate the observational predictions of different realistic models of the early universe and compare them with the data, at the linear and at the second-order level. In order to be able to do that, we will extend second-order perturbation theory itself. The set of governing equations we will derive are too complicated to be solved analytically, even at linear order. This necessitates the development of numerical methods to solve the set of equations, which again we will do at first- and second-order in the perturbations.

在宇宙学标准模型中，小的不均匀性是在早期宇宙中空间的指数膨胀期间产生的，称为暴胀。这些小的不均匀性，只有在100000分之一的水平，是印在“原始密度扰动”，主要有三个可观察到的影响今天：它导致宇宙微波辐射（CMB）辐射略有各向异性和偏振，可以观察到的微波望远镜，如WMAP和普朗克卫星。第二个效应是在大爆炸遗留下来的中性氢的分布中也产生各向异性。这些各向异性今天可以用射电望远镜，如LOFAR，通过氢的21厘米跃迁来映射。原始波动的第三个作用是充当大尺度结构形成的种子，星系、星系团甚至天空中更大结构的分布，我们可以在星系调查中测量这些结构。当物质“福尔斯”落入原初涨落的势威尔斯中时，这些结构通过引力坍缩形成。这种结构形成的模型需要另一种成分，暗物质，它只有通过与正常物质的引力相互作用才能被注意到，并且增强了原始波动的引力吸引力。原始密度扰动是由暴胀过程中标量场的真空涨落产生的：要么是由暴胀本身的场（暴胀）产生，要么是由单独的标量场（曲率）产生。然而，根据早期的宇宙模型，可能会涉及更多的领域。为了找到正确的模型，我们必须将理论预测与观测数据进行比较。近年来，可获得的数据量及其质量有了显著提高，特别是WMAP和其他实验绘制的CMB地图以及2dF和SDSS大尺度结构调查。将于2008年发射的普朗克卫星将进一步改进关于宇宙微波背景辐射的数据。然而，最近人们已经意识到，在小尺度上，中性氢通过其21厘米跃迁的映射可以提供一个新的，甚至可能更丰富的早期宇宙数据来源。计划于2009年完成的LOFAR射电望远镜已于2007年4月开始采集数据，并计划进行更多的实验。早期宇宙的每个模型都有不同的可观测预测，例如CMB中热点和冷点的分布和大小，CMB各向异性的“光谱”以及它们的统计特性。如果这些场相互作用，或者与引力场相互作用，这将导致另一个观测结果，非高斯性。而计算谱线性（一阶）微扰理论是足够的，因为我们处理的是与场涨落成比例的量，为了处理非高斯性，我们需要二阶微扰理论，因为现在我们必须处理场涨落的平方量。二阶微扰理论今天仍处于起步阶段，但对于计算非高斯性和其他高阶效应是必不可少的。因此，我们将计算早期宇宙的不同现实模型的观测预测，并在线性和二阶水平上将它们与数据进行比较。为了能够做到这一点，我们将扩展二阶微扰理论本身。我们将推导出的控制方程组太复杂了，即使在线性阶下也无法解析求解。这就需要发展数值方法来求解方程组，我们将在一阶和二阶扰动下再次进行。

项目成果

Modelling non-dust fluids in cosmology

• DOI: 10.1088/1475-7516/2013/01/002
• 发表时间: 2013-01-01
• 期刊: JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
• 影响因子: 6.4
• 作者: Christopherson, Adam J.;Carlos Hidalgo, Juan;Malik, Karim A.
• 通讯作者: Malik, Karim A.

The magnitude of the non-adiabatic pressure in the cosmic fluid

宇宙流体中非绝热压力的大小

• DOI: 10.48550/arxiv.1108.0639
• 发表时间: 2011
• 作者: Brown I

An update on single field models of inflation in light of WMAP7

根据 WMAP7 对通货膨胀单场模型的更新

• DOI: 10.1088/1475-7516/2010/08/037
• 发表时间: 2010
• 期刊: Journal of Cosmology and Astroparticle Physics
• 影响因子: 6.4
• 作者: Alabidi L

Can cosmological perturbations produce early universe vorticity?

• DOI: 10.1088/0264-9381/28/11/114004
• 发表时间: 2010-10
• 期刊: Classical and Quantum Gravity
• 影响因子: 3.5
• 作者: Adam J. Christopherson;Karim A. Malik

Comparing different formulations of non-linear cosmological perturbation theory

比较非线性宇宙微扰理论的不同表述

• DOI: 10.48550/arxiv.1101.3525
• 发表时间: 2011
• 作者: Christopherson A