Connecting tests of General Relativity on small and large scales

我们有充分的理由相信广义相对论(GR)是对引力的正确描述。广义相对论的天体物理约束，无论是通过太阳系的约束，还是通过对不同配置的双星脉冲星的精确测量，都具有显著的准确性。在任何天体物理学背景下，GR都以优异的成绩通过了测试。新的实验，如先进的LIGO、处女座、GEO600、重力和事件视界望远镜，推动我们探索重力进入新的区域的能力，在这些区域，强大的重力将发挥作用，我们预计会有大量数据极大地扩展我们对GR的理解。然而，我们不应该盲目地接受大范围的GR，而不是像我们对其他基本力量所做的那样，对它进行同样的精确度。首先，所有关于物理过程的推论(以及由此产生的宇宙学约束)都是基于引力物理的。正是通过引力，我们了解到宇宙的膨胀正在加速，我们已经假设了宇宙常量或暗能量的存在。这是一个惊人的发现，对我们对基础物理的理解具有深远的影响。此外，正是通过引力物理(特别是通过广义相对论微扰的演化)，我们对非引力物理施加了限制，例如，膨胀势的形式或中微子的质量。在这些关于宇宙的开创性和基础性推论中，GR在宇宙尺度上是正确的假设是至关重要的。然而，在这样做的过程中，我们将GR从一个经过充分测试的制度推断为一个迄今尚未进行测试的制度。特别是，我们正在从太阳系的数量级(大约10-5秒)测量引力物理，并将它们外推近15个数量级(到1010秒)，无论以什么标准衡量，这都是一个巨大的外推。此外，虽然在局部引力势方面与重力测试制度有相似之处，但在局部曲率方面，这两个制度有很大的不同[6]。虽然目前GR的约束对应于曲率大于10-36厘米-2，但宇宙引力在曲率小于10-50厘米-2时起作用。换句话说，我们正在根据普林斯顿大学天体物理学家吉姆·皮布尔斯所描述的“壮观的外推”，对宇宙的基本性质得出深刻的结论。因此，与任何物理理论一样，这个博士项目的目的是测试我们的引力理论在它所应用的制度中的作用。我已经在线性体制中发展了一种形式主义，现在将其扩展到非线性体制。在准静态状态下工作时，我将利用这样一个事实：虽然物质扰动确实变得是非线性的，但度规扰动不会。我将特别小心地加入“引力屏蔽”的参数化，这是一种非线性效应，通常出现在对GR的修改中，在线性理论中没有表现出来；为此，我将最多加入三个新参数(它们封装了筛选过程的质量/长度尺度以及小尺度上的振幅和适当的渐近极限)，它们将涵盖所有可能形式的筛选的现象学(变色龙、对称子和文申因)。然后我将走得更远，将我的形式主义与天体物理尺度上的弱场参数化联系起来；显而易见的第一步将是将参数化后牛顿(PPN)框架与我的框架连接起来，为此，我将使用费米法线坐标或共形费米坐标来将我的形式主义转换出宇宙框架。

We have strong reasons to believe that general relativity (GR) is the correct description of gravity. Astrophysical constraints of general relativity, either through constraints in the Solar System or through exquisite measurements of binary pulsars in different configurations have remarkable accuracy. In any astrophysical setting, GR has passed with flying colours. New experiments, such as advanced LIGO, Virgo, GEO600, Gravity and the Event Horizon Telescope push our ability to probe gravity into new regimes where strong gravity will play a role and we expect a flood of data which will vastly extend our understanding of GR. Nevertheless we shouldn't blindly accept GR on large scales without subjecting it to the same level of precision that we do for other fundamental forces. For a start, all inferences about physical processes (and resulting cosmological constraints) are based on gravitational physics. It is through gravity that we have learnt that the expansion of the universe is accelerating, and that we have posited the existence of either a cosmological constant or dark energy. This is a striking discovery with profound consequences for our understanding of fundamental physics. Furthermore it is through gravitational physics (in particular through the evolution of general relativistic perturbations) that we place constraints on non-gravitational physics such as, for example, the form of the inflationary potential or the mass of the neutrino. The assumption that GR is correct on cosmological scales is crucial in these ground-breaking and fundamental inferences about the universe. Yet, in doing so, we are extrapolating GR from a regime where it has been well tested to one where there are, as yet, no tests. In particular, we are taking measurements of gravitational physics from scales of order the Solar System (at about 10-5 parsecs) and extrapolating them almost fifteen orders of magnitude (to 1010 parsecs), a huge extrapolation by any measure. Furthermore, while there are similarities to the regime in which gravity has been tested in terms of the local gravitational potential, in terms of the local curvature, the regimes are vastly different [6]. While current constraints of GR correspond to curvatures greater than 10-36 cm-2, cosmological gravity comes into play at curvatures less than 10-50 cm-2. In other words, we are drawing profound conclusions about the fundamental nature of the universe based on what the Princeton astrophysicist Jim Peebles has described "a spectacular extrapolation". The aim of this PhD project is then, as with any physical theory, to test our theory of gravity in the regime in which it is being applied. I have developed a formalism in the linear regime and will now extend it into the non-linear regime. Working in the quasi-static regime, I will use the fact that while the matter perturbations do become non-linear, the metric perturbations don't. I will be particularly careful to include a parametrization of "gravitational screening", a non-linear effect that generally arises in modifications to GR and does not show up in linear theory; to do so I will incorporate at most three new parameters (which encapsulate the mass/length scale of the screening process as well as the amplitude and appropriate asymptotic limit on small scales) which will cover the phenomenology of all possible forms of screening (chameleon, symmetron and Vainshtein). I will then go even further and connect my formalism with weak field parametrizations on astrophysical scales; the obvious first step will be to connect the Parametrized Post Newtonian (PPN) framework with the my framework and to do so, I will work with Fermi normal coordinates or conformal Fermi coordinates to transform my formalism out of the cosmological frame.