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）是引力的正确描述。广义相对论的天体物理学约束，无论是通过太阳系的约束，还是通过对不同配置的双星系统的精确测量，都具有显着的准确性。在任何天体物理学环境中，GR都以优异的成绩通过了。新的实验，如先进的LIGO，Virgo，GEO 600，引力和事件视界望远镜，将我们探测引力的能力推向新的领域，强引力将发挥作用，我们期待大量的数据将大大扩展我们对GR的理解。首先，所有关于物理过程（以及由此产生的宇宙学约束）的推论都是基于引力物理学的。正是通过引力，我们了解到宇宙的膨胀正在加速，并且我们已经假设了宇宙常数或暗能量的存在。这是一个惊人的发现，对我们理解基础物理学有着深远的影响。此外，正是通过引力物理学（特别是通过广义相对论微扰的演化），我们对非引力物理学施加了约束，例如暴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本的推论中，GR在宇宙学尺度上是正确的假设是至关重要的。然而，在这样做的时候，我们正在从一个已经经过很好测试的制度推断GR到一个还没有测试的制度。特别是，我们正在从太阳系的尺度（大约10-5秒差距）测量引力物理，并将它们外推近15个数量级（到1010秒差距），这是一个巨大的外推。此外，虽然在局部引力势方面与重力测试的区域有相似之处，但在局部曲率方面，这些区域有很大的不同[6]。虽然目前的GR约束对应的曲率大于10-36 cm-2，宇宙引力开始发挥作用的曲率小于10-50 cm-2。换句话说，我们正在根据普林斯顿天体物理学家吉姆皮布尔斯所描述的“壮观的外推”得出关于宇宙基本性质的深刻结论。这个博士项目的目的是，然后，与任何物理理论，以测试我们的引力理论在该制度中，它正在应用。我已经发展了一个线性区域的形式主义，现在将把它扩展到非线性区域。在准静态范围内工作，我将使用这样一个事实，即虽然物质扰动确实变成非线性的，但度量扰动不会。我将特别小心地包括“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，而不会出现在线性理论中;为了做到这一点，我将最多纳入三个新参数（其中包含筛选过程的质量/长度尺度以及小尺度上的幅度和适当的渐近极限）这将涵盖所有可能的屏蔽形式的现象学（变色龙，变色龙和范施泰因）。然后我将更进一步，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;显然，第一步将是将参数化后牛顿（PPN）框架与我的框架联系起来，为此，我将使用费米正规坐标或共形费米坐标将我的形式主义从宇宙学框架中转换出来。

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.