Connecting tests of General Relativity on small and large scales

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.