Title: The Effective Field Theory Approach to Fluid Dynamics, Modified Gravity Theories, and Cosmology
Description: The effective field theory approach is powerful in understanding the low energy phenomena without invoking the UV degrees of freedom. We construct a low energy Lagrangian for ordinary fluid systems (in constrast to superfluid), pure from symmetry considerations and EFT principles. The dynamical fields are the Goldstone excitations, associated with spontaneously broken spacetime translations. It is organized as derivatively coupled theory involving multiple scalar fields. This formalism enables us to study fluid's quantum mechanical properties and dissipative effects. Cosmological models can be built by naturally coupling the fluid EFT to gravity. From the EFT point of view, GR is the unique low energy theory for the spin-2 graviton field and any infrared modification corresponds to adding new degrees of freedom. We focus on two popular classes of modified gravity models, --- the chameleon like theories and the Galileon theory, --- and perform a few reliability checks for their qualifications as modified gravity theories.

Furthermore, guiled by the EFT spirit, we develop a cosmological model where primordial inflation is driven by a `solid', defined, in a similar manner as the EFT of fluid. The symmetry breaking pattern differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard EFT description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations, and exhibits various unusual features.