Disquisitions on the cosmological principle: Non-trivial realisations with some phenomenological consequences

The Cosmological Principle is one of the pillars of the standard model of cosmology and it is commonly realised in a trivial way with homogeneous SO(3)-scalars. I will discuss several scenarios where the matter sector realises the Cosmological Principle in a non-trivial manner by resorting to combinations of spacetime and internal symmetries.

These scenarios include the effective field theory of fluids and solids (as well as their dual formulations), but more general setups based on e.g. vector fields with internal symmetries. A natural consequence of some of these scenarios is the appearance of a second helicity-2 mode in the cosmological perturbations that produces oscillations of gravitational waves with distinctive signatures.

I will also discuss some intriguing realisations that occur on shell and lead to the possibility of having preferred directions in an exactly isotropic background universe.