Copernican Paradigm beyond FLRW

Abstract

We present the dipole cosmological principle, i.e., the notion that the Universe is a Copernican cosmology that agrees with the cosmic flow. It suits the most symmetric paradigm that generalizes the Friedmann–Lemaître–Robertson–Walker ansatz in the context of numerous suggestions that have appeared in the literature for non-kinematic components in the cosmic microwave background dipole. Field equations in our “dipole cosmology” are still ODEs, but we now have four instead of two Friedmann equations. The two extra functions can be regarded as additional scale factors that break the isotropy group from SO(3) to U(1) and a “tilt” that denotes the cosmic flow. The result is an axially isotropic Universe. We examined the dynamics of the expansion rate, anisotropic shear, and tilt in some cases. One important observation is that the cosmic flow (tilt) can grow while the anisotropy (shear) dies down.