On cosmological expansion and local physics

Abstract

We find an exact convergence in the local dynamics described by two supposedly antagonistic approaches applied at the local, solar system scale: one starting from an expanding universe perspective such as FLRW, the other based on a local model ignoring any notion of expansion, such as static Schwarzschild dS. Both models are in complete agreement when the local effects of the expansion are circumscribed to the presence of the cosmological constant. We elaborate on the relevant role of static backgrounds like the Schwarzschild-dS metric in standard form as the most proper coordinatizations to describe physics at the local scale. We also elaborate on the popular expanding 3-space picture—to be distinguished from that of the expanding universe—and point out the confusion of scales which is typically associated with it. Finally, making use of an old and too often forgotten relativistic kinematical invariant, we address some remaining misunderstandings on space expansion, cosmological and gravitational redshifts. As a byproduct we propose a unique and unambiguous prescription to match the local and cosmological expression of a specific observable.