On cosmological expansion and local physics

TL;DR

This paper demonstrates the agreement between local and cosmological models of the universe when considering the effects of the cosmological constant, clarifying misunderstandings about space expansion and proposing a method to connect local and cosmological observations.

Contribution

It shows the convergence of local and cosmological models under the influence of the cosmological constant and clarifies misconceptions about space expansion using relativistic invariants.

Findings

Local and cosmological models agree with cosmological constant effects.

Static backgrounds like Schwarzschild-dS are effective for local physics.

Clarification of space expansion misunderstandings using relativistic invariants.

Abstract

We find an exact convergence in the local dynamics described by two supposedly antagonistic approaches in modern cosmology: one starting from an expanding universe perspective such as FLRW, the other based on a local model ignoring any notion of expansion, such as 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 in 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. Finally, making use of an old and too often forgotten relativistic kinematical invariant, we clarify some widespread misunderstandings on space expansion, cosmological and gravitational redshifts. As a byproduct we propose a {\sl unique and unambiguous} prescription to match the local and cosmological expression of a specific observable.