Influence of cosmological expansion in local experiments

TL;DR

This paper investigates how the universe's expansion affects local experiments by analyzing specific spacetime models, calculating frequency shifts, and clarifying previous misconceptions in the literature.

Contribution

It provides a detailed analysis of the influence of cosmological expansion on local measurements using McVittie and Kottler spacetimes, clarifying prior conflicting claims.

Findings

Cosmological expansion has a negligible effect on local frequency shifts.

The influence on light signal exchange is minimal at galaxy cluster scales.

Clarifies misconceptions about local effects of cosmic expansion in existing literature.

Abstract

Whether the cosmological expansion can influence the local dynamics, below the galaxy clusters scale, has been the subject of intense investigations in the past three decades. In this work, we consider McVittie and Kottler spacetimes, embedding a spherical object in a FLRW spacetime. We calculate the influence of the cosmological expansion on the frequency shift of a resonator and estimate its effect on the exchange of light signals between local observers. In passing, we also clarify some of the statements made in the literature.