The Friedmann–Lemaître–Robertson–Walker metric and the principle of equivalence

Abstract

Abstract The evidence in favor of a Universe expanding at a constant rate, in contrast to the various episodes of deceleration and acceleration expected in the standard model, has been accumulating for over a decade now. In recent years, this inference has been strengthened by a study of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in relation to Einstein’s principle of equivalence. This earlier work concluded that the choice of lapse function g tt = 1 characterizing the FLRW solution to Einstein’s equations is inconsistent with any kind of accelerated cosmic expansion. In this paper, we demonstrate and confirm this important result by directly testing the self-consistency of four well-known FLRW cosmologies. These include the Milne universe, de Sitter space, the Lanczos universe, and the R h = ct model. We show that only the constantly expanding models (Milne and R h = ct) are consistent with the principle of equivalence, while de Sitter and Lanczos fail the test. We discuss some of the many consequences of this conclusion.