The lapse function in Friedmann—Lemaître–Robertson–Walker cosmologies

Abstract

The Friedmann-LemaTtre-Robertson-Walker (FLRW) metric, the backbone of modem cosmology, is founded on the cosmological principle, which assumes homogeneity and isotropy throughout the cosmos. One of its simplifications is the choice of lapse function g(tt) = 1, regardless of which stress-energy tensor T-mu v is used in Einstein's field equations. It is sometimes argued that this selection is justified by gauge freedom, given that g(tt) in FLRW may be a function solely of t, not of the spatial coordinates, permitting a redefinition of the time. We show in this paper, however, that the comoving frame in the Hubble expansion is non inertial for all but a few special cases of the expansion factor a(t). Changing the gauge changes the frame of reference and cannot alter this property of the expansion profile, since it would of necessity reformat the metric using the coordinates of a noncomoving observer. We therefore suggest that the pre-selection of g(tt )= 1, independently of the equation of state in the cosmic fluid, incorrectly avoids the time dilation that ought to be present relative to the actual free-falling frame when (a) over dot not equal 0. (C) 2019 Elsevier Inc. All rights reserved.