TY - JOUR

T1 - The lapse function in Friedmann—Lemaître–Robertson–Walker cosmologies

AU - Melia, F.

N1 - Funding Information:
I acknowledge Amherst College, USA for its support through a John Woodruff Simpson Fellowship.
Publisher Copyright:
© 2019 Elsevier Inc.

PY - 2019/12

Y1 - 2019/12

N2 - The Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the backbone of modern 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 gtt=1, regardless of which stress–energy tensor Tμν is used in Einstein's field equations. It is sometimes argued that this selection is justified by gauge freedom, given that gtt 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 non-comoving observer. We therefore suggest that the pre-selection of gtt=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 ä≠0.

AB - The Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the backbone of modern 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 gtt=1, regardless of which stress–energy tensor Tμν is used in Einstein's field equations. It is sometimes argued that this selection is justified by gauge freedom, given that gtt 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 non-comoving observer. We therefore suggest that the pre-selection of gtt=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 ä≠0.

KW - Cosmological principle

KW - FLRW metric

KW - Local Flatness Theorem

KW - Zero active mass

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U2 - 10.1016/j.aop.2019.167997

DO - 10.1016/j.aop.2019.167997

M3 - Article

AN - SCOPUS:85074103780

SN - 0003-4916

VL - 411

JO - Annals of Physics

JF - Annals of Physics

M1 - 167997

ER -