TY - JOUR

T1 - The Friedmann-Lemaître-Robertson-Walker metric

AU - Melia, Fulvio

N1 - Funding Information:
We gratefully acknowledge the advice and supervisory support of Dr. E. Berry and Dr. S. F. Tanner [Medical Physics, University of Leeds]. Dr. Tanner is further thanked for providing medical data and evaluation thereof. O. Kubassova acknowledges with thanks the UK Research Councils for financial support via a Dorothy Hodgkin Award.
Funding Information:
O. Kubassova acknowledges with thanks the UK Research Councils for financial support via a Dorothy Hodgkin Award.
Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022/1/30

Y1 - 2022/1/30

N2 - The Friedmann-Lemaître-Robertson-Walker (FLRW) metric used to describe the cosmic spacetime is based on the cosmological principle, which assumes homogeneity and isotropy throughout the Universe. It also adopts free-fall conditions via the selection of a constant lapse function, gtt = 1, regardless of whether or not the chosen energy-momentum tensor Tαβ produces an accelerated expansion. This is sometimes justified by arguing that one may shift the gauge, if necessary, transforming the time dt to a new coordinate dt′g ttdt, thereby re-establishing a unitary value for gt′t′. Previously, we have demonstrated that this approach is inconsistent with the Friedmann equations derived using comoving coordinates. In this paper, we advance this discussion significantly by using the Local Flatness Theorem in general relativity to prove that gtt in FLRW is inextricably dependent on the expansion dynamics via the expansion factor a(t), which itself depends on the equation-of-state in Tαβ. One is therefore not free to choose gtt arbitrarily without ensuring its consistency with the energy-momentum tensor. We prove that the use of FLRW in cosmology is valid only for zero active mass, i.e. ρ + 3p = 0, where ρ and p are, respectively, the total energy density and pressure in the cosmic fluid.

AB - The Friedmann-Lemaître-Robertson-Walker (FLRW) metric used to describe the cosmic spacetime is based on the cosmological principle, which assumes homogeneity and isotropy throughout the Universe. It also adopts free-fall conditions via the selection of a constant lapse function, gtt = 1, regardless of whether or not the chosen energy-momentum tensor Tαβ produces an accelerated expansion. This is sometimes justified by arguing that one may shift the gauge, if necessary, transforming the time dt to a new coordinate dt′g ttdt, thereby re-establishing a unitary value for gt′t′. Previously, we have demonstrated that this approach is inconsistent with the Friedmann equations derived using comoving coordinates. In this paper, we advance this discussion significantly by using the Local Flatness Theorem in general relativity to prove that gtt in FLRW is inextricably dependent on the expansion dynamics via the expansion factor a(t), which itself depends on the equation-of-state in Tαβ. One is therefore not free to choose gtt arbitrarily without ensuring its consistency with the energy-momentum tensor. We prove that the use of FLRW in cosmology is valid only for zero active mass, i.e. ρ + 3p = 0, where ρ and p are, respectively, the total energy density and pressure in the cosmic fluid.

KW - FLRW metric

KW - General relativity

KW - cosmology

KW - lapse function

UR - http://www.scopus.com/inward/record.url?scp=85125541281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85125541281&partnerID=8YFLogxK

U2 - 10.1142/S021773232250016X

DO - 10.1142/S021773232250016X

M3 - Article

AN - SCOPUS:85125541281

VL - 37

JO - Modern Physics Letters A

JF - Modern Physics Letters A

SN - 0217-7323

IS - 3

M1 - 2250016

ER -