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- W4214669288 abstract "The Friedmann-Lema{^i}tre-Robertson-Walker (FLRW) metric used to describe thecosmic spacetime is based on the cosmological principle, which assumes homogeneityand isotropy throughout the Universe. It also adopts free-fall conditions via theselection of a constant lapse function, $g_{tt}=1$, regardless of whether or notthe chosen energy-momentum tensor $T^{alphabeta}$ produces an acceleratedexpansion. This is sometimes justified by arguing that one may shift the gauge,if necessary, transforming the time $dt$ to a new coordinate$dt^primeequivsqrt{g_{tt}},dt$, thereby re-establishing a unitary value for$g_{t^prime t^prime}$. Previously, we have demonstrated that this approachis inconsistent with the Friedmann equations derived using comoving coordinates.In this paper, we advance this discussion significantly by using the LocalFlatness Theorem in general relativity to {it prove} that $g_{tt}$ in FLRW isinextricably dependent on the expansion dynamics via the expansion factor $a(t)$,which itself depends on the equation-of-state in $T^{alphabeta}$. One istherefore not free to choose $g_{tt}$ arbitrarily without ensuring its consistencywith the energy-momentum tensor. We prove that the use of FLRW in cosmology isvalid only for zero active mass, i.e., $rho+3p=0$, where $rho$ and $p$ are,respectively, the total energy density and pressure in the cosmic fluid." @default.
- W4214669288 created "2022-03-02" @default.
- W4214669288 creator A5048777040 @default.
- W4214669288 date "2022-02-28" @default.
- W4214669288 modified "2023-10-16" @default.
- W4214669288 title "The Friedmann-Lemaitre-Robertson-Walker Metric" @default.
- W4214669288 doi "https://doi.org/10.31219/osf.io/fkema" @default.
- W4214669288 hasPublicationYear "2022" @default.
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