In big bang cosmology, Friedmann-Lemaître-Robertson-Walker metric is considered, it seems, a generic property of the universe only on large scales. But if the metric applies over all time, then it should apply at all scales and for all eras, should it not, including in previous eras way back in time when the universe was much smaller ? If so, is there an inconsistency in attributing the FLRW metric to only large scales?
According to the LambdaCDM standard cosmological model, the FLRW metric definitely applies to all times, including the moment of the Big Bang and shortly thereafter. However, the FLRW metric does not apply on small spatial scales, ie. distance scales smaller than, say, those of galactic clusters. This is not a contradiction, but a physical consequence of the fact that galaxies and clusters are gravitationally self-bound. Outside a galaxy or cluster, the FLRW metric becomes predominant at what is called the "turnaround radius", Exact calculations of the turnaround radius are still a matter of discussion among physicists, a topic which shows up from time to time in Physical Review D. Roughly speaking, the turnaround radius would be the distance at which the cosmic expansion rate given by FLRW exceeds the escape velocity of the central mass as described by the Schwarzschild metric.
According to the LambdaCDM standard cosmological model, the FLRW metric definitely applies to all times, including the moment of the Big Bang and shortly thereafter. However, the FLRW metric does not apply on small spatial scales, ie. distance scales smaller than, say, those of galactic clusters. This is not a contradiction, but a physical consequence of the fact that galaxies and clusters are gravitationally self-bound. Outside a galaxy or cluster, the FLRW metric becomes predominant at what is called the "turnaround radius", Exact calculations of the turnaround radius are still a matter of discussion among physicists, a topic which shows up from time to time in Physical Review D. Roughly speaking, the turnaround radius would be the distance at which the cosmic expansion rate given by FLRW exceeds the escape velocity of the central mass as described by the Schwarzschild metric.
See
1 A.Chubikalo, A Espinosa, V.Kuligin Spatial curvature as a distorted mapping of Euclidean space, Boson Journal of Modern Physics (BJMP) Vol. 4, Issue 2, ISSN 2454-8413 , October, 13, 2018.
If you are interested, i have just finished the gravitation and cosmology in the daon theory project. It can also be found in http://viXra.org/abs/2002.0450
JES
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