Relativists have told me that the only acceptable metrics discovered for an expanding universe, so far, are the conformal "Robertson-Walker" type metrics:(adsbygoogle = window.adsbygoogle || []).push({});

ds^2 = a(t)^2 [ -dt^2 + dr^2 ]

where t is the "conformal time".

the theoretical and experimental investigation of a(t)

(the expansion scale factor) It's form for mass dominated and radiation dominated regimes is well known... as are the phenomenal "phase change"... "inflation" scenarios.

The conformal time of the Robertson - Walker metrics, naturally lead to the following quesions:

Take two "linearized" Riemannian metrics, g and h, on a smooth manifold M, then of course they are referred to as being "conformally equivalent", if, g = uh for a positive function u on M. What is needed is a quantum gravitational manifesto, generalizing classical GR and QM.

As a thought experiment Let's Assume a cosmological model with a constant mass density, Take for example, a homogenous universe filled with a motionless dust. Will a clock run at a different rate if the mass density parameter is varied?

Make the supposition of two identical Universes having only one difference between them, which is the mass density. That is to say, one universe with mass density X and another with mass density Y. Will the the clocks appear to run at different rates in the two Universes? Will they have different time dilation factors? It seems that they should.

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# Universal Time Dilation?

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