[jeffreyH (OP)]

Has anyone ever calculated this value? If so what value was approximated?

[Kryptid]

9.9 x 10^-30 grams per cubic centimeter, it seems: https://map.gsfc.nasa.gov/universe/uni_matter.html

[evan_au]

...and declining over time...

[jeffreyH (OP)]

If we take ρ to be the energy density at time t then at time t + Δt we then have an energy density of Δρ. This indicates that the gravitational energy at any spacetime location is also decreasing over time. It also indicates a gradient in time dilation. As energy decreases the clocks run faster.

[jeffreyH (OP)]

Locally this is inconsequential but on the scale of the universe it could make a big difference.

[jeffreyH (OP)]

The question is how much slower were the clocks running at different ages of the universe? How would this impact our view of the expansion of the universe?

[yor_on]

I don't know Jeffrey, but it seems to me that the mainstream definition of a 'Big Bang' is that all 'clocks' are synchronized. As the universe inflates you get matter and matter 'bends space' and space tells matter how to move (geodesics). As that happens the synchronicity disappear, and what you are left with is your local definition of a clock rate. That will be what you use to measure all other 'clocks' against. If we presume there is no 'outside' to this universe then there also will be no 'objective clock rate' that you can use.

Against it, and this is my own view, is the fact that as long as you are in a same frame of reference all clocks ticks the same. If we presume they do then there is some reason in suggesting that there is a 'golden standard' of sorts. It's like turning you head, you need new definitions for it.

[jeffreyH (OP)]

If we look at energy density we have U = E/V where E is energy and V is volume. This then becomes ΔU = E/ΔV. So that energy is conserved and volume is changing. This has to affect clocks.

[alancalverd]

As energy decreases the clocks run faster.

But only as seen from a point where Δρ = 0. Nothing changes within the observable universe.

[jeffreyH (OP)]

As energy decreases the clocks run faster.

But only as seen from a point where Δρ = 0. Nothing changes within the observable universe.

There is always that of course.

[Bill S]

But only as seen from a point where Δρ = 0. Nothing changes within the observable universe.

Thanks Alan.  I was working towards the idea that nothing observable would change, but was some way off finding a reason.

Would you mind saying a bit more about this, for the benefit of the non-cognoscenti, whom I, sadly, represent.