(1 - 2 GM/ r c^2) ^ 1/2 and Big Bang

kurious

In general relativity the equation
t1 = t2 ( 1 - 2 GM/ r c ^ 2) ^1/2
is often mentioned.
If the mass, M, is equal to the mass of the universe - 10 ^ 52 kg -
then r cannot be less than 10 ^ 24 metres without invoking
the idea that a time can be imaginary.
But could an equally valid interpretation be that the universe started
out no smaller than 10 ^ 24 metres?
The temperature of the universe one second after the Big Bang is
thought to be 10 ^10 K, and if the temperature of the cosmic microwave
background nowadays,
is extrapolated back from 10^26 metres to 10 ^ 24 metres, this would
give about this temperature [( 10^26 )^4 / (10^24)^4 x 1000 = 10^11 K
( the term of 1000 allows for redshift of cmbr photons).
The above scenario would mean that general relativity does not break
down at the time of the big bang and so quantum gravity might not be
needed to explain the Big Bang.

DW

Shwarzschild geometry applies to vacuum outside a localized spherically symmetric matter distribution. It does not apply to uniform matter distributions of global extent. So, no.

kurious

What if the matter is spherically distributed and the vacuum is outside the spherical mass distribution.If we associate the vacuum with vacuum particles, at the time of the Big Bang these particles might have existed outside the spherical mass distribution.
If the gap between the quarks and leptons in the spherical mass distribution was smaller than the average wavelength of a vacuum particle then the vacuum particles would have been unable to get into the sphere and so the vacuum would have existed outside it.The vacuum particles would have had to have had a wavelength of about 10^ - 3 metres.This is also the wavelength the cmbr photons would have had to be locked inside the sphere of mass.And it is a MICROWAVE wavelength!

DW

Then you don't have the universe that we actually have and so the predictions based on your localized matter universe model are irrelevent.

kurious

DW

Then you don't have the universe that we actually have and so the predictions based on your localized matter universe model are irrelevent.

KURIOUS:
The universe we have now would not necessarily be the universe at the time of the Big Bang.If vacuum particles have wavelengths then what I have said is plausible.
It is most unlikely that vacuum particles do not have wavelengths!

DW

No, what I am referring to has nothing to do with the fact that they do have wavelengths. It has to do with the fact that their distribution is globally uniform, rather than confined to a sphere of finite extent.