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RE: Freezing-in and freezing-out dark matter
Freeze out and freeze in, both amazing concepts are well explained here in your thought provoking post.
In Dirac's Large Number Hypothesis, he had the ratio of the total mass of the Universe divided by the mass of a proton is of the order of 1078. Do you know if he included dark matter and dark energy in the number he used for the total mass of the universe?
What do you think the total mass of the universe is?
Does the total mass (or total energy) of the universe increase, decrease or remain constant over the eons?
Thanks for your comment!
First, Dirac Large Number Hypothesis is a coincidence that Dirac observed and that is not really considered in today's physics. Just to point down this before starting ;)
The coincidence was recasted in terms of time (the age of the universe) and the ratio of the electromagnetic and gravitational interaction strengths between a proton and an electron. Therefore: no dark matter was necessary :)
We know that the universe is flat, so that its total energy density equals 9.9 x 10-30 g/cm3. Given that the observable universe is of about 14 billions light-years, then we get our answer (summing over both the luminous and dark stuff) :)
However, when you try to disentangle the various components (radiation, mass, dark energy, etc...), those vary with time.
Thank you for your wisdom.
The observable universe being 14 billion light-years means that we are observing stars that are about 14 billion years old. But 14 billion years ago the expanding universe was much much smaller. So what we are observing is stars in a tiny universe where the distance the light traveled to reach us is much less than 14 billion light-years, meaning that the light is much younger than 14 billion years old. It gets complicated. Do you know if there is a simple equation that explains this?
I am not so sure to follow the question... Do you mind rephrasing? :D
Sorry for the delay, I think I've been in a Spacetime warp right here on Earth
;-)
OK, here goes...
The light we see from the edge of our universe was emitted almost 14 billion years ago. I don't think the universe had a radius of almost 14 billion light years back when the light was emitted.
Spacetime been expanding for all that time, so that the distance to the farthest galaxies that emitted the light was much smaller when the light was emitted.
What was the approx. distance to the farthest galaxies when they emitted their light?
Do you know if there is a simple equation that clarifies the relationship between the age of the light and the distance it traveled in an expanding universe, maybe something like this?
A c = D = D0 S(t)
A = Age of the light
c = speed of light
D = Distance light traveled
D0 = Distance of light source at time of emission
S(t) = Spacetime expansion factor as a function of time
This is why we usually talk about the observable universe. This one has a radius of 14 billions light years. We however do not know what lies beyond it.
You may want to read about 'comoving distances' Does it help?
Thanks. Looking on wikipedia, comoving distances explains it, not as simple as I was guessing though.
With the universe, nothing is never really simple :p