Size of Universe at CMB last Scattering

[zadignose]

I hope that this will be a simple question, but I had difficulty finding an answer by searching.

If the Cosmic Microwave Background radiation was radiated over 13 billion years ago, and we are able to see it now, then does this mean that the radius of the universe at that time must have been at least 13 billion light years? If not, then how could it be explained?

 

[marcus]

I hope that this will be a simple question, but I had difficulty finding an answer by searching.

If the Cosmic Microwave Background radiation was radiated over 13 billion years ago, and we are able to see it now, then does this mean that the radius of the universe at that time must have been at least 13 billion light years? If not, then how could it be explained?

Light travel time is a poor measure of distance to use in cosmology because the rate of expansion has varied so much over the course of history---there is no simple relation between travel time and the actual distance (so-called "proper distance") that you would have measured if you could have paused expansion at the moment the light was emitted or at the end of its journey when it was received.

So try not to think of light travel time as indicative of distance.

One way to find out the distances is to click on the "Lightcone" link at the end of this post. The top row of the table is for the CMB, because it comes to us with wavelengths stretched by a a factor of S=1090. The redshift z = S - 1, by definition, so z = 1089.

If you will take the trouble to click on the Lightcone link you will see that the distance to the matter that emitted the CMB (which we are now detecting) is NOW 45.332 billion lightyears and back then when the matter emitted the light (which we are now detecting as microwaves) its distance from our matter (that eventually became the Earth and us) was only 0.042 billion lightyears.

 

[Chronos]

We can rather easily deduce the age of the universe at the time the CMB photons were emitted, but, I'm not aware of any reliable estimate on the size of the CMB sphere at that time. Using the usual redshift calculations, it is estimated 'we' were about 42 million light years from the CMB surface at that time, but, that really doesn't make a whole lot of sense. It is certainly worth asking how could 'we' be 42 million light years distant from the surface of last scattering when the universe was less than 400,000 years old?