Is there an equation showing the change in the frequency of the cosmic background radiation over time?

Question

I'm curious as to whether there was ever a time when the background radiation was in the visible spectrum. What frequency was it 300,000 years after the big bang when the universe first became transparent? And from the big bang up until 300,000 years, did that opaque haze which filled the universe change color/frequency, or would it have always been some shade of white or gray, varying only in brightness?

Update:

And no, this isn't a homework assignment. :-) Just regular nerdly curiosity.

supastremph · Accepted Answer

The simplest option, if you are assuming big bang cosmology, is to use the temperature and Wien's displacement law, and treat the universe as a blackbody.  Inasmuch as you can feel certain of a temperature at a time after the big bang, you can be certain of the predominant wavelength of the radiation present.  The wavelength (freq = c/wavelength) follows  this form:

http://en.wikipedia.org/wiki/Wien's_displacement_law

vorenhutz · Answer

it would've been about 3000 K, the surface temperature of your average red dwarf star. much of it would've been in the visible. the universe cools as it expands... the CMBR temperature is now about 2.7 K, indicating an expansion by a factor of about 1100 since then. at earlier times it would've been hotter, and the light bluer.

Quadrillian · Answer

You might find the answer on this page:

http://en.wikipedia.org/wiki/CMB


or on one of it's links.

Cheers!

dreamland 2^[]^2 angel · Answer

http://www.daviddarling.info/encyclopedia/B/Big_Bang.html

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Is there an equation showing the change in the frequency of the cosmic background radiation over time?

4 Answers