You misunderstood the question I think. The question mentions that cosmic microwave background can be detected, and asks if cosmic gravitational wave background could be detected, and what typical wavelength it would have.

BTW, the CMB was first detected on Earth, not by a satellite

@PM2Ring Really? That's interesting. I thought they could not be detected from the earth's surface?

See en.wikipedia.org/wiki/…

That's actually quite interesting. Thanks @PM2Ring and DKNguyen.

Edited answer specifically for gravitational waves - thanks for the information guys. Cheers.

Whoops. Thanks @PM2Ring

"the waves would have significantly increased in wavelength" -- but they would also have started out extremely small. The effects nearly cancel, i.e., during the relevant period (radiation-dominated) the temperature was approximately following a redshift path anyway, so even Planck-era thermal radiation would turn into millimeter waves today like the CMB. See my answer.

It is commonly hypothesized that gravitational waves decrease in frequency (increase in wavelength) over cosmological distances due to the expansion of the universe –similar to how the wavelength of light is red-shifted by the expansion of the universe. Your answer denies the existence of gravitational waves, which contradicts the evidence we have now.

Whoa, what I intended is that my answer "denies the existence" of a thermal gravitational wave background (and I link to a paper). I talk about other gravitational waves from many localized sources that could combine into a "background". And I definitely agree that gravitational waves are redshifted -- I don't think anything in my answer or comment contradicts that. If you downvoted my answer and you still think these things aren't made clear, please let me know how I can improve it.

I get what you mean, though to someone who has basic knowledge of physics, the statement hypothetical gravitational waves would have too short a wavelength (too high a frequency) to detect with known technology. But as noted, they are unlikely to exist anyway could be interpreted as "hypothetical" meaning exists in the understanding only, and in what other way could "they are unlikely to exist anyway" be interpreted? This also it denies they were detected in the first place. Perhaps you could make it a little more clear? I'll have a read of your paper soon.

I'll edit -- I said "these hypothetical gravitational waves" meaning the thermal ones discussed in the preceding sentences. And in the hypothetical that such waves exist from the very early universe, I disagree with your statement that they would be extremely long (millions of km) now. Yes, they are heavily redshifted, but they also started out tiny because the early universe was so hot. To first order it makes little difference (to the current wavelength) at what epoch the radiation was "released", since all fields were cooling and redshifting together anyway.

Yes, I know exactly what your intention was. Though someone, as I said, who has basic knowledge, will not be able to immediately make the distinction between thermal background and traditional G waves. They may get the impression that the existence of gravity waves is still up for debate, when clearly the evidence suggests otherwise.

If it's OK with you, I have made a slight edit to your answer, just so it is clear to other readers. A great majority of our members have year 12/first year uni education in physics while a lot are just enthusiasts. Thanks.

Thus, what are the wavelengths of the gravitational wave background? There is no clear answer to the question asked.

You're right. As far as I am aware, there is no clear answer anywhere. I speculate that they have extremely long wavelength.

One can do more than speculate. There are plenty of papers that make direct predictions of the cosmic GW background spectrum based in some cases on reasonably well understood physics (e.g. the electroweak phase transition) as well as other more speculative models.