Considering electromagnetic CMB can only see light as old as 380,000 years after the Big Bang, whilst theoretically those being gravitational should be formed from the beginning, what would their wavelength be, and do we have the technology to detect them in the foreseeable future?
[Physics] What would the wavelength of the Cosmic Background Gravitational Wave radiation be
cosmic-microwave-backgroundcosmological-inflationcosmologygravitational-wavesgravity
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At a basic level:
The universe, in the beginning was very hot. So hot in fact that there were no atoms, only electrons and protons and neutrons and photons flying around. The photons were scatting off of the electrons and protons, as they interacted strongly because the electrons and protons are charged. The universe was much like the plasma you find in plasma balls, but turned up to 11. It was opaque. You could not see through it.
As the universe expanded, it cooled and at around 380,000 years after the big bang, it was cold enough that stable atoms could form. At this point, all of the photons that were flying around suddenly stopped reacting with all of the free electrons and protons, since they started to form atoms that had no net charge, behaving much like a very dilute gas, like the air. The universe became transparent. Just as we can see through air, at this point the photons could travel unimpeded. This is referred to as the "surface of last scattering", but you shouldn't think of it as a surface, you should think of it as a moment in time where the universe went from being opaque to light to being mostly transparent to light.
Having suddenly nothing to interact with, those photons just starting travelling in straight lines. Some of those photons were just the right distance from us and were pointed in just the right direction that they are hitting us just now. In fact, they are hitting us continuously since the entire universe was filled with this photons just before the universe went "transparent".
So, the CMB isn't at the edges, its everywhere, its all of the photons that are still to this day flying off in every which direction. Occasionally those photons hit something, but since the universe is mostly empty space, the fraction that hit something is completely negligible. It is safe to assume they have not interacted with anything since the "surface of last scattering" nearly 14 billion years ago.
Nowadays, those photons are long in wavelength, nearly 1 mm, because as the universe has continued to expand, they continue to cool and stretch in wavelength.
The CMB origin at about 380,000 years after the Big Bang is indeed the furthest we can see, IN THE ELECTROMAGNETIC spectral domain. And you are right that this is not about the full universe vs the observable universe, you are talking about a portion of the observable universe which is simply occluded from us not in principle, but because photons could not propagate from freely out until then.
So, theoretically the universe is about 13.8 billion years old, and we can 'see' into the past only to 380,000 years after the Big Bang.
The reason we don't stop there, in either theory or in understanding what's behind that apparent 'wall', is that 1) we know a lot about what happened before the 380,000 year 'wall' from what needed to be there in order for us to see what we see after, AND maybe more important 2) for those who don't believe what they can't see, we will be able to see behind the 'wall' with gravitational waves.
Gravitational waves (GWs) are affected little by that 'wall' and all we need to do is build a large enough interferometer pair, to see them. LIGO which detected GWs from black holes merging, cannot detect those cosmologically originated GWs because their wavelengths are much larger. We need space based interferometers with legs a million Kms or larger -- that's in the planning for the next decade, with 2 or 3 satellites forming the 1 or 3 legs (funding dependent). And later bigger ones. We spect to see behind the wall using that gravitational astronomy.
As for your 3 questions:
Matter behinds the wall. We know there had to be matter, but it was mostly uncondensed and very energetic charged particles, mostly electrons and protons. At 380,000 years they recombined into hydrogen atoms and a few other things, and the photons we see now as the CMB could escape. We know actually a lot more, eg, about the very small inhomogeneities and anisotropies in the CMB which came from the same on the density of matter, and which served as seeds of galaxies and stars. Before electrons and protons it was even hotter, and it was quarks, gluons and electrons and a few other particles, and before that particles we have not seen in the lab. We know the basic physics for those things but still expect there will be more energetic particles, perhaps remnants of the Big Bang that became dark matter, and other exotic particles. As it gets hotter it's quantum gravity like string theory claims, and for which we still don't know what the right theory is.
We do think we know that there are galaxies that we can not see now. Even many of the ones we see now, emitted their light long ago, and will not see their light emittEd now ever. They are traveling away from us now too fast, and light emitted from them will never reach us. But we are seeing the light from many such galaxies now, that they emitted billions of years ago. Yes, the cosmological horizon is, we think, real
Nothing overtook the CMB. Galaxies and stars were formed maybe a few million years after tHe CMB broke free. Remember the universe was expanding, so if they are younger than the CMB they were created closer to us, and it's why we can see them. General Relativistic geometry can be tricky, but for cosmology it's good to think in terms of time from the Big Bang or back from us. Keep in mind the CMB was released everywhere in space, and what we see now are photons that reached us now. They traveled for 13.8 billion minus 380,000 years. We have seen galaxies going back to a couple hundred million years from the Big Bang (but sorry, I may not have the number exactly right, or most updated).
For an intro to the chronology of the universe see the wiki article at https://en.m.wikipedia.org/wiki/Chronology_of_the_universe
It's got the different cosmological periods or epochs, including the recombination time (the 'wall') and other important cosmological times. We still have a lot to learn, but the most mysterious epochs from our knowledge of elementary particle physics are those that are the earliest: the Planck epoch (we just don't know what makes thing up then, maybe string theory or other quantum gravity theory will get to it sometime), the strong unification era (we know a little bit after how and when the stron and electroweak force unify, but still plenty uncertainty), and the inflationary epoch (we have inflation theories, some version seems right but we're not sure which, or the field that caused it). We tend to know a lot about the rest, from theory and observation, but still we think we'll find surprises.
Your final two questions:
A. The current observable universe is about 46 billion light years in radius. We see pretty far out, but have not seen the edge, or what is called the horizon (we would not fall off). Unfortunately, if anybody is around in a quite few billions of years we will see even the closest galaxies get too far from us to be able to see them (or their successors) because the expansion will have taken them past our then horizon
B. There will always be CMB around as they were created everywhere in space. However, they will be way way redshifted- right now they've been redshifted by a factor of 1100, and we see it as high microwaves, 100 Ghz range. Another factor of a million say they'll be 100 KHz but much weaker, and eventually they'll get too weak and low frequency for us to detect.
Best Answer
It is unlikely that we can detect gravitational waves from the Big Bang with current technology. Due to universal expansion, such waves would have very large wavelengths.
We would need interferometers that are thousands, perhaps millions, of kilometers long to detect them. The LIGO observatory simply would not be sufficient. To put things into perspective, consider that the arms of the LIGO interferometer have a length of $4km$. But it is important to note that the effective LIGO arm length is $1600km$ (the light beam inside the interferometer is reflected back and forth 400 times) and LIGO is most "sensitive" at a frequency of about $150Hz$, which would correspond to a wavelength of $\lambda \approx 2000km$ meaning the LIGO arms have a length of $\approx\frac{\lambda}{2}$.
There is a proposal called "LISA" that will involve a system of satellites in space separated by large distances ($\gt 10^6$ km), that could possibly detect gravitational waves (gravitational waves that where emitted before the photon epoch - up to 380,000 years after the Big Bang as you mentioned).
From that link:
"The Laser Interferometer Space Antenna (LISA) is a proposed space probe to detect and accurately measure gravitational waves—tiny ripples in the fabric of spacetime—from astronomical sources. LISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft arranged in an equilateral triangle with sides 2.5 million kilometres long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave...
Potential sources for signals [that LISA could detect] are merging massive black holes at the center of galaxies, massive black holes orbited by small compact objects, known as extreme mass ratio inspirals, binaries of compact stars in our Galaxy, and possibly other sources of cosmological origin, such as the very early phase of the Big Bang , and speculative astrophysical objects like cosmic strings and domain boundaries."