Questions about the g-wave caused by the big bang: 1)was there a g-wave produced? 2) when will it reach us? 3) will it be too weak for us to detect(atleast now?)?
As the universe itself was created by the event, it's like asking when the shockwave will hit the center of the nuke's fireball. However, remnant waves were supposed to have affected cosmic background, and very possibly contributed to the large scale clustering structure of the universe. These "fingerprints" were claimed to have been found, but it turned out it was just dust.
I'm not sure how much research is being done about this, but it could be that omnipresent "standing" waves of extremely low amplitude and long wavelength are permeating the universe still.
- Not directly by the big bang itself, but in the early universe for sure processes were taking place which led to gravitational waves, most prominent the cosmic inflation.
- They reach us all the time, same as the microwave background does.
- Too weak for direct observation, but observation by their impact on the CMB seems in range.