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I was looking for some explicit information on the implications of the LIGO results or probing eras prior to the or near to the Big Bang singularity.

So, my question is therefore, what, if any, are the implications of the LIGO results or probing the very earliest (and then some) epochs in our Universe's history? And are there further future implications of using gravitational wave detection for testing our current cosmological theories?

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Gravitational waves from the big bang may well be "heard", but not by LIGO. The waves emitted at or around the inflationary epoch of the big bang are expected to be mostly at much lower frequencies (milli-Hz or lower) than those announced today by LIGO. There are various sources of noise that make LIGO insensitive to GWs at frequencies below about 10-20 Hz.

It will take space-based interferometers like the proposed eLISA, with longer interferometer arms and well away from terrestrial sources of noise to stand a chance of detecting such GWs. I suppose one implication of the LIGO detection is that it make governments more likely to fund eLISA!

If they are detected - they might "sound" something like this (if upshifted into the audible range) - from the LIGO website. It sounds like white(ish) noise because of the broad continuum of frequencies expected.

In terms of what might be fund from these waves - hopefully somebody that knows a bit more will answer. There appear to be many possible competing mechanisms that kick in as the universe rolls out of its inflationary phase, including phase transitions, cosmic strings and others. The universe will be transparent to such waves, so they would travel to us unimpeded, but redshifted. Back of the envelope calculations based on the horizon scale of the universe suggest that LISA would be sensitive to waves produce between $10^{-18}$ and $10^{-10}$ s after the big bang (source: the eLISA white paper).

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