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Will gravitational waves of cosmological origin be weaker or stronger (higher amplitude $h \simeq\Delta L/L$) than those created from astrophysical sources?

I'm having a real hard time finding the amplitude of cosmological gravitational waves (from inflation and from cosmic defects (strings etc.)) in terms of $h$, so that I can make a comparison.

Any help on this would be great.

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up vote 3 down vote accepted

You probably should look here first for some relatively up-to-date predictions of signal-to-noise from cosmological sources.

Astrophysicists are very confident that advanced LIGO will see signals from merging compact objects like neutron star binaries and black hole binaries, on the order of a few tens per year (see first link). It is far less certain whether gravitational waves from the very early universe will be detected by LIGO, eLISA, or even the Big Bang Observer if it ever gets built. The answer you get will be different depending on who you ask and how optimistic they are.

Regarding signals from the end of inflation, the frequency at which the signal peaks depends on, among other parameters, an unknown inflationary energy scale. I'm afraid I can't provide you with the expected signal in terms of $\Delta L / L$, but you can see some predictions for this sort of signal plotted against the LIGO, LISA, and BBO noise curves in this paper, and how they vary with the energy scale. The chances of detection don't seem very high, and require the inflationary energy scale to be quite low, $< 10^9$ GeV, to be in a favorable frequency range. (Take these results with a grain of salt, though - they are based on highly simplified models and should not be viewed as definitive).

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Hello and thanks for your answer. In third paper you cited (GW Production at the End of Inf.), it says that $\Omega_{gw}h \sim 10^{-11}$. This is the kind of information I was looking for. However, I do not understand this relation. If the Universe contains a larger contribution of GWs, then shouldn't the amplitude $h$ be larger, not smaller? Additionally, you say (rightly) say that the energy scale for the model in this paper is $\sim 10^{9}$ GeV, but how low is this (likely, unlikely, extremely unlikely)? – user12345 Sep 30 '12 at 10:39
The $h$ in the papers I've cited refers to the non-dimensional Hubble parameter, such that the dimensional Hubble parameter can be written 100 h km/s/Mpc, and practically $h$ can be thought of as a constant of around 0.7 . It is not $\Delta L / L$. – kleingordon Sep 30 '12 at 21:13
Regarding the energy scale, much of the original work on inflation postulated that it occurred at around the GUT scale, approximately $10^{16}$ GeV. There have been a variety of suggestions for how a lower energy scale might be possible, many of them cited in the papers in the answer. I'm afraid I'm not qualified to make statements on their likelihood. – kleingordon Sep 30 '12 at 21:18

there is chance to detect the waves

Observable Spectra of Induced Gravitational Waves from inflation

...A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space based gravitational wave detectors; such as NASA's LISA and BBO detectors, and the Japanese DECIGO detector...

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