# Cosmological consequences of the mass-energy content of gravitational waves

This paper published in 1969 indicates that a majority of the mass-energy of the universe may be contained in gravitational waves:

"Turning next to phenomena on a galactic scale, we find it conceivable that over the past ~10^10 years the Galaxy may have radiated away as much as 10 times its present mass."

Has the reasoning in the paper been refuted by actual gravitational wave detections over the past decade?

Apparently two merging solar mass scale black holes of about the same size lose about 5% of their mass to gravitational radiation. I'm not sure how that percentage scales with mass, but assuming it does not change with mass as long as the black holes are approximately the same size, it would be possible to convert a very high percentage of the mass of an initial distribution of stellar-mass black holes into gravitational radiation. E.g., if pairs of stellar-mass BHs, then pairs of ~2 stellar mass BHs, then pairs of ~4 stellar mass BHs and so on are merged, with 5% of the mass radiated away each time, ~65% (1-0.95^20) of the mass would be radiated away by the time a million-stellar-mass supermassive black hole is formed. Some supermassive black holes are as large as 10 billion stellar masses, which would allow ~84% of the mass to be radiated away.

Added 6/26/20: Mass loss could possibly provide a component of cosmological expansion. If two objects are orbiting each other and then lose mass, their orbits should expand. It seems that if a cluster of gravitationally interacting bodies - stars or galaxies - lose mass, then the cluster should expand.

• I want to point out that the formation of supermassive black hole by stellar black hole mergers is very unlikely, if not impossible Jun 18, 2020 at 20:40
• Correct me if I'm wrong, but it seems to me the article and the estimates are based on those Weber observations cited there? Those observations were duplicated many times and always gave a null result. You can find more infos here: en.m.wikipedia.org/wiki/Weber_bar Jun 18, 2020 at 20:48
• I'm sure you're right about that. The reasoning is what I'm curious about. Jun 18, 2020 at 21:02
• I always assumed that when mass is lost, the curvature it caused is "relaxed" as it were and this ripples outwards as the associated gravity wave. Positive energy lost by the objects is balanced by negative energy lost via the relaxation. Am I wrong? Jun 26, 2020 at 16:03
• I'm just imagining what would happen if, e.g., the masses of the Earth and Moon were abruptly reduced by, say, 50%. Both bodies would be moving too fast relative to the common center of mass to continue in their circular orbits, so the orbits would change to ellipses that extend beyond the original orbital radii. Jun 26, 2020 at 16:13

Depending on your model, I think this contribution should have been seen by cosmological inference from the cosmic microwave data (CMB). Since gravitational waves behave (energetically) in the same wave as light waves do, your $$\Omega_{\rm rad}$$ which is the radiative energy density, would be changed to $$\Omega_{\rm rad}\rightarrow \Omega_{\rm rad, eff}=\Omega_{\rm rad} + \Omega_{\rm GW}$$. However, to deduce now observables from this model is not an easy, since $$\Omega_{\rm GW}$$ is not constant over time. You have to make assumptions about how many galaxies at what cosmic time (or redshift) emit how many gravitational waves. In principle you can then compare this value of $$\Omega_{\rm rad, eff}$$ with the measured value from the CMB here.
Also, the current non-detection of a GW background puts upper bounds on astrophysical models of GW emission that produce a GW background. I would assume that this rules out the order of magnitude which is given above, but one would have to again carry out the computation for $$\Omega_{\rm rad,eff}$$ and compare that to the upper bounds.